slope_different_PMFs.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pickle\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import utils\n",
    "def run_extremes(N, W, pmf_cust, pmf_serv, gurobi_flag = 0):\n",
    "    Ex = round (np.sum(np.outer(pmf_cust,pmf_serv)*W), 3) \n",
    "    print(\"Expected cost for c = 0 case:\", Ex )\n",
    "    if gurobi_flag == 1:\n",
    "        fluid_sol = utils.fluid_solution_gurobi(N, W, pmf_cust, pmf_serv)\n",
    "    else:\n",
    "        fluid_sol = utils.fluid_solution(N, W, pmf_cust, pmf_serv,0)\n",
    "#     print(\"\\nFluid Solution:\\n\")\n",
    "#     print(fluid_sol)\n",
    "    return([Ex,fluid_sol])\n",
    "def plot_from_sim_paths(file_name, save_file= 0, frac = 0):\n",
    "    with open(file_name,'rb') as f:\n",
    "        C_paths_M, Q_paths_M, average_cost_B, average_queue_B, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "    (average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M, frac)\n",
    "    # (average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B, frac)\n",
    "    [Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "    utils.qc_plot(Ex,fluid_sol,average_queue_B,average_new,average_queue_M,average_cost_M, save_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 3.854\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
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      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
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      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
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      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
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      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
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      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
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      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
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      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
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      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
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      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
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      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_random.pkl'\n",
    "plot_from_sim_paths(file_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.07975418 0.01919971 0.02258319 0.063418   0.01690154 0.00436386\n",
      " 0.0713188  0.03781694 0.07588844 0.02035429 0.07178959 0.01772757\n",
      " 0.037173   0.05643021 0.03212186 0.04991935 0.04187258 0.00426407\n",
      " 0.0004976  0.06667127 0.05168924 0.07233958 0.01511579 0.04976147\n",
      " 0.02102789] [0.07027825 0.01713261 0.02124712 0.01177862 0.08442459 0.04251858\n",
      " 0.01297518 0.04118533 0.05410482 0.03633735 0.07573665 0.07874273\n",
      " 0.04071133 0.06564617 0.00056744 0.03949442 0.04429773 0.07808677\n",
      " 0.00240852 0.00708916 0.06218571 0.01051105 0.04341731 0.04109408\n",
      " 0.01802848]\n",
      "average cost B [2.58351137 2.06562733 1.95014654 1.80451426 1.79812803 1.79203623\n",
      " 1.78596836 1.78686234 1.78344374 1.78228997 1.78190651 1.78353781\n",
      " 1.78116084 1.78339821 1.78184871 1.78252353 1.78255975 1.78325649\n",
      " 1.78260114 1.78296198 1.78205191 1.78425139 1.7844665  1.78308966\n",
      " 1.78338244 1.7843901  1.78310274]\n",
      "average cost M [3.85460504 3.85118272 3.85547001 3.8543488  3.74963317 3.30268054\n",
      " 2.93331425 2.61956563 2.40725361 2.36342353 2.3554947  2.31614046\n",
      " 2.25894971 2.23198889 2.12195638 2.05886503 1.99858175 1.9682901\n",
      " 1.94579839 1.91928775 1.90520796 1.86782402 1.84643592 1.8362532\n",
      " 1.82288735 1.81363997 1.80412624 1.79084061 1.78633376 1.79061766\n",
      " 1.7878923  1.78872476 1.79089755 1.78394787 1.7897663  1.78273484\n",
      " 1.7783927  1.77690671]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_random.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M, Q_paths_M, average_cost_B, average_queue_B, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "print(pmf_cust,pmf_serv)\n",
    "average_cost_B = average_new\n",
    "Q_paths_M = np.transpose( np.asarray( Q_paths_M )  )\n",
    "C_paths_M = np.transpose( np.asarray( C_paths_M ) )\n",
    "average_cost_M = np.sum(C_paths_M,axis=0)/(Q_paths_M.shape[0] - Q_paths_M[-1,:])\n",
    "average_queue_M = np.average(Q_paths_M,axis = 0)\n",
    "print(\"average cost B\", average_cost_B)\n",
    "print(\"average cost M\", average_cost_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.07975418, 0.01919971, 0.02258319, 0.063418  , 0.01690154, 0.00436386,\n",
      " 0.0713188 , 0.03781694, 0.07588844, 0.02035429, 0.07178959, 0.01772757,\n",
      " 0.037173  , 0.05643021, 0.03212186, 0.04991935, 0.04187258, 0.00426407,\n",
      " 0.0004976 , 0.06667127, 0.05168924, 0.07233958, 0.01511579, 0.04976147,\n",
      " 0.02102789]\n"
     ]
    }
   ],
   "source": [
    "print(np.array2string(pmf_cust, separator=', '))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.07027825, 0.01713261, 0.02124712, 0.01177862, 0.08442459, 0.04251858,\n",
      " 0.01297518, 0.04118533, 0.05410482, 0.03633735, 0.07573665, 0.07874273,\n",
      " 0.04071133, 0.06564617, 0.00056744, 0.03949442, 0.04429773, 0.07808677,\n",
      " 0.00240852, 0.00708916, 0.06218571, 0.01051105, 0.04341731, 0.04109408,\n",
      " 0.01802848]\n"
     ]
    }
   ],
   "source": [
    "print(np.array2string(pmf_serv, separator=', '))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 3.854\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
      " [4.12310563 4.47213595 5.         5.65685425 6.40312424 3.16227766\n",
      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n",
      "1.7826530162902825\n"
     ]
    }
   ],
   "source": [
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "Cstar_mw = fluid_sol['Cost']\n",
    "print(Cstar_mw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.07827447 0.00381086 0.0245906  0.01943424 0.07391414 0.03565764\n",
      " 0.07130462 0.07117261 0.06682536 0.03308101 0.05953029 0.0051557\n",
      " 0.03435233 0.07129302 0.00158834 0.0141003  0.02215531 0.01652954\n",
      " 0.01115552 0.05777464 0.02204853 0.03920496 0.01989729 0.07503096\n",
      " 0.07211773] [0.06569886 0.03296924 0.07109283 0.01299347 0.03854542 0.07026348\n",
      " 0.04758437 0.05636051 0.02369232 0.06004832 0.04094853 0.04532835\n",
      " 0.0426359  0.03927098 0.07764115 0.04960136 0.00989021 0.00462842\n",
      " 0.02639694 0.08071246 0.0259038  0.0342378  0.02513366 0.01179175\n",
      " 0.00662988]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_random_batch.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M0, Q_paths_M0, average_cost_B2, average_queue_B2, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "print(pmf_cust,pmf_serv)\n",
    "average_cost_B2 = average_new\n",
    "# print(\"average cost B\", average_cost_B)\n",
    "# print(\"average cost M\", average_cost_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.07975418, 0.01919971, 0.02258319, 0.063418, 0.01690154, 0.00436386, 0.0713188, 0.03781694, 0.07588844, 0.02035429, 0.07178959, 0.01772757, 0.037173, 0.05643021, 0.03212186, 0.04991935, 0.04187258, 0.00426407, 0.0004976, 0.06667127, 0.05168924, 0.07233958, 0.01511579, 0.04976147, 0.02102789] [0.07027825, 0.01713261, 0.02124712, 0.01177862, 0.08442459, 0.04251858, 0.01297518, 0.04118533, 0.05410482, 0.03633735, 0.07573665, 0.07874273, 0.04071133, 0.06564617, 0.00056744, 0.03949442, 0.04429773, 0.07808677, 0.00240852, 0.00708916, 0.06218571, 0.01051105, 0.04341731, 0.04109408, 0.01802848]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_random_batch_new.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M0, Q_paths_M0, average_cost_B2, average_queue_B2, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "print(pmf_cust,pmf_serv)\n",
    "average_cost_B2 = average_new\n",
    "# print(\"average cost B\", average_cost_B)\n",
    "# print(\"average cost M\", average_cost_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 3.899\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
      " [4.12310563 4.47213595 5.         5.65685425 6.40312424 3.16227766\n",
      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n",
      "1.8706340911603188\n"
     ]
    }
   ],
   "source": [
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "Cstar_batch = fluid_sol['Cost']\n",
    "print(Cstar_batch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8706340911603188\n"
     ]
    }
   ],
   "source": [
    "Cstar = fluid_sol['Cost']\n",
    "print(Cstar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  500.5 ,   750.25,  1250.5 ,  2000.5 ,  2500.5 ,  5000.5 ,\n",
       "        7475.5 , 10000.5 , 12500.5 , 14900.5 , 17350.5 , 20000.5 ,\n",
       "       22325.5 , 25000.5 , 27275.5 , 29600.5 , 32000.5 , 34500.5 ,\n",
       "       36875.5 , 39200.5 , 41850.5 , 44600.5 , 46375.5 , 50000.5 ])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B[average_cost_B<=Cstar]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([], dtype=float64)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B2[average_cost_B2<=Cstar_mw]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.98372339  1.13962333] [0.64192364]\n",
      "[-0.80278537  2.31342909] [0.26625434]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1eef907af98>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M[8:28]-Cstar_mw)\n",
    "yM2 = np.log(average_queue_M[8:28])\n",
    "xB2 = np.log(average_cost_B-Cstar_batch)\n",
    "yB2 = np.log(average_queue_B)\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Maxweight\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Batching\"\n",
    "            , str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.82317082  1.5190308 ] [0.93638786]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\HP\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:5: RuntimeWarning: invalid value encountered in log\n",
      "  \"\"\"\n"
     ]
    },
    {
     "ename": "LinAlgError",
     "evalue": "SVD did not converge in Linear Least Squares",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-93-3605cfc590a0>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     21\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgrid\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     22\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mxB2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0myB2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'x'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmarkersize\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmarkeredgewidth\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmarkeredgecolor\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"darkblue\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 23\u001b[1;33m \u001b[0mpB\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mresB\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpolyfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mxB2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0myB2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfull\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     24\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpB\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mresB\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     25\u001b[0m \u001b[0mpredict2_2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpoly1d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpB\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Users\\HP\\Anaconda3\\lib\\site-packages\\numpy\\lib\\polynomial.py\u001b[0m in \u001b[0;36mpolyfit\u001b[1;34m(x, y, deg, rcond, full, w, cov)\u001b[0m\n\u001b[0;32m    626\u001b[0m     \u001b[0mscale\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mNX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlhs\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mlhs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    627\u001b[0m     \u001b[0mlhs\u001b[0m \u001b[1;33m/=\u001b[0m \u001b[0mscale\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 628\u001b[1;33m     \u001b[0mc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mresids\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrank\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlstsq\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlhs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrhs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrcond\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    629\u001b[0m     \u001b[0mc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mscale\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m  \u001b[1;31m# broadcast scale coefficients\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    630\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Users\\HP\\Anaconda3\\lib\\site-packages\\numpy\\linalg\\linalg.py\u001b[0m in \u001b[0;36mlstsq\u001b[1;34m(a, b, rcond)\u001b[0m\n\u001b[0;32m   2234\u001b[0m         \u001b[1;31m# lapack can't handle n_rhs = 0 - so allocate the array one larger in that axis\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2235\u001b[0m         \u001b[0mb\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mm\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn_rhs\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2236\u001b[1;33m     \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mresids\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrank\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgufunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrcond\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2237\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mm\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2238\u001b[0m         \u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m...\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Users\\HP\\Anaconda3\\lib\\site-packages\\numpy\\linalg\\linalg.py\u001b[0m in \u001b[0;36m_raise_linalgerror_lstsq\u001b[1;34m(err, flag)\u001b[0m\n\u001b[0;32m    107\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    108\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m_raise_linalgerror_lstsq\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0merr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 109\u001b[1;33m     \u001b[1;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"SVD did not converge in Linear Least Squares\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    110\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    111\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mget_linalg_error_extobj\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcallback\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mLinAlgError\u001b[0m: SVD did not converge in Linear Least Squares"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M[12:30]-Cstar)\n",
    "yM2 = np.log(average_queue_M[12:30])\n",
    "xB2 = np.log(average_cost_B[2:20]-Cstar)\n",
    "yB2 = np.log(average_queue_B[2:20])\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Maxweight\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Batching\"\n",
    "            , str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.98372339  1.13962333] [0.64192364]\n",
      "[-1.08563556  2.08349728] [0.09069302]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x21cc2138b70>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M[8:28]-Cstar_mw)\n",
    "yM2 = np.log(average_queue_M[8:28])\n",
    "xB2 = np.log(average_cost_B2-Cstar_mw)\n",
    "yB2 = np.log(average_queue_B2)\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Maxweight\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Batching\"\n",
    "            , str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358] [0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358]\n",
      "average cost B [2.42228835 1.89246396 1.75434009 1.52077873 1.5028646  1.48263351\n",
      " 1.46882431 1.46164082 1.44895139 1.4431132  1.4388033  1.43628854\n",
      " 1.43339095 1.43392909 1.4310243  1.43059244 1.42920713 1.42996139\n",
      " 1.42725054 1.42938585 1.4265146  1.42612977 1.42597078 1.42630427\n",
      " 1.42448514 1.42519221 1.426246  ]\n",
      "average cost M [3.60802658 3.60850982 3.60577035 3.60668998 3.5467621  3.17486504\n",
      " 2.81199579 2.48593158 2.26944353 2.2184499  2.21690264 2.14557829\n",
      " 2.07328114 2.04772978 1.9418681  1.85479839 1.76759317 1.73487802\n",
      " 1.71534042 1.6721496  1.66737798 1.59640902 1.56968149 1.55676557\n",
      " 1.52269271 1.49760855 1.47811705 1.45685711 1.45677524 1.45269149\n",
      " 1.44431659 1.43994111 1.43853819 1.43611982 1.43382281 1.42727516\n",
      " 1.42389102 1.42034184]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_geometric.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M, Q_paths_M, average_cost_B, average_queue_B, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "print(pmf_cust,pmf_serv)\n",
    "average_cost_B = average_new\n",
    "Q_paths_M = np.transpose( np.asarray( Q_paths_M )  )\n",
    "C_paths_M = np.transpose( np.asarray( C_paths_M ) )\n",
    "average_cost_M = np.sum(C_paths_M,axis=0)/(Q_paths_M.shape[0] - Q_paths_M[-1,:])\n",
    "average_queue_M = np.average(Q_paths_M,axis = 0)\n",
    "print(\"average cost B\", average_cost_B)\n",
    "print(\"average cost M\", average_cost_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 3.608\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
      " [4.12310563 4.47213595 5.         5.65685425 6.40312424 3.16227766\n",
      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_from_sim_paths(file_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 3.608\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
      " [4.12310563 4.47213595 5.         5.65685425 6.40312424 3.16227766\n",
      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n"
     ]
    }
   ],
   "source": [
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4142135623969405\n"
     ]
    }
   ],
   "source": [
    "Cstar = fluid_sol['Cost']\n",
    "print(Cstar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.98489593  2.19850206] [0.20774588]\n",
      "[-2.01599008  1.72975035] [0.03127438]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x295c55390b8>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M[20:41]-Cstar)\n",
    "yM2 = np.log(average_queue_M[20:41])\n",
    "xB2 = np.log(average_cost_B[5:15]-Cstar)\n",
    "yB2 = np.log(average_queue_B[5:15])\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Maxweight\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Batching\"\n",
    "            , str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 4.311\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
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      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_reverse_geometric.pkl'\n",
    "plot_from_sim_paths(file_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358] [0.00859358 0.00954842 0.01060935 0.01178817 0.01309797 0.0145533\n",
      " 0.01617033 0.01796703 0.01996337 0.02218152 0.02464613 0.02738459\n",
      " 0.03042733 0.03380814 0.0375646  0.04173844 0.04637605 0.05152894\n",
      " 0.05725438 0.06361598 0.07068442 0.07853824 0.08726472 0.0969608\n",
      " 0.10773422]\n",
      "average cost B [3.46660691 3.27105026 3.25060415 3.23880355 3.23428089 3.23734796\n",
      " 3.23849153 3.23266798 3.2373854  3.23513884 3.23134565 3.23337027\n",
      " 3.23446431 3.23596946 3.23821011 3.23573468 3.23981254 3.23605542\n",
      " 3.23394411 3.23458125 3.23803452 3.23272495 3.23381604 3.23379405\n",
      " 3.23322313 3.23633525 3.23273043]\n",
      "average cost M [4.31423252 4.30596688 4.31199192 4.31033658 4.20321492 3.83998931\n",
      " 3.65661628 3.56629016 3.47896202 3.4512984  3.45400389 3.44956203\n",
      " 3.43946198 3.44452617 3.39107352 3.37459116 3.34402312 3.3493701\n",
      " 3.3305715  3.32363706 3.31090776 3.30053229 3.29434307 3.28825848\n",
      " 3.2948894  3.29018216 3.28961014 3.27823875 3.27878856 3.2808346\n",
      " 3.28218652 3.27756088 3.27633197 3.28449116 3.27694823 3.27118457\n",
      " 3.26988385 3.26453047]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_reverse_geometric.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M, Q_paths_M, average_cost_B, average_queue_B, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "print(pmf_cust,pmf_serv)\n",
    "average_cost_B = average_new\n",
    "Q_paths_M = np.transpose( np.asarray( Q_paths_M )  )\n",
    "C_paths_M = np.transpose( np.asarray( C_paths_M ) )\n",
    "average_cost_M = np.sum(C_paths_M,axis=0)/(Q_paths_M.shape[0] - Q_paths_M[-1,:])\n",
    "average_queue_M = np.average(Q_paths_M,axis = 0)\n",
    "print(\"average cost B\", average_cost_B)\n",
    "print(\"average cost M\", average_cost_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358] [0.00859358 0.00954842 0.01060935 0.01178817 0.01309797 0.0145533\n",
      " 0.01617033 0.01796703 0.01996337 0.02218152 0.02464613 0.02738459\n",
      " 0.03042733 0.03380814 0.0375646  0.04173844 0.04637605 0.05152894\n",
      " 0.05725438 0.06361598 0.07068442 0.07853824 0.08726472 0.0969608\n",
      " 0.10773422]\n",
      "average cost B [3.46660691 3.27105026 3.25060415 3.23880355 3.23428089 3.23734796\n",
      " 3.23849153 3.23266798 3.2373854  3.23513884 3.23134565 3.23337027\n",
      " 3.23446431 3.23596946 3.23821011 3.23573468 3.23981254 3.23605542\n",
      " 3.23394411 3.23458125 3.23803452 3.23272495 3.23381604 3.23379405\n",
      " 3.23322313 3.23633525 3.23273043]\n",
      "average cost M [4.31423252 4.30596688 4.31199192 4.31033658 4.20321492 3.83998931\n",
      " 3.65661628 3.56629016 3.47896202 3.4512984  3.45400389 3.44956203\n",
      " 3.43946198 3.44452617 3.39107352 3.37459116 3.34402312 3.3493701\n",
      " 3.3305715  3.32363706 3.31090776 3.30053229 3.29434307 3.28825848\n",
      " 3.2948894  3.29018216 3.28961014 3.27823875 3.27878856 3.2808346\n",
      " 3.28218652 3.27756088 3.27633197 3.28449116 3.27694823 3.27118457\n",
      " 3.26988385 3.26453047]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_reverse_geometric_batch.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M0, Q_paths_M0, average_cost_B2, average_queue_B2, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "average_cost_B2 = average_new\n",
    "print(pmf_cust,pmf_serv)\n",
    "print(\"average cost B\", average_cost_B)\n",
    "print(\"average cost M\", average_cost_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358] [0.00859358 0.00954842 0.01060935 0.01178817 0.01309797 0.0145533\n",
      " 0.01617033 0.01796703 0.01996337 0.02218152 0.02464613 0.02738459\n",
      " 0.03042733 0.03380814 0.0375646  0.04173844 0.04637605 0.05152894\n",
      " 0.05725438 0.06361598 0.07068442 0.07853824 0.08726472 0.0969608\n",
      " 0.10773422]\n",
      "average cost B [3.46660691 3.27105026 3.25060415 3.23880355 3.23428089 3.23734796\n",
      " 3.23849153 3.23266798 3.2373854  3.23513884 3.23134565 3.23337027\n",
      " 3.23446431 3.23596946 3.23821011 3.23573468 3.23981254 3.23605542\n",
      " 3.23394411 3.23458125 3.23803452 3.23272495 3.23381604 3.23379405\n",
      " 3.23322313 3.23633525 3.23273043]\n",
      "average cost M [4.31423252 4.30596688 4.31199192 4.31033658 4.20321492 3.83998931\n",
      " 3.65661628 3.56629016 3.47896202 3.4512984  3.45400389 3.44956203\n",
      " 3.43946198 3.44452617 3.39107352 3.37459116 3.34402312 3.3493701\n",
      " 3.3305715  3.32363706 3.31090776 3.30053229 3.29434307 3.28825848\n",
      " 3.2948894  3.29018216 3.28961014 3.27823875 3.27878856 3.2808346\n",
      " 3.28218652 3.27756088 3.27633197 3.28449116 3.27694823 3.27118457\n",
      " 3.26988385 3.26453047]\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_reverse_geometric_batch_new.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M0, Q_paths_M0, average_cost_B2, average_queue_B2, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "average_cost_B2 = average_new\n",
    "print(pmf_cust,pmf_serv)\n",
    "print(\"average cost B\", average_cost_B)\n",
    "print(\"average cost M\", average_cost_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "average_cost_B = np.concatenate((average_cost_B, average_cost_B2))\n",
    "average_queue_B = np.concatenate((average_queue_B, average_queue_B2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.50000e+00, 2.55000e+01, 5.05000e+01, 5.00500e+02, 7.50250e+02,\n",
       "       1.25050e+03, 2.00050e+03, 2.50050e+03, 5.00050e+03, 7.47550e+03,\n",
       "       1.00005e+04, 1.25005e+04, 1.49005e+04, 1.73505e+04, 2.00005e+04,\n",
       "       2.23255e+04, 2.50005e+04, 2.72755e+04, 2.96005e+04, 3.20005e+04,\n",
       "       3.45005e+04, 3.68755e+04, 3.92005e+04, 4.18505e+04, 4.46005e+04,\n",
       "       4.63755e+04, 5.00005e+04, 5.05000e+01, 1.00500e+02, 1.50400e+02,\n",
       "       2.00500e+02, 2.50500e+02, 3.00100e+02, 3.50200e+02, 4.00500e+02,\n",
       "       4.50100e+02, 5.00500e+02, 5.05000e+01, 1.00500e+02, 1.50400e+02,\n",
       "       2.00500e+02, 2.50500e+02, 3.00100e+02, 3.50200e+02, 4.00500e+02,\n",
       "       4.50100e+02, 5.00500e+02])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_queue_B)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_B = average_cost_B[sorted_indices]\n",
    "average_queue_B = average_queue_B[sorted_indices]\n",
    "\n",
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_queue_M)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_M = average_cost_M[sorted_indices]\n",
    "average_queue_M = average_queue_M[sorted_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.50000e+00, 2.55000e+01, 5.05000e+01, 5.05000e+01, 5.05000e+01,\n",
       "       1.00500e+02, 1.00500e+02, 1.50400e+02, 1.50400e+02, 2.00500e+02,\n",
       "       2.00500e+02, 2.50500e+02, 2.50500e+02, 3.00100e+02, 3.00100e+02,\n",
       "       3.50200e+02, 3.50200e+02, 4.00500e+02, 4.00500e+02, 4.50100e+02,\n",
       "       4.50100e+02, 5.00500e+02, 5.00500e+02, 5.00500e+02, 7.50250e+02,\n",
       "       1.25050e+03, 2.00050e+03, 2.50050e+03, 5.00050e+03, 7.47550e+03,\n",
       "       1.00005e+04, 1.25005e+04, 1.49005e+04, 1.73505e+04, 2.00005e+04,\n",
       "       2.23255e+04, 2.50005e+04, 2.72755e+04, 2.96005e+04, 3.20005e+04,\n",
       "       3.45005e+04, 3.68755e+04, 3.92005e+04, 4.18505e+04, 4.46005e+04,\n",
       "       4.63755e+04, 5.00005e+04])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 4.311\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
      " [4.12310563 4.47213595 5.         5.65685425 6.40312424 3.16227766\n",
      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n"
     ]
    }
   ],
   "source": [
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.2353891814339213\n"
     ]
    }
   ],
   "source": [
    "Cstar = fluid_sol['Cost']\n",
    "print(Cstar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "average_queue_B_good = average_queue_B[average_cost_B > Cstar]\n",
    "average_cost_B_good = average_cost_B[average_cost_B > Cstar]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.46660691 3.27105026 3.2486122  3.2486122  3.25060415 3.23915642\n",
      " 3.23915642 3.2391459  3.2391459  3.24616184 3.24616184 3.23753417\n",
      " 3.23753417 3.23773052 3.23773052 3.24007103 3.24007103 3.24003469\n",
      " 3.24003469 3.23880355 3.23734796 3.23849153 3.2373854  3.23596946\n",
      " 3.23821011 3.23573468 3.23981254 3.23605542 3.23803452 3.23633525]\n"
     ]
    }
   ],
   "source": [
    "print(average_cost_B_good)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.50000e+00 2.55000e+01 5.05000e+01 5.05000e+01 5.05000e+01 1.00500e+02\n",
      " 1.00500e+02 1.50400e+02 1.50400e+02 2.50500e+02 2.50500e+02 3.50200e+02\n",
      " 3.50200e+02 4.00500e+02 4.00500e+02 4.50100e+02 4.50100e+02 5.00500e+02\n",
      " 5.00500e+02 5.00500e+02 1.25050e+03 2.00050e+03 5.00050e+03 1.73505e+04\n",
      " 2.00005e+04 2.23255e+04 2.50005e+04 2.72755e+04 3.45005e+04 4.63755e+04]\n"
     ]
    }
   ],
   "source": [
    "print(average_queue_B_good)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.50000e+00, 2.55000e+01, 5.05000e+01, 5.05000e+01, 5.05000e+01,\n",
       "       1.00500e+02, 1.00500e+02, 1.50400e+02, 1.50400e+02, 2.00500e+02,\n",
       "       2.00500e+02, 2.50500e+02, 2.50500e+02, 3.00100e+02, 3.00100e+02,\n",
       "       3.50200e+02, 3.50200e+02, 4.00500e+02, 4.00500e+02, 4.50100e+02,\n",
       "       4.50100e+02, 5.00500e+02, 5.00500e+02, 5.00500e+02, 7.50250e+02,\n",
       "       1.25050e+03, 2.00050e+03, 2.50050e+03, 5.00050e+03, 7.47550e+03,\n",
       "       1.00005e+04, 1.25005e+04, 1.49005e+04, 1.73505e+04, 2.00005e+04,\n",
       "       2.23255e+04, 2.50005e+04, 2.72755e+04, 2.96005e+04, 3.20005e+04,\n",
       "       3.45005e+04, 3.68755e+04, 3.92005e+04, 4.18505e+04, 4.46005e+04,\n",
       "       4.63755e+04, 5.00005e+04])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.63629693 -0.3783582 ] [0.35110958]\n",
      "[-1.50507585 -1.7804249 ] [66.1337483]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ee823a6dd8>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M[5:25]-Cstar)\n",
    "yM2 = np.log(average_queue_M[5:25])\n",
    "xB2 = np.log(average_cost_B_good-Cstar)\n",
    "yB2 = np.log(average_queue_B_good)\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Maxweight\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Batching\", str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(5.5, 3.4666069106103783)]\n",
      "[(25.5, 3.2710502635843763)]\n",
      "[(50.5, 3.2486122022657766), (50.5, 3.2486122022657766), (50.5, 3.250604150732126)]\n",
      "[(100.5, 3.2391564187268287), (100.5, 3.2391564187268287)]\n",
      "[(150.4, 3.2391459002876304), (150.4, 3.2391459002876304)]\n",
      "[(200.5, 3.234328282688557), (200.5, 3.234328282688557)]\n",
      "[(250.5, 3.2461618381152024), (250.5, 3.2461618381152024)]\n",
      "[(300.1, 3.233669400678054), (300.1, 3.233669400678054)]\n",
      "[(350.2, 3.2375341659408656), (350.2, 3.2375341659408656)]\n",
      "[(400.5, 3.237730516079287), (400.5, 3.237730516079287)]\n",
      "[(450.1, 3.2400710341439174), (450.1, 3.2400710341439174)]\n",
      "[(500.5, 3.2400346866710774), (500.5, 3.2400346866710774), (500.5, 3.238803554546416)]\n",
      "[(750.25, 3.234280892728098)]\n",
      "[(1250.5, 3.23734796210138)]\n",
      "[(2000.5, 3.2384915296535306)]\n",
      "[(2500.5, 3.2326679819530644)]\n",
      "[(5000.5, 3.237385401825137)]\n",
      "[(7475.5, 3.2351388393192044)]\n",
      "[(10000.5, 3.2313456547772206)]\n",
      "[(12500.5, 3.233370272523461)]\n",
      "[(14900.5, 3.2344643121879106)]\n",
      "[(17350.5, 3.2359694581073675)]\n",
      "[(20000.5, 3.238210106246781)]\n",
      "[(22325.5, 3.235734677778846)]\n",
      "[(25000.5, 3.239812538793186)]\n",
      "[(27275.5, 3.2360554224263653)]\n",
      "[(29600.5, 3.233944106869623)]\n",
      "[(32000.5, 3.2345812487966743)]\n",
      "[(34500.5, 3.2380345192691933)]\n",
      "[(36875.5, 3.232724947319479)]\n",
      "[(39200.5, 3.233816044365523)]\n",
      "[(41850.5, 3.2337940549752124)]\n",
      "[(44600.5, 3.2332231258922124), (46375.5, 3.2363352458943955)]\n",
      "[(50000.5, 3.2327304298609567)]\n"
     ]
    }
   ],
   "source": [
    "used_points = set()\n",
    "average_queue_reduced = []\n",
    "average_cost_reduced = []\n",
    "proximity_threshold = 1\n",
    "points = np.column_stack((average_queue_B, average_cost_B))\n",
    "for i, (x1, y1) in enumerate(points):\n",
    "    if i in used_points:\n",
    "        continue\n",
    "\n",
    "    cluster = [(x1, y1)]\n",
    "    used_points.add(i)\n",
    "\n",
    "    for j, (x2, y2) in enumerate(points[i+1:], start=i+1):\n",
    "        if j in used_points:\n",
    "            continue\n",
    "\n",
    "        distance = abs(x2-x1)\n",
    "        if distance <= 0.05*x1:\n",
    "            cluster.append((x2, y2))\n",
    "            used_points.add(j)\n",
    "\n",
    "    xavg = sum(x for x, _ in cluster) / len(cluster)\n",
    "    yavg = sum(y for _, y in cluster) / len(cluster)\n",
    "    print(cluster)\n",
    "    average_queue_reduced.append(xavg)\n",
    "    average_cost_reduced.append(yavg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "average_queue_reduced = np.asarray(average_queue_reduced)\n",
    "average_cost_reduced = np.asarray(average_cost_reduced)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.50000e+00 2.55000e+01 5.05000e+01 1.00500e+02 1.50400e+02 2.00500e+02\n",
      " 2.50500e+02 3.00100e+02 3.50200e+02 4.00500e+02 4.50100e+02 5.00500e+02\n",
      " 7.50250e+02 1.25050e+03 2.00050e+03 2.50050e+03 5.00050e+03 7.47550e+03\n",
      " 1.00005e+04 1.25005e+04 1.49005e+04 1.73505e+04 2.00005e+04 2.23255e+04\n",
      " 2.50005e+04 2.72755e+04 2.96005e+04 3.20005e+04 3.45005e+04 3.68755e+04\n",
      " 3.92005e+04 4.18505e+04 4.54880e+04 5.00005e+04]\n",
      "[3.46660691 3.27105026 3.24927619 3.23915642 3.2391459  3.23432828\n",
      " 3.24616184 3.2336694  3.23753417 3.23773052 3.24007103 3.23962431\n",
      " 3.23428089 3.23734796 3.23849153 3.23266798 3.2373854  3.23513884\n",
      " 3.23134565 3.23337027 3.23446431 3.23596946 3.23821011 3.23573468\n",
      " 3.23981254 3.23605542 3.23394411 3.23458125 3.23803452 3.23272495\n",
      " 3.23381604 3.23379405 3.23477919 3.23273043]\n"
     ]
    }
   ],
   "source": [
    "print(average_queue_reduced)\n",
    "print(average_cost_reduced)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "average_queue_B_good = average_queue_reduced[np.array(average_cost_reduced) > Cstar]\n",
    "average_cost_B_good = average_cost_reduced[np.array(average_cost_reduced) > Cstar]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.63629693 -0.3783582 ] [0.35110958]\n",
      "[-1.43665435 -1.07198149] [47.05326332]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ee80505f60>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M[5:25]-Cstar)\n",
    "yM2 = np.log(average_queue_M[5:25])\n",
    "xB2 = np.log(average_cost_B_good-Cstar)\n",
    "yB2 = np.log(average_queue_B_good)\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Maxweight\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Batching\", str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.50000e+00, 2.55000e+01, 5.05000e+01, 5.05000e+01, 5.05000e+01,\n",
       "       1.00500e+02, 1.00500e+02, 1.50400e+02, 1.50400e+02, 2.50500e+02,\n",
       "       2.50500e+02, 3.50200e+02, 3.50200e+02, 4.00500e+02, 4.00500e+02,\n",
       "       4.50100e+02, 4.50100e+02, 5.00500e+02, 5.00500e+02, 5.00500e+02,\n",
       "       1.25050e+03, 2.00050e+03, 5.00050e+03, 1.73505e+04, 2.00005e+04,\n",
       "       2.23255e+04, 2.50005e+04, 2.72755e+04, 3.45005e+04, 4.63755e+04])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B[np.array(average_cost_B) > Cstar]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([400.5  , 450.46 , 475.395, 500.5  ])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B2[np.array(average_cost_B2) <= Cstar]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_cost_B2)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_B2 = average_cost_B2[sorted_indices]\n",
    "average_queue_B2 = average_queue_B2[sorted_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "average_queue_B_good = average_queue_B2[average_cost_B2 > Cstar]\n",
    "average_cost_B_good = average_cost_B2[average_cost_B2 > Cstar]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.63629693 -0.3783582 ] [0.35110958]\n",
      "[-0.14045062  4.36885374] [4.28176332]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c280b1f208>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M[5:25]-Cstar)\n",
    "yM2 = np.log(average_queue_M[5:25])\n",
    "xB2 = np.log(average_cost_B_good[:]-Cstar)\n",
    "yB2 = np.log(average_queue_B_good[:])\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Maxweight\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Batching\", str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>yM</th>\n",
       "      <th>qM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.615386</td>\n",
       "      <td>1.85037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.049373</td>\n",
       "      <td>2.85586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.499793</td>\n",
       "      <td>4.48076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.903299</td>\n",
       "      <td>6.70799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.935106</td>\n",
       "      <td>6.92478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.968740</td>\n",
       "      <td>7.16165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2.112899</td>\n",
       "      <td>8.27219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2.197931</td>\n",
       "      <td>9.00636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2.323413</td>\n",
       "      <td>10.21046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2.555729</td>\n",
       "      <td>12.88069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2.875660</td>\n",
       "      <td>17.73713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>3.128721</td>\n",
       "      <td>22.84475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3.272948</td>\n",
       "      <td>26.38903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3.419099</td>\n",
       "      <td>30.54188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>3.547246</td>\n",
       "      <td>34.71758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>3.724788</td>\n",
       "      <td>41.46245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.038908</td>\n",
       "      <td>56.76431</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>4.231059</td>\n",
       "      <td>68.79007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.444920</td>\n",
       "      <td>85.19303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>4.658020</td>\n",
       "      <td>105.42714</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          yM         qM\n",
       "0   0.615386    1.85037\n",
       "1   1.049373    2.85586\n",
       "2   1.499793    4.48076\n",
       "3   1.903299    6.70799\n",
       "4   1.935106    6.92478\n",
       "5   1.968740    7.16165\n",
       "6   2.112899    8.27219\n",
       "7   2.197931    9.00636\n",
       "8   2.323413   10.21046\n",
       "9   2.555729   12.88069\n",
       "10  2.875660   17.73713\n",
       "11  3.128721   22.84475\n",
       "12  3.272948   26.38903\n",
       "13  3.419099   30.54188\n",
       "14  3.547246   34.71758\n",
       "15  3.724788   41.46245\n",
       "16  4.038908   56.76431\n",
       "17  4.231059   68.79007\n",
       "18  4.444920   85.19303\n",
       "19  4.658020  105.42714"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame.from_dict({'yM': yM2,'qM': average_queue_M[5:25]})\n",
    "df1.head(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>yB</th>\n",
       "      <th>qB</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.921973</td>\n",
       "      <td>50.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.324100</td>\n",
       "      <td>75.4975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.610158</td>\n",
       "      <td>100.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.832306</td>\n",
       "      <td>125.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.013897</td>\n",
       "      <td>150.4900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.167596</td>\n",
       "      <td>175.4925</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5.300814</td>\n",
       "      <td>200.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.418243</td>\n",
       "      <td>225.4825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5.523459</td>\n",
       "      <td>250.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.618506</td>\n",
       "      <td>275.4775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.705315</td>\n",
       "      <td>300.4600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5.785201</td>\n",
       "      <td>325.4475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5.859190</td>\n",
       "      <td>350.4400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5.928092</td>\n",
       "      <td>375.4375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>6.053053</td>\n",
       "      <td>425.4100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          yB        qB\n",
       "0   3.921973   50.5000\n",
       "1   4.324100   75.4975\n",
       "2   4.610158  100.5000\n",
       "3   4.832306  125.5000\n",
       "4   5.013897  150.4900\n",
       "5   5.167596  175.4925\n",
       "6   5.300814  200.5000\n",
       "7   5.418243  225.4825\n",
       "8   5.523459  250.5000\n",
       "9   5.618506  275.4775\n",
       "10  5.705315  300.4600\n",
       "11  5.785201  325.4475\n",
       "12  5.859190  350.4400\n",
       "13  5.928092  375.4375\n",
       "14  6.053053  425.4100"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame.from_dict({'yB': yB2,'qB': average_queue_B_good[:]})\n",
    "df1.head(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 50.5   ,  75.4975, 100.5   , 125.5   , 150.49  , 175.4925,\n",
       "       200.5   , 225.4825, 250.5   , 275.4775, 300.46  , 325.4475,\n",
       "       350.44  , 375.4375, 400.5   , 425.41  , 450.46  , 475.395 ,\n",
       "       500.5   ])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 50.  75. 100. 125. 150. 175. 200. 225. 250. 275. 300. 325. 350. 375.\n",
      " 400. 425. 450. 475. 500.]\n"
     ]
    }
   ],
   "source": [
    "lol = np.floor(average_queue_B2)\n",
    "print(lol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[20000.         13333.33333333 10000.          8000.\n",
      "  6666.66666667  5714.28571429  5000.          4444.44444444\n",
      "  4000.          3636.36363636  3333.33333333  3076.92307692\n",
      "  2857.14285714  2666.66666667  2500.          2352.94117647\n",
      "  2222.22222222  2105.26315789  2000.        ]\n"
     ]
    }
   ],
   "source": [
    "new_lol = 1000000/lol\n",
    "print(new_lol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "103916.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.ceil(new_lol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[250000.         125000.          83333.33333333  66666.66666667\n",
      "  55555.55555556  50000.          47619.04761905  41666.66666667\n",
      "  33333.33333333  25000.          20000.          13333.33333333\n",
      "  11111.11111111]\n"
     ]
    }
   ],
   "source": [
    "new_Q = np.asarray([4, 8, 12, 15, 18, 20, 21, 24, 30, 40, 50, 75, 90])\n",
    "new_lol = 1000000/new_Q\n",
    "print(new_lol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "822624.0"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.ceil(new_lol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x21c80ae85f8>]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(average_queue_M, 'x')\n",
    "plt.plot(average_queue_B2, 'rx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'yB2' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-1-ebfe5835a336>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0myB2\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'yB2' is not defined"
     ]
    }
   ],
   "source": [
    "yB2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMFs\n",
      "[0.10773422 0.0969608  0.08726472 0.07853824 0.07068442 0.06361598\n",
      " 0.05725438 0.05152894 0.04637605 0.04173844 0.0375646  0.03380814\n",
      " 0.03042733 0.02738459 0.02464613 0.02218152 0.01996337 0.01796703\n",
      " 0.01617033 0.0145533  0.01309797 0.01178817 0.01060935 0.00954842\n",
      " 0.00859358] [0.00859358 0.00954842 0.01060935 0.01178817 0.01309797 0.0145533\n",
      " 0.01617033 0.01796703 0.01996337 0.02218152 0.02464613 0.02738459\n",
      " 0.03042733 0.03380814 0.0375646  0.04173844 0.04637605 0.05152894\n",
      " 0.05725438 0.06361598 0.07068442 0.07853824 0.08726472 0.0969608\n",
      " 0.10773422]\n",
      "average cost B [3.46660691 3.27105026 3.25060415 3.23880355 3.23428089 3.23734796\n",
      " 3.23849153 3.23266798 3.2373854  3.23513884 3.23134565 3.23337027\n",
      " 3.23446431 3.23596946 3.23821011 3.23573468 3.23981254 3.23605542\n",
      " 3.23394411 3.23458125 3.23803452 3.23272495 3.23381604 3.23379405\n",
      " 3.23322313 3.23633525 3.23273043]\n",
      "average cost M [4.31423252 4.30596688 4.31199192 4.31033658 4.20321492 3.83998931\n",
      " 3.65661628 3.56629016 3.47896202 3.4512984  3.45400389 3.44956203\n",
      " 3.43946198 3.44452617 3.39107352 3.37459116 3.34402312 3.3493701\n",
      " 3.3305715  3.32363706 3.31090776 3.30053229 3.29434307 3.28825848\n",
      " 3.2948894  3.29018216 3.28961014 3.27823875 3.27878856 3.2808346\n",
      " 3.28218652 3.27756088 3.27633197 3.28449116 3.27694823 3.27118457\n",
      " 3.26988385 3.26453047]\n",
      "Expected cost for c = 0 case: 4.311\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
      " [4.12310563 4.47213595 5.         5.65685425 6.40312424 3.16227766\n",
      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n",
      "3.2353891814339213\n"
     ]
    }
   ],
   "source": [
    "file_name = '../lspu_25_largeq_reverse_geometric_batch_new_2.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    C_paths_M0, Q_paths_M0, average_cost_B2, average_queue_B2, average_new, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "print(\"PMFs\")\n",
    "average_cost_B2 = average_new\n",
    "print(pmf_cust,pmf_serv)\n",
    "print(\"average cost B\", average_cost_B)\n",
    "print(\"average cost M\", average_cost_M)\n",
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "Cstar = fluid_sol['Cost']\n",
    "print(Cstar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.63629693 -0.3783582 ] [0.35110958]\n",
      "[-0.82774026  0.49404348] [0.0624679]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x15b8609ec88>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M[5:25]-Cstar)\n",
    "yM2 = np.log(average_queue_M[5:25])\n",
    "xB2 = np.log(average_cost_B2-Cstar)\n",
    "yB2 = np.log(average_queue_B2)\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'black')\n",
    "\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Maxweight\",str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)), \"Batching\", str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}