probab_curves.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import rv_discrete\n",
    "from matplotlib import pyplot as plt\n",
    "import cvxpy as cp\n",
    "import pickle\n",
    "# import gurobipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import utils\n",
    "def run_extremes(N, W, pmf_cust, pmf_serv, gurobi_flag = 1):\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)\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",
    "        M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "    Q_paths_M = M_res[\"Q_paths\"]\n",
    "    C_paths_M = M_res[\"C_paths\"]\n",
    "    Q_paths_B = B_res[\"Q_paths\"]\n",
    "    C_paths_B = B_res[\"C_paths\"]\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_cost_B,average_queue_M,average_cost_M, save_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_from_sim_paths_steps(file_name, steps = 10**5, save_file= 0, frac = 0):\n",
    "    with open(file_name,'rb') as f:\n",
    "        M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "    [Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "    Q_paths_M = np.asarray( M_res[\"Q_paths\"] )\n",
    "    C_paths_M = np.asarray( M_res[\"C_paths\"] )\n",
    "    Q_paths_B = np.asarray( B_res[\"Q_paths\"] )\n",
    "    C_paths_B = np.asarray( B_res[\"C_paths\"] )\n",
    "    QPM = Q_paths_M[:,0:steps]\n",
    "    CPM = C_paths_M[:,0:steps]\n",
    "    QPB = Q_paths_B[:,0:steps]\n",
    "    CPB = C_paths_B[:,0:steps]\n",
    "    (average_cost_M, average_queue_M) = utils.average_paths(CPM,QPM, frac)\n",
    "    (average_cost_B, average_queue_B) = utils.average_paths(CPB,QPB, frac)\n",
    "    utils.qc_plot(Ex,fluid_sol,average_queue_B,average_cost_B,average_queue_M,average_cost_M)\n",
    "def comparison_plot(file_name, steps = 10**4, frac = 0):\n",
    "    with open(file_name,'rb') as f:\n",
    "        M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "        \n",
    "    Ex = round (np.sum(np.outer(pmf_cust,pmf_serv)*W), 3) \n",
    "    fluid_sol = {'Cost':0}\n",
    "    \n",
    "    Q_paths_M = np.asarray( M_res[\"Q_paths\"] )\n",
    "    C_paths_M = np.asarray( M_res[\"C_paths\"] )\n",
    "    Q_paths_B = np.asarray( B_res[\"Q_paths\"] )\n",
    "    C_paths_B = np.asarray( B_res[\"C_paths\"] )\n",
    "    \n",
    "    QPM = Q_paths_M[:,0:steps]\n",
    "    CPM = C_paths_M[:,0:steps]\n",
    "    QPB = Q_paths_B[:,0:steps]\n",
    "    CPB = C_paths_B[:,0:steps]\n",
    "    (avg_C_M, avg_Q_M) = utils.average_paths(CPM,QPM, frac)\n",
    "    (avg_C_B, avg_Q_B) = utils.average_paths(CPB,QPB, frac)\n",
    "    # [Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "    \n",
    "    plt.figure( figsize=(20,6) ) \n",
    "    plt.subplot(1,2,1)\n",
    "    ylim = max( max( avg_Q_B ), max( avg_Q_M ) )\n",
    "    plt.plot([fluid_sol['Cost'],fluid_sol['Cost']],[0,ylim],linewidth = 3)\n",
    "    # Batching data\n",
    "    plt.plot(avg_C_B,avg_Q_B,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "    # Max Weight data\n",
    "    plt.plot(avg_C_M, avg_Q_M,'go',markersize = 8)\n",
    "    plt.plot([Ex],[1],'r*',markersize = 12, markeredgewidth=3)\n",
    "    plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "    plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "    plt.title(\"Reduced steps\", weight='bold',fontsize=15)\n",
    "    plt.legend(['Fluid', 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "    \n",
    "    print(\"old MW\", avg_C_M)\n",
    "    print(\"old B\", avg_C_B)\n",
    "    \n",
    "    (avg_C_M, avg_Q_M) = utils.average_paths(C_paths_M,Q_paths_M, frac)\n",
    "    (avg_C_B, avg_Q_B) = utils.average_paths(C_paths_B,Q_paths_B, frac)\n",
    "    plt.subplot(1,2,2)\n",
    "    ylim = max( max( avg_Q_B ), max( avg_Q_M ) )\n",
    "    plt.plot([fluid_sol['Cost'],fluid_sol['Cost']],[0,ylim],linewidth = 3)\n",
    "    # Batching data\n",
    "    plt.plot(avg_C_B,avg_Q_B,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "    # Max Weight data\n",
    "    plt.plot(avg_C_M, avg_Q_M,'go',markersize = 8)\n",
    "    plt.plot([Ex],[1],'r*',markersize = 12, markeredgewidth=3)\n",
    "    plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "    plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "    plt.title(\"Original\", weight='bold',fontsize=15)\n",
    "    plt.legend(['Fluid', 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "    \n",
    "    print(\"new MW\", avg_C_M)\n",
    "    print(\"new B\", avg_C_B)\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 0.92\n",
      "Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (win64)\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i7-8550U CPU @ 1.80GHz, instruction set [SSE2|AVX|AVX2]\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 8 rows, 16 columns and 32 nonzeros\n",
      "Model fingerprint: 0xdfb4e2e3\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [1e+00, 1e+00]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [1e-02, 5e-01]\n",
      "Presolve removed 1 rows and 1 columns\n",
      "Presolve time: 0.02s\n",
      "Presolved: 7 rows, 15 columns, 30 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    5.0412536e-01   4.069200e-01   0.000000e+00      0s\n",
      "       3    5.8941125e-01   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 3 iterations and 0.02 seconds (0.00 work units)\n",
      "Optimal objective  5.894112550e-01\n",
      "Objective Value: 0.59\n",
      "x:  [[0.01 0.1  0.15 0.24]\n",
      " [0.   0.1  0.   0.  ]\n",
      " [0.   0.   0.1  0.  ]\n",
      " [0.   0.   0.   0.3 ]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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uXcuIESPqb10UfW7kJt6VlZX06NGDAwcOUFtby7HHHgvA5s2bmTJlCqeeeipnnnkmGzZsALyFXGfPng3Aa6+9xqhRoxg3bhzTp09nxIgR9Z/x4YcfMmXKFIYPH87NN98MeIvHRu4EcOmll7apbUAhTEREJGfdtequJgEsoraulrtX3d2m9//ud7/LY489Rm1tLX/7298444wz6vcdf/zxLF26lNdff53//M//5LbbbgPgP/7jP9i0aRPz5s2jqKiIP/7xj/Ts2bPB+55yyim8/vrrALz00kuMGDGC1157jVdeeaX+M4qLi/nd737H6tWrmT17Ntddd12T+oqKirjnnntYsWIFnTp1arBvzZo1PPzww6xdu5aHH36Yf/zjH9x+++306NGDNWvW8NBDD7WpbUDrhImIiOSs6n3ViffvT7y/OaNGjeL999/nz3/+M9/85jcb7Nu9ezdXXHEFGzduxMz4/PPPAQiFQtx///2MGjWK//N//g8TJkxo8r6dO3dm2LBhrF+/nldffZUbb7yRpUuXcvDgQc4880xqampYvnw5F198cf05n332WYP32LVrF3v27GH8+PEAfO973+PJJ5+s33/OOefU31fyxBNP5L333uPLX/5ym9qjyfdo13cTERGRDqN/z/7s3Lcz/v4e/dv8GVOnTuWmm26iqqqK6uovQt1Pf/pTJk2axLx589iyZUv9fR8BNm7cSO/evfnwww/rt02ePJlt27aRl5dHRUUFZ555Js888wxdunTh61//OldeeSUHDx5k9uzZhMNhDj30UNasWRO3Ludcwrq7detW/7xTp07U1dW1/Ms3Q8ORIiIiOeq6vOvo3rl7zH3dO3fn2rxr2/wZl112GT/72c8YOXJkg+27d++un6h///33N9h+ww03sHTpUqqrq3n00UcBWLRoEWvWrKGiogKAs846izvvvJNx48YxcOBAqqur2bBhAyeddBKHHHIIxxxzDI888gjgBa433nijwef369ePPn36sHLlSgDmzp0b6Pt06dKlvteurRTCREREctT0CdMZ2m9okyDWvXN3hvYbyvQJ09v8GUcddRQ33HBDk+0333wzt956KxMmTODgwYP123/0ox9x3XXXcdxxx3HvvfcyY8YMtm/f3uT8M844g23btnHWWWcB3tDnqFGjMPPug/nQQw9x7733cvLJJ3PSSSdRWVnZ5D3uvfdeiouLGTduHM65+uHHRIqLixk1alS7TMy35rrjMk1eXp5btWpVustokyEznqp/vuX281p8flVVVYNuW/mC2iYxtU98apvE1D6JZVr7rF+/nhNOOCHQsTUHapi1bBZ3r7qb6v3V9O/Rn2vzrmX6hOn07tq7zbXs2bOHPn36tPl9kqGmpobevb3vePvtt/PRRx/x3//9361+v1jtbmarnXN5sY7XnDAREZEc1rtrb8omlVE2qSzdpaTcU089xa9+9Svq6uo4+uijGwyLpoJCmIiIiOSk73znO3znO99J2+drTpiIiIhIGiiEiYiIiKSBQpiIiEiu27ULQiEwg06dvNeSdAphIiIiue6llyCyWkI4DC+/nN56coRCmIiISK6rqkr8OgOsXr2akSNHMmzYMH74wx82u+J9c7Zs2dLght3poBAmIiKSay6+2Bt6jPzccUfD/b/5TcP9UfdgTJdrr72W8vJyNm7cyMaNG1m4cGG6S2ozhTAREZFcsncvRN2oOpCnnvLOa4EHH3yQUaNGMX78eC677LKWfV4jH330EZ9++injxo3DzLj88suZP39+k+NefPFFRo8ezejRoxkzZgx79uzBOcf06dMZMWIEI0eO5OGHH25TLe1J64SJiIjkkpUroba2Zefs3w+vvAJf+1qgw998801+8YtfsGzZMrp16xbzXotLlizhRz/6UZPtPXv2ZPny5Q22ffDBBwwePLj+9eDBg/nggw+anDt79mz+8Ic/MGHCBGpqaujevTuPP/44a9as4Y033mDnzp2cdtpp9bc6SjeFMBERkVxyzjkwZw5cd50XrprTowfcdVfgAAbwwgsvcNFFFzFgwAD27NnDYYcd1uSYSZMmsWbNmkDvF2v+V+QekdEmTJjAjTfeyKWXXsoFF1zA4MGDefnll7nkkkvo1KkTgwYN4uyzz+a1115j1KhRgb9PsiiEiYiI5Jorr4TTToOLLoING+Ifd8IJ8MgjcNJJLXp751zMkBStJT1hgwcPZuvWrfWvt27dypFHHtnk3BkzZnDeeefx9NNPM3bsWJ577rk2T+BPJs0JExERyUUnneSFrEROOKHFAQzgnHPO4S9/+QvV1dUAfPzxx02OifSENf5pHMAAjjjiCPr06cPKlStxzvHggw9SUFDQ5LjNmzczcuRIbrnlFvLy8tiwYQNnnXUWDz/8MAcPHmTHjh0sXbqU008/vcXfKRnUEyYiIpKL1qyBefMSH/P44/DGG3DyyS1665NOOomf/OQnnH322ZgZp556aptvjn333Xdz5ZVXsn//fqZOncrUqVObHHPnnXeyZMkSOnXqxIknnsjUqVPp2rUrK1as4OSTT8bMmDlzJl/60pfYsmVLm+ppDwphIiIiueiaaxq+7tEDiouhvLzhXLFrroEVK1r89ldccQVXXHEFe/bsoU+fPm0sFvLy8li3bl3CY373u9/F3D5r1ixmzZrVYNuQIUOafb9k03CkiIhILqqoaPj6tdfgzju9x0THSbtRCBMREclFI0bA9u1w661QU/PF3K+TTvJe33qrt78Vc8IkGA1HioiI5KqBA+GXv2y6vVev2NulXaknTEREJAtl8tIM2ag17a0QJiIikmW6d+9OdXW1gliKOOeorq6me/fuLTpPw5EiIiJZJrK46Y4dO9JdCrW1tS0OJx1R9+7dG9xaKQiFMBERkSzTpUsXjjnmmHSXAUBVVRVjxoxJdxkZScORIiIiImmgECYiIiKSBgphIiIiImmQ0hBmZp3M7HUze9J/fZiZPWtmG/3HfqmsR0RERCRdUt0TdgOwPur1DOB559xw4Hn/tYiIiEjWS1kIM7PBwHlA9E2oCoAH/OcPAIWpqkdEREQknSxVC7mZ2aPAr4A+wE3OufPNbJdz7tCoYz5xzjUZkjSzYqAYYNCgQafOnTs3JTUny5UL99Y/v39KrxafX1NTQ+/evduzpKyhtklM7ROf2iYxtU9iap/4cr1tJk2atNo5lxdrX0rWCTOz84HtzrnVZjaxpec758qBcoC8vDw3cWKL3yKzLHyq/mlrvktVVVWrzssFapvE1D7xqW0SU/skpvaJT20TX6oWa50AfMvMvgl0Bw4xsz8B28zsCOfcR2Z2BLA9RfWIiIiIpFVK5oQ55251zg12zg0Bvgu84Jz7PvAEcIV/2BVAZSrqEREREUm3dK8TdjvwDTPbCHzDfy0iIiKS9VJ+70jnXBVQ5T+vBs5JdQ0iIiIi6ZbunjARERGRnKQQJiIiIpIGCmEiIiIiaaAQJiIiIpIGCmEiIiIiaaAQJiIiIpIGCmEiIiIiaaAQJiIiIpIGgRZrNbPOwGXAGCD6VujOOXd1MgoTERERyWZBV8yfA3zPf25R2x2gECYiIiLSQkFDWAHwGfAXYBde+BIRERGRVgoawrYCK51zVyWzGBEREZFcETeEmdm/RL38DfBLM7sAWAPURXY4595PWnUiIiIiWSpRT9i7MbY90ui1a+Y9RERERCSGRAHKEuxryTEiIiIi0kjcEOac0xpiIiIiIkkSKGiZ2Qtmdm2jbd82s/9OTlkiIiIi2S1ob9dEYHijbZOA69u1GhEREZEckXBSvZndF/Xy3KjXIeCbwP5kFSYiIiKSzZq7svFKvCsgHXCi/xNtYRJqEhEREcl6zYWwMv+xBHiFL0LXQeAfNF2yQkREREQCSBjCnHNlAGYGsMI5tzgVRYmIiIhku6ALrb4OdDezbzXa/hnwd+dcrIVdRURERCSOoCFsPglu2m1mTwGXOuf2tEdRIiIiItku6BIV7+OFsIPANv/RAf/0H88DfpKMAkVERESyUdAQ9gfgTeBI59yRwJH+6zuBo4GNQGES6hMRERHJSkFD2M3AWufcTgD/cS1ws3PuA+Bh4F+SU6KIiIhI9gk6J6wW+K6Z1QIb8FbP/1fgI3//YUBN+5cnIiIikp2ChrBfAb8HivzXFtluZofgrZ5f1b6liYiIiGSvQCHMOXeXmb0FfB9vPtgHwP8455b6hwxNUn0iIiIiWSloTxjOuSrU2yUiIiLSLgKFMDPrC9wIjAF6R+1yzrlzklGYiIiISDYL2hP2v8AUvpgLFhF3AVcRERERiS9oCDsb+BhvvbBdKHyJiIiItEnQEPZ34A3nXGkSaxERERHJGUFD2MPAT81sLbAGqIvsiLpCUkREREQCask6YQ6Y1Wi7a8F7iIiIiIgvaICK3MBbRERERNpB0MVahyS5DhEREZGcEvQG3pjZYWZWbGa/NrO+ZnaWmQ1KZnEiIiIi2SpQCDOzk4D1wN3ATf7mZ4DS5JQlIiIikt2C9oTdARwKvAPgnNsNvAh8PTlliYiIiGS3oCHsdGA+8GTUtvfwbuYtIiIiIi0UNITtpeE9IwFGAdXtW46IiIhIbggawl4GJgMXApjZq8BYQAu1NlJZuYlwOPZqHuGwo7JyU4orEhERkUwUNIRNB7YAg/Fu4p0HvAvclpyyOqbS0mUUFs5n2rRFTYJYOOyYNm0RhYXz2fXyjjRVKCIiIpki6Dph/zCzkcD5wNF4gexp59y+JNbWoVRWbqKsbAUAc+asA6CiYjKhkNUHsMj23ct20nVQd3oO75O2ekVERCS9Aq8T5pzb75x7xDk32zn3qAJYQ/n5QykqGlH/es6cdUybtoi6unCDAAbQa2RfegxrPMVOREREckncnjAzOxjgfOec070jgVDIqKiYDHzREzZnzroG4QugqGgEzw+sw8xSXqOIiIhkjkQ9YRbgJ+hir93N7FUze8PM3jSzMn/7YWb2rJlt9B/7teXLpFskiEX3iEUrKhpBRcVkBTARERFJGKKOCfgTxGfA15xzJwOjgSlmNhaYATzvnBsOPO+/7tBCIaO8/NyY+8rLzyUUUgATERGRBCHMOfdekJ8gH+I8Nf7LLv6PAwqAB/ztDwCFrf8qmSEcdhQXL465r7h4cdzlK0RERCS3pGw+l5l1AlYDw4A/OOdeMbNBzrmPAJxzH5nZ4amqJxkaXwXZWGS7G+g0JCkiIpLjzLnU9syY2aHAPOAHwMvOuUOj9n3inGsyL8zMioFigEGDBp06d+7c1BTbAuGwY9asLSxc+MVNBKZM6c9NNw1h9uyG23uN7Ev/qUdgZtw/pVeLP6umpobevXV1ZSxqm8TUPvGpbRJT+ySm9okv19tm0qRJq51zebH2pfzKRufcLjOrAqYA28zsCL8X7Ahge5xzyoFygLy8PDdx4sRUlRtYZeUmFi5cXf86Mgk/FDImTWrYQ7Z37W56Du9Dz+F9aM13qaqqatV5uUBtk5jaJz61TWJqn8TUPvGpbeILvE4Y1F/leGJLP8TMBvo9YJhZD+DrwAbgCeAK/7ArgMqWvnemKCgYRknJOKBhAIOmV032nTBAC7WKiIjkuEA9YX5w+j1+YDKz4cBzwJ3Oud8FeIsjgAf8eWEh4C/OuSfNbAXwFzO7GngfuLgV3yFjlJZOYMyYQeTnD21yFWQkiBUUDOOGFW+nqUIRERHJFEGHI38OFPnPnXPuXTP7BLgUaDaEOef+BoyJsb0aOCdgDR1CQcGwuPtCIVMIExERESD4cORFeFc23h217Q3guHavSERERCQHBA1h/YC3gANR23rgrZovIiIiIi0UNIRtwLua8QQAM/t3vIVV1yenLBEREZHsFjSE/QIYCHzDf/1boDtwezKKEhEREcl2gUKYc+4JYCqwEK/36xngm/52EREREWmhwIu1OucWAYuSWIuIiIhIzgi6Tth9cXY559zV7ViPiIiISE4I2hN2JeD44mrIyHMHKISJiIiItFDQEFYW9bwTMBL4FhCvh0xEREREEggUwpxzZY23mVk5cFS7VyQiIiKSA4LOCfuXRpsOAb4CnNzuFYmIiIjkgKDDke/G2b62vQoRERERySVBF2u1Rj/7geV4E/ZFREREpIWCzgkLGtZEREREJIDA4crMDjOzYjP7tZn1NbOzzGxQMosTERERyVaBQpiZnYR3u6K7gZv8zc8ApckpK3tUVm4iHHYx9znnqKzclOKKREREJBME7Qm7AzgUeAfAObcbeBH4enLKyg6lpcsoLJzPtGmLmgQx5xzVz3xEYeF8SkuXpalCERERSZegIex0YD7wZNS294Aj27ugbFFZuYmyshUAzJmzrkEQiwSwvWt3A1BWtkI9YiIiIjkmaAjbC/RutG0UUN2+5WSP/PyhFBWNqH8dCWJ1deEGAQygqGgE+flD01GmiIiIpEnQEPYyMBm4EMDMXgXGAkuTVFeHFwoZFRWTmwSxLl3uaBLAKiomEwpZrLcRERGRLBU0hE0HtgCD8dYJy8NbwPW25JSVHWIFsWi9RvZVABMREclRgUKYc+4feDft/g5wM/CvwCjn3PtJrC0rhEJGefm5Mff1n3KEApiIiEiOCnrbIpxz+4FHklhLVgqHHcXFi2Puq174EeHbnYKYiIhIDgq6TtjBOD91yS6wIwuHHdOmLWLOnHUx9+9duzvm8hUiIiKS/Vp778joH4khVgArKhrB55/fSK+Rfeu3NV6+QkRERHJD0BB2TNTPMODbwId4E/YlhgULNjcJYBUVk+ncOUT/qUc0CWILFmxOR5kiIiKSJkEn5r8X9fOOc64SeAi4KrnldVwFBcMoKRkHNF2GwswaBLGSknEUFAxLW60iIiKSeoEm5pvZzxptOgS4AujS7hVlkdLSCYwZM4j8/KFNJt9HgthDP5+kACYiIpKDgl4dWQpET1qKJIqH2rWaLJQoYJmZApiIiEiOChrCHqRhCNsLvA78T7tXJCIiIpIDAoUw59yVSa5DREREJKcEnRP2wyDHOed+27ZyRERERHJD0OHIO2k4HBmPQpiIiIhIAEFD2EvABGAH3o27jwEGAsuAcHJKExEREcleQUPYKrw1xSY65w6aWWdgCbDKOffjpFUnIiIikqWCrpg/DdjhnDsI4JyrA3YCVyerMBEREZFsFrQnbAdQYGbPAm8DXwG+BryTrMJEREREslnQEDYD+DNwDl74MuCgv11EREREWijoOmGPmtka4LvAkcAHwMPOuU1JrE1EREQkawXtCcMPXP8vibWIiIiI5IygE/NFREREpB0phImIiIikgUKYiIiISBq0KISZWXczOzFZxYiIiIjkikAhzMx6mNm9QA3wNzM7xsw2m9kPklueiIiISHYK2hP2c6DIP96cc+8CnwCXJquwXFFZuYlwOPa90cNhR2WlVgERERHJRkFD2EXAauDuqG1vAMe1e0U5ZNfLOygsnM+0aYuaBLFw2DFt2iIKC+dTWrosTRWKiIhIsgQNYf2At4ADUdt64K2cL62wb+Medi/bCcCcOesaBLFIAJszZx0AZWUr1CMmIiKSZYKGsA3AFOAEADP7d6AQWJ+csrJfj2G96TWyb/3rSBCrqws3CGAARUUjyM8fmo4yRUREJEmChrBfAAOBb/ivfwt0B25PRlG5wMzoP/UIiopG1G+bM2cdXbrc0SSAVVRMJhRSp6OIiEg2CRTCnHNPAFOBhXi9X88A3/S3N8vMvmxmS8xsvZm9aWY3+NsPM7NnzWyj/9ivld+jQzIzKiomNwhi0RTAREREslfgdcKcc4ucc+c550Y45853zi1swefUAT92zp0AjAX+3V9vbAbwvHNuOPC8/zqnhEJGefm5MfeVl5+rACYiIpKlAt3A28zuiLPrM+DvwGPOuU/jne+c+wj4yH++x8zWA0cBBcBE/7AHgCrgliA1ZYtw2FFcvDjmvuLixeoJExERyVKBQhjwH0Dsxaw8ZWY20Tn3TnNvZGZDgDHAK8AgP6DhnPvIzA4PWE9WcM41mYQfLbJdQUxERCT7mHOJspV/kNmfgYuBtXhzwo4HRgFP+M+PB/7snEu4eKuZ9QZeBH7hnHvczHY55w6N2v+Jc67JvDAzKwaKAQYNGnTq3Llzg327DHXlwr0456h+5iP2rt1dv33KlP7cdNMQZs/ewsKF1Q22T58+pD6I1dTU0Lt375TX3RGobRJT+8SntklM7ZOY2ie+XG+bSZMmrXbO5cXaFzSEPQgMdM5Njdr2DLAduBJ4DhjmnDs6wXt0AZ4EFjnn7vC3vQ1M9HvBjgCqnHNfSVRLXl6eW7VqVbM1Z7IhM55i38Y97Hh8a/226En4jdcJA5g/v5CCgmEAVFVVMXHixFSX3SGobRJT+8SntklM7ZOY2ie+XG8bM4sbwoJOzL8A6NpoW2fgAueluCog7lCimRlwL7A+EsB8TwBX+M+vACoD1tPh9Rzeh74TBgBNr4IMhRpeNVlSMq4+gImIiEh2CDon7F1gopltBN4GhgHDgUhXzQl4vWLxTAAuA9aa2Rp/221464z9xcyuBt7HG/LMGYd+dSAPTP8q+flDm8z5igSxgoJhCmAiIiJZKGgIuxZYAAz1fwB2Adea2SH++9wd+1Rwzr1M/FscnROwhqyUKGCFQqYAJiIikqUChTDn3Mv+VY3n4y0t8QHwpHMuMqv8X5NTnoiIiEh2CtoThh+4HjKzPvi9WmZ2SKL1wUREREQktkAT881ssJk9bWb78IYhP/F/Pk5ibSIiIiJZK2hP2B+AKcksRERERCSXBF2i4izgr8CDeCvnnwFsBq5KUl0iIiIiWS1oCOsJrAC2+a/X4q18f1syihIRERHJdkGHIz8GegPv4E3KfwwYS9MFXEVEREQkgKA9YeuAU/HWCgsDU4F+wOIk1SUiIiKS1YL2hE0FQs65A2Y2EbgQb2jy90mqS0RERCSrNRvCzKwzsAhYBvzMX/3+5WQXJiIiIpLNmh2OdM7VAccDRyS/HBEREZHcEHRO2H8ChWZ2tpl1SWZBIiIiIrkg6Jywu/HWB3sBwKz+XtzOORf41kciIiIi4mlJgLKA20RERESkGUFD2DFJrUJEREQkxwSaE+ace8859x7QDTgp8trfJglUVm4iHHYx9znnqKzclOKKREREJBMECmFmdpiZPQesB54wsyFmVmdmP09ueR1baekyCgvnM23aoiZBzDlH9TMfUVg4n9LSZWmqUERERNIl6NWRs4CvAQcAc85tAVYC5yeprg6vsnITZWUrAJgzZ12DIBYJYHvX7gagrGyFesRERERyTNAQNgWoAu6J2vYWcGx7F5Qt8vOHUlQ0ov51JIjV1YUbBDCAoqIR5OcPTUeZIiIikiZBQ1gP4KNG2wbg9YxJDKGQUVExuUkQ69LljiYBrKJiMqGQLjQVERHJJUFD2N/whh7PADCzWUA+8EaS6soKsYJYtF4j+yqAiYiI5KigIez/4l0ZORZvbbAfA2GgNDllZY9QyCgvPzfmvv5TjlAAExERyVFBl6h4GcjDWzn/aeAu4DR/uyQQDjuKixfH3Fe98KO4y1eIiIhIdgu6RMUFwNvOuX93zp3vnLveOfe3JNfW4YXDjmnTFjFnzrqY+/eu3R1z+QoRERHJfkGHIx8FPjSzP5jZ6cksKFvECmBFRSP4/PMb6TWyb/22xstXiIiISG4IGsJeBPoB1wIrzGyDmd1mZv+SvNI6tgULNjcJYBUVk+ncOUT/qUc0CWILFmxOR5kiIiKSJkHnhE0CjgR+ALwEDAN+Dig5xFFQMIySknFA02UozKxBECspGUdBwbC01SoiIiKpF/QG3jjntpvZfcAOoBMwgeA9aTmptHQCY8YMIj9/aJOrICNB7KGfT1IAExERyUGBQpiZFQLfwVsrrCfeMhUfAQ8lrbIskShgmZkCmIiISI4K2hP2uP+4H5gLPAg865wLJ6UqERERkSwXNIS9BDwAPOKc2xPZaGb9nHOfJKUyERERkSwWKIQ5586OPDezLni3LLoM78bePZJTmoiIiEj2Cjwx38zOBL4PXAz0xZsXpsWtRERERFohYQgzs6/g9Xh9Dzg6stl//DtQnLzSRERERLJXcz1h6/F6uwz4BHgSmIc3Uf8t59zS5JYnIiIikp2CDkf+Ffixc+5F8JZWEBEREZHWay6EvQ/8CzAGeMHMtuH1homIiIhIGyRc8d45NwSYCNwH7Aa+BFyNN0Q5ycx+leT6RERERLJSs7cdcs4tdc79G14Auwh4Avgc7wrJm5NbnoiIiEh2CnzvR+fcAefc4865b+MFsmuBl5NWmYiIiEgWa9UNuJ1zu5xzf4xexFVEREREgmtVCBMRERGRtlEIExEREUkDhTARERGRNFAIy3CVlZsIh2PfojMcdlRWbkpxRSIiItIeFMIyWGnpMgoL5zNt2qImQSwcdkybtojCwvmUli5LU4UiIiLSWgphGaqychNlZSsAmDNnXYMgFglgc+asA6CsbIV6xERERDoYhbAMlZ8/lKKiEfWvI0Gsri7MrFlb6gMYQFHRCPLzh6ajTBEREWklhbB2VHOghpIlJQycNZBQWYiBswZSsqSEmgM1LX6vUMioqJjcJIh16XIHCxdW128rKhpBRcVkQiHdVF1ERKQjae4G3hJQzYEaxlaMZfMnm6mtqwVg576dzFw+k8fWP8bKaSvp3bV3i94zEsSABj1fEQpgIiIiHVdKesLM7D4z225m66K2HWZmz5rZRv+xXypqSZZZy2Y1CGARtXW1bP5kM7OWzWrV+4ZCRnn5uTH3nX/+sXHP05WTIiIimS1Vw5H3A1MabZsBPO+cGw4877/usO5adVeTABZRW1fL3avubtX7hsOO4uLFMfddeOETXH31Ql05KSIi0gGlJIQ555YCHzfaXAA84D9/AChMRS3JUr2vOvH+/Yn3x9L4KshY7r//zQZBTFdOioiIdAzmXOyFQNv9g8yGAE8650b4r3c55w6N2v+Jcy7mkKSZFQPFAIMGDTp17ty5yS+4hQqXF7L7891x9x/a5VDmjZ8HwJUL99Zvv39Kr5jHh8OOWbO2NJiEP2VKf266aQi/+tVGnn/+0wbHT558GNOnH8Ps2U3PmT59SM7MG6upqaF375bNvcslap/41DaJqX0SU/vEl+ttM2nSpNXOubxY+zrExHznXDlQDpCXl+cmTpyY3oJiuMHdwMzlM2MOSXbv3J0fjvsh9XUvfKp+X7zvUlm5iYULV9e/jp6EbwZf/nIt99//Zv3+RYs+ZtGihp2NuThxv6qqKm6bitonEbVNYmqfxNQ+8alt4kvnEhXbzOwIAP9xexprabPpE6YztN9Qunfu3mB7987dGdpvKNMnTG/R+xUUDKOkZBzQNEyFQsa9907hyitPint+LgYwERGRjiSdIewJ4Ar/+RVAZRprabPeXXuzctpKbh5/MwN7DiRkIQb2HMjN429u1fIUAKWlE5g/vzBmmIoEscce+1bMc8vLz1UAExERyWApGY40sz8DE4EBZrYVKAFuB/5iZlcD7wMXp6KWZOrdtTdlk8oom1TWbu9ZUDAs4f4nn3wn5vbi4sXqCRMREclgKQlhzrlL4uw6JxWfn42au3Iysl1BTEREJDPptkUdUKwAVlQ0gs8/vzHm/SYbryPWWGXlprjHaNFXERGR5FAI64CWL9/VJIBVVEymc+dQzPtNLliwOe57lZYuo7BwfsywpkVfRUREkkchrAP66lf7JbxyMjqIlZSMizuvrLJyE2VlK4CmvWZa9FVERCS5OsQ6YdJUaekExowZRH7+0JhXTlZUTKagYFjCif35+UMpKhpRH7Qij+Xl51JcvLhJb1t+/tAkfBMREZHcpBDWgSUKWKGQNXtlZSSsAQ2CWOPJ/lpzTEREpP1pODLHNR6+bEwBTEREJDkUwoRQyCgvPzfmPi36KiIikhwKYUI47CguXhxzX3Hx4maXuBAREZGWUwjLcUEWfQ2y1piIiIi0jEJYhqk5UEPJkhIGzhpIqCzEwFkDKVlSQs2Bmnb/rPZe9DUWLQQrIiISm0JYBqk5UMPYirHMXD6Tnft24nDs3LeTmctnMrZibLsHsQULNrfboq+xaCFYERGR+BTCMsisZbPY/MlmautqG2yvratl8yebmbVsVrt+XkHBsHZZ9DUWLQQrIiKSmEJYBrlr1V1NAlhEbV0td6+6u90/s7R0AvPnF8ZchiISxObPL6S0dEKL3jeyEGxEJIjV1YVjDoFqIVgREck1Wqw1g1Tvq068f3/i/a3V1kVf452nhWBFRETiU09YBunfs3/i/T0S7880WghWREQkPoWwDHJd3nV079w95r7unbtzbd61Ka6o7RItBHvPPd+IGcB01aSIiOQChbAMMn3CdIb2G9okiHXv3J2h/YYyfcL0NFXWeokWgh0xYg51deEmx+uqSRERyQUKYRmkd9ferJy2kpvH38zAngMJWYiBPQdy8/ibWTltJb279k53iS3S3EKwGzfu4sQT76sPYrpqUkREcokm5qdAzYEaZi2bxV2r7qJ6XzXWvQ996s7jkLoLmhzbu2tvyiaVUTapLA2Vtp94C8Hec883GDFiDhs37gK+CGLr1hVxzTXP6qpJERHJGQphSRZZgDV6/S9nn/Jp58fY12kZNQemdLgeriDiLQQbChlvvXUVJ554X4Mg1q3bfzU4X5P2RUQk22k4MsniLcDq7AB19s92X4A1UyRaCLZz5xBvvXUVw4cfGvNcBTAREckFCmFJlmgBVmcHkrIAa6ZItBBs584h1q0rinleefm5gQOY7k0pIiIdlUJYkqVrAdZMUVAwLO4yFNdc82zMc4qLFwe6WbjuTSkiIh2ZQliSZdsCrO2huasmG99rMhbdm1JERDo6hbAkS7QAq7muHXIB1raId9Xk55/fGPNek/GCWLx7Ux48GPv9dZWliIhkGoWwJIu3AKu5rnR2X4q5AGvNgRpKlpQwcNZAQmUhBs4aSMmSEmoO1KSq7KSJd9Vk586hJrc4mjNnHQsWbI75PrFuiTRnzjq+/vXVca/KFBERySQKYUkWawHWkOvLIXUX8qXPftNkeYrIkhYzl89k576dOBw79+1k5vKZjK0Y2+GDWKKrJhsHq5KScc3eXFz3phQRkY5KISwFIguwbp++nYM/O8iXax/i0LpLCdGjybHxlrSoratl8yebs2JJi0RXTUaC1fz5hZSWTmj2vRLdm7IlV1mKiIikmkJYhkm0pEVtXW3WLGkR76pJ8IJVoh6waInuTRn0KksREZF0UAjLMNm0pEWy57a1x1WWmUBrnYmI5CaFsAyTLUtaJHtuW7yrLJ977tQWXWWZblrrTEQkdymEZZhES1p079y9wyxpkey5bfGusuzUKfZVk/GuskwnrXUmIpLbFMIyTLwlLbp37s7QfkNjLmmRiZI9ty3WVZb76vYyZ8scBv3mcO4/+pt0++nPYeIibi05OfAcs1SKt9ZZXV24Q651pmFVEZGWUQjLMLGWtBjYcyA3j7+ZldNWNlnSIl2am++Virlt0VdZ7qvby9iKscz9x9z64c/POn1Kl0kv8cThP8rIpT3irXXWpcsdHW6tMw2rioi0XOd0FyBNRZa0KJtUlu5SYorM94oebozM93ps/WOsnLaS/j37s3Pfzrjv0V5z2yI9XJHhzwPhAw32f+4+qx/+zMT2jAQxIOYFBh0hgDUeVgXqa441rDpmzKCM7JkUEUk19YRJiwWZ75XquW0deWmPjr7WWbYNqwal4VcRaSuFMGmxIIEn1XPbUjH8mawlNzr6WmfZNKwalIZfRaQ9KIRJiwUJPKme25bspT2SteRGtqx1lku3kNJVrSLSXhTCpMWCBp7Gt2vaPn07ZZPKknJxQbKHP5Ox5Ea8tc4+//zGDrXWWUSQYdUgvYmZfgP7XB1+bQsN3YrEphAmLZaJa5lFhj+7hro2qac9hj+TMecs3lpnnTuHOsxaZ9GaG1b9tHZPs72JHeEG9rk4/NoWGroViU8hTFosE9cyiwx/fvfL303K8Gcy5pzFWuss8hd247/oS0rGZfQVhUGGVc++9ZpmexM7yg3s2zr8mum9fe1FQ7ciiSmESYtl6lpmvbv2pmhIUVKGP5M15yx6rbPGf2FH/qKfP7+Q0tIJrXr/VAg6rLqmS2WzvYkd6SrX1l7V2hF6+9qLhm4l5XbtglAIzKBTJ+91lEwbGlcIk1ZJ5XyvTJDMIdiCgmFx/8IOhSyje8CgBcOqPfcmfJ/q/dUd6gb2rb2qtaP09rWHTBq6jfQ+Dpg5ACszQmUhrMwYMHNAVvZC5qyXXgLn/38vHIaXX67flYlD41qsVSSA6ROm89j6x5r85dnRbieVDJFh1bKyFXGHVQHm7OsFveIHsf49+tf3CiU6JhMEGX4FYgaLIL19mbiwcGtlwoLEsRaYdnh/CVfvr+bXy35dv9B0tv5DMtPVHKhh1rJZ/OG1PzT5x1aPzj244Ywb+MlZP2nw5xM55/ev/Z6P938MwOxF8OOoc2f/Mp/pqwEMPg9ByUHmfN6FB8tChEMH6N+zP9eeeh3vPjSaP83x5t2mclFp9YSJBJCpQ7CZIsiw6neOLWq2NzETL/porK1XtXak3r72ku4FieP1PkZ8dvCzrOuF7Eiih+hj/f7vr9vPr5f9mtP+v9Pqeywj54z6wf+j+paPcaXgSuHHKxqee9MK/H0O98uD/OURoOvnHAx9Vv+Pvl++eDt/6nYtdP0MSO3QuEKYSEC5NgTbUs0Nq1Zc9atmL+jIxIs+GmvrVa3JXtMuE6V7QeJEvY8RmTbnMJc0F5LB67ncWL2xPijPWjaLj7ZtYurb4RZ91nl/h54N727HwdABOKwaxlel/KpmhTARSYkgvYkdocexrVe1doTevvaUCQsSN9f7WH9cFvZCdgRBQjLAQXewPijfteouRm/5jJ51LfusnnVwxtYYO7rU0f3M11K+rIzmhIlIygS5OX2m38AevOHXMWMGkZ8/NO7wa0HBsJhzSnJpfmG8odvy8nMpLl5cvz3RHLr20L9n/4RzDeuPy8JeyI4gaEiGL4Jy9b5qXjgWriyAu54iUBjb1xmuOw+WHBt7/4FOe1K+rp96wkREWqG1V7V2hN6+9pIpCxIn6n2MyMZeyI6iuSH6Bsf6QTlyzgNj4LRiWD8g8XlvDfCOe2BM/GO6HuyT8juTKISJiKRYrswvzJQFiePNNYzo1qlb1vVCdiRBQjJAJ+tUH5Sjz3nr8OZD2PqB3nFxfd6Z2pdOS/kt4tIewsxsipm9bWabzGxGuusREZH2kwkLEkf3Pg7oOQDz/wcwoMcAbplwS9b1QnYkzYVkAMMY3n94fVCOnNOtUzdO/ggu2JD4My5cD6P+GXtfp3BX+Lg/LJ+Y8nv1pjWEmVkn4A/AVOBE4BIzOzGdNYmISPvKhAWJI72PO6bvIFwSJlwSxpU4dty8Iyt7ITuSxiG5sZ6de3LLhFt47d9eq/9zipxzy4RbqHi64fT2fZ3hzjO8x2j3LAAccKALncLdMIyBPQdy29kz+P5nd8OBbkBq79Wb7on5pwObnHPvAJjZXKAAeCutVYmIiEjKtOaCnMg5PH0xjBxZv73nmnX8x0knwZtvwogv5h3+9VsPQtm2mMtQhCc6ujjvIpJU3qvXnEvtJLQGH252ETDFOTfNf30ZcIZz7vpGxxUDxQCDBg06de7cuSmvtT1dufCLVcPvn9KrxefX1NTQu7f+1RaL2iYxtU98apvE1D6JqX3iS0XbdNm1i8GPPMJ73/8+4R496reH9u/n6D/9ia0XX8znhx7Kyy9/wvjxh8bsmQ2HHcuX7+KrX+3XrrVNmjRptXMuL9a+dIewi4HJjULY6c65H8Q7Jy8vz61atSpVJSbFkBlP1T/fcvt5LT6/qqqKiRMntmNF2UNtk5jaJz61TWJqn8TUPvHletuYWdwQlu7hyK3Al6NeDwY+TFMtKdOa4CUiIiLZJd1XR74GDDezY8ysK/Bd4Ik01yQiIiKSdGntCXPO1ZnZ9cAioBNwn3PuzXTWJCIiIpIK6R6OxDn3NPB0uusQERERSaV0D0eKiIiI5CSFMBEREZE0UAgTERERSQOFMBEREZE0UAgTERERSQOFMBEREZE0UAgTERERSQOFMBEREZE0UAgTERERSQNzzqW7hhYxsx3Ae+muI80GADvTXUSGUtskpvaJT22TmNonMbVPfLneNkc75wbG2tHhQpiAma1yzuWlu45MpLZJTO0Tn9omMbVPYmqf+NQ28Wk4UkRERCQNFMJERERE0kAhrGMqT3cBGUxtk5jaJz61TWJqn8TUPvGpbeLQnDARERGRNFBPmIiIiEgaKIRlEDObYmZvm9kmM5sR55iJZrbGzN40sxdbcm5H18b22WJma/19q1JXdWo01zZmNt3/7mvMbJ2ZHTSzw4Kcmw3a2D65/rvT18wWmNkb/v+vioKemw3a2D5Z/bsDgdqnn5nNM7O/mdmrZjYi6Lk5wTmnnwz4AToBm4Fjga7AG8CJjY45FHgL+Bf/9eFBz+3oP21pH//5FmBAur9Hutqm0fH5wAv63Wm+ffS74wBuA37tPx8IfOwfq9+dBO2T7b87LWifWUCJ//x44Pmg5+bCj3rCMsfpwCbn3DvOuQPAXKCg0THfAx53zr0P4Jzb3oJzO7q2tE+2a+mf/yXAn1t5bkfUlvbJdkHaxgF9zMyA3nghoy7guR1dW9onFwRpnxOB5wGccxuAIWY2KOC5WU8hLHMcBfwj6vVWf1u044B+ZlZlZqvN7PIWnNvRtaV9wPsP5WJ/e3GSa021wH/+ZtYTmAI81tJzO7C2tA/od+f3wAnAh8Ba4AbnXDjguR1dW9oHsvt3B4K1zxvABQBmdjpwNDA44LlZr3O6C5B6FmNb40tXOwOnAucAPYAVZrYy4LkdXavbxzn3d2CCc+5DMzsceNbMNjjnlia35JRpyZ9/PrDMOfdxK87tqNrSPqDfncnAGuBrwFC8Nngp4LkdXavbxzn3Kdn9uwPB2ud24L/NbA1eSH0dr6cwF35/mqWesMyxFfhy1OvBeP+yanzMQufcXufcTmApcHLAczu6trQPzrkP/cftwDy8rvBs0ZI//+/ScKhNvzsNNW4f/e5AEd4wv3PObQLexZvbo98dT7z2yfbfHQjQPs65T51zRc650cDlePPm3g1ybk5I96Q0/Xg/eL047wDH8MUkxZMaHXMC3th6Z6AnsA4YEeTcjv7TxvbpBfTxj+kFLAempPs7pbJt/OP64s1X6dXSczvyTxvbJ+d/d4C7gVL/+SDgA7wbMut3J3H7ZPXvTgva51C+uFDh34AHg56bCz8ajswQzrk6M7seWIR31ch9zrk3zewaf/89zrn1ZrYQ+BsQBiqcc+sAYp2bli+SJG1pHzM7FpjnzZulM/C/zrmF6fkm7S9I2/iHfhtY7Jzb29y5qf0GydWW9sH7SzXXf3d+DtxvZmvxhpBucV5Ps/67k6B9sv2/OxC4fU4AHjSzg3hXr1+d6Nx0fI900or5IiIiImmgOWEiIiIiaaAQJiIiIpIGCmEiIiIiaaAQJiIiIpIGCmEiIiIiaaAQJiIiIpIGCmEiklTm2WJmzv85Id01dTRmVuq33f3prkVE2o9CmIgk21l4N+2NuCyZH2ZmXZL5/iIi7UUhTESS7fv+4+v+4/fMX0bczF70e3guiBxsZkv8bRf5r79qZlVm9omZfWhm95lZf3/fkKgetmvM7ENgsZl1MbNnzeyfZnbAzHaZ2RNm9uWoz/mqma01s71m9j9mNtd/nzujjvmWmb1qZp+a2Xtm9hsz6xnvi5rZCWY2z69zv5mtMbOjo2p9xMw+8r/LEjM7I+rc75nZW/55H5vZCr/GUqDEP+wKv8aq1v5hiEjm0G2LRCRpzKwbcJH/8sfAY3i9YmcBLwIP+s+/AzxuZoP8158AC8xsBN79QA8ATwJH4N0weYiZndPo434BzAf+ifcPzCPwbolSA4wD8vHuUTfFzA4FFuDd164KOBz4eqPaJwOVwE7/8UTgRuAwv4bG3/VLwEtAf7zA+RTeDZv7mdlO4AW8++Qt9d/zAuAFMxuFd+Pi+4HPgYeAbsApwFBgJfAKcAawHlgMbGra2iLS0SiEiUgynY8XdLbjha4n8YYjv++/fgT4HXC+mfXCC2wh4C/Ouc/M7Fq84PQ6sM3/GQtMAr4C1EZ91sXOuRciL8zs23jB60vAWmAMMNHMQlF1vQN8zTnnzGwNcHLU+/3Qf3wdqMYLQqfg9Ub9u3NuX6Pv+n28ALYGyHPOhf06OuMFrmP8z5vof948oBDvXnq/xLt/3na8IPmWc+4dM+vknDtoZmPxQtirzrn/SNTgItJxKISJSDJFhiIXOOfCfvC4DLjYzK53zn1qZvOBS/CC0b/6xz/gPw7xH8/wf6INA9ZFvV4WeWJmZwJL8IJNtG5AH+Ao//Xb7osb6K6nYQiLfPY3/J/6tweObfTZ4IUs8IJSOLLRv1Fx5L2iP2+D/3i0c67GD5wleD10mNlWvLaqQkSykuaEiUhSmFk/4Jv+y6vNzAGP+6/74vVSgTckCfAD4KvARufcCn/bFv/xDuecRX6AY51zT0Z/nnPus6iXF+IFsIVALxoGOAM+8J8Pi9p+fKOvEPnsHzb67KHOucYBDOBd//E0v7fN+zCvJyzyXsdF5sPh9eQBvOc/PuCcOwo4ErgBGAz81N930H/Uf7NFsoh6wkQkWf4VbyjxU7xeqYgTgeF4vTyPAs8CHwET/P3/E3VsOfBvwA1mdizeXKoTgPEkDiTb/Mcz8IY7z260/0lgFzDczJ4D6oBRjY75PV6InGlm44H9/jH9+aLXK9qfgBl4w56vmtlq4FRgGt78sC14c7yW+HPEvu2/532Rmv0J9x8CI/1tu/zHf/iPU83sd0CVc+6xBN9fRDoA/atKRJLlUv/xj865wsgPXqgCL1D0d84dxJuMDuCICmHOuTfwJswvxZuw/1284cTbm/ns3+PNrermn/eL6J3OuV14PXHr8Cbt7wCe8Hd/5h/zDF5QegMvjF0AhIH/jvWBzrl/Amf6n3sUcDneP3Q/cc7tBc7BuzDheP87vQic45yLTLJ/Fm/O2dXASXjB7cf+vkfwLjLoBVyPNydORDo4+2J6gohI7jCzvs653f7zEPAmXkCa5py7N63FiUhOUAgTkZxkZo/gDUOuxxuu/BreUOBJfk+ZiEhSaThSRHLVX/EuBPgJcBzwMHC2ApiIpIp6wkRERETSQD1hIiIiImmgECYiIiKSBgphIiIiImmgECYiIiKSBgphIiIiImmgECYiIiKSBv8/gcwGJob4TQAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "file_name = \"../sim_paths_prob_curve9.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "    M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "utils.qc_plot(Ex,fluid_sol,average_queue_B,average_cost_B,average_queue_M,average_cost_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.         1.         1.         1.41421356]\n",
      " [1.         0.         1.41421356 1.        ]\n",
      " [1.         1.41421356 0.         1.        ]\n",
      " [1.41421356 1.         1.         0.        ]] [0.5 0.1 0.1 0.3] [0.01 0.2  0.25 0.54]\n"
     ]
    }
   ],
   "source": [
    "print(W, pmf_cust, pmf_serv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 0.92\n",
      "Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (win64)\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i7-8550U CPU @ 1.80GHz, instruction set [SSE2|AVX|AVX2]\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 8 rows, 16 columns and 32 nonzeros\n",
      "Model fingerprint: 0xdfb4e2e3\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [1e+00, 1e+00]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [1e-02, 5e-01]\n",
      "Presolve removed 1 rows and 1 columns\n",
      "Presolve time: 0.02s\n",
      "Presolved: 7 rows, 15 columns, 30 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    5.0412536e-01   4.069200e-01   0.000000e+00      0s\n",
      "       3    5.8941125e-01   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 3 iterations and 0.02 seconds (0.00 work units)\n",
      "Optimal objective  5.894112550e-01\n",
      "Objective Value: 0.59\n",
      "x:  [[0.01 0.1  0.15 0.24]\n",
      " [0.   0.1  0.   0.  ]\n",
      " [0.   0.   0.1  0.  ]\n",
      " [0.   0.   0.   0.3 ]]\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 = \"../sim_paths_prob_curve9.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "    M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "utils.qc_plot(Ex,fluid_sol,average_queue_B,average_cost_B,average_queue_M,average_cost_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def minmax(average_cost_M, average_queue_M, average_cost_B, average_queue_B):\n",
    "    len_M = len(average_cost_M)\n",
    "    len_B = len(average_cost_B)\n",
    "    max_val = 0\n",
    "    for i in range(len_M):\n",
    "        shifted = np.abs(average_queue_B - average_queue_M[i])\n",
    "        idx = shifted.argmin()\n",
    "        if(max_val < average_cost_B[idx] - average_cost_M[i]):\n",
    "            max_val = average_cost_B[idx] - average_cost_M[i]\n",
    "            (cM,qM,cB,qB)= ( average_cost_M[i], average_queue_M[i], average_cost_B[idx], average_queue_B[idx] )\n",
    "    return cM, qM, cB, qB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6255789606480454 2.6889 0.7191472939388639 2.5\n"
     ]
    }
   ],
   "source": [
    "cM, qM, cB, qB = minmax(average_cost_M, average_queue_M, average_cost_B, average_queue_B)\n",
    "print(cM, qM, cB, qB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(Ex, fluid_sol, avg_Q_B, avg_C_B, avg_Q_M, avg_C_M, cM, qM, cB, qB):\n",
    "    plt.figure( figsize=(10,6) ) \n",
    "\n",
    "    # C = 0 Case\n",
    "    # C = Inf/Fluid Case\n",
    "    ylim = max( max( avg_Q_B ), max( avg_Q_M ) )\n",
    "    plt.plot([fluid_sol['Cost'],fluid_sol['Cost']],[0,ylim],linewidth = 3)\n",
    "    # Batching data\n",
    "    plt.plot(avg_C_B,avg_Q_B,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "    # Max Weight data\n",
    "    plt.plot(avg_C_M, avg_Q_M,'go',markersize = 8)\n",
    "    plt.plot([Ex],[1],'r*',markersize = 12, markeredgewidth=3)\n",
    "    # Batching data\n",
    "    plt.plot([cB],[qB],'rx',markersize = 12, markeredgewidth=3)\n",
    "    # Max Weight data\n",
    "    plt.plot([cM],[qM],'ro',markersize = 10)\n",
    "\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.legend(['Fluid', 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "    # plt.legend([ 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "    plt.grid(True)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "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(Ex,fluid_sol,average_queue_B,average_cost_B,average_queue_M,average_cost_M, cM, qM, cB, qB)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot all 14 manually cuz why not\n",
    "10k steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 1.07\n",
      "Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (win64)\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i7-8550U CPU @ 1.80GHz, instruction set [SSE2|AVX|AVX2]\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 8 rows, 16 columns and 32 nonzeros\n",
      "Model fingerprint: 0xc225e780\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [1e+00, 1e+00]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [1e-02, 7e-01]\n",
      "Presolve removed 1 rows and 1 columns\n",
      "Presolve time: 0.01s\n",
      "Presolved: 7 rows, 15 columns, 30 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    7.8696808e-01   4.069200e-01   0.000000e+00      0s\n",
      "       3    8.7225397e-01   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 3 iterations and 0.01 seconds (0.00 work units)\n",
      "Optimal objective  8.722539674e-01\n",
      "Objective Value: 0.87\n",
      "x:  [[0.01 0.1  0.15 0.44]\n",
      " [0.   0.1  0.   0.  ]\n",
      " [0.   0.   0.1  0.  ]\n",
      " [0.   0.   0.   0.1 ]]\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 = \"../sim_paths_prob_curve13.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "    M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "cM, qM, cB, qB = minmax(average_cost_M, average_queue_M, average_cost_B, average_queue_B)\n",
    "plot(Ex,fluid_sol,average_queue_B,average_cost_B,average_queue_M,average_cost_M, cM, qM, cB, qB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "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(Ex,fluid_sol,average_queue_B,average_cost_B,average_queue_M,average_cost_M, cM, qM, cB, qB)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Acceptable (in terms of minmax working) plots for all 14 (10k steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The actual plot we need: gap vs probab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs = np.arange(0.05,0.75,0.05)\n",
    "i = 0\n",
    "zero_probs = np.zeros(probs.size)\n",
    "gaps = np.zeros(probs.size)\n",
    "for p in probs:\n",
    "    file_name = \"../sim_paths_prob_curve\" + str(i) + '.pkl'\n",
    "    with open(file_name,'rb') as f:\n",
    "        M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "    Q_paths_M = M_res[\"Q_paths\"]\n",
    "    C_paths_M = M_res[\"C_paths\"]\n",
    "    Q_paths_B = B_res[\"Q_paths\"]\n",
    "    C_paths_B = B_res[\"C_paths\"]\n",
    "    zero_probs[i]  = np.dot(pmf_cust,pmf_serv)\n",
    "    # zero_probs[i] = round (np.sum(np.outer(pmf_cust,pmf_serv)*W), 3) \n",
    "    (average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "    (average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "    # [Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "    cM, qM, cB, qB = minmax(average_cost_M, average_queue_M, average_cost_B, average_queue_B)  \n",
    "    gaps[i] = cB - cM\n",
    "    i = i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f94edc9160>]"
      ]
     },
     "execution_count": 8,
     "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(zero_probs,gaps, 'x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.4505, 0.424 , 0.3975, 0.371 , 0.3445, 0.318 , 0.2915, 0.265 ,\n",
       "       0.2385, 0.212 , 0.1855, 0.159 , 0.1325, 0.106 ])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zero_probs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.13179941, 0.14484083, 0.13211606, 0.13743616, 0.13421139,\n",
       "       0.11184234, 0.1118254 , 0.10549941, 0.0962796 , 0.09356833,\n",
       "       0.0648127 , 0.04037473, 0.03545665, 0.05170681])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "i = 0\n",
    "zero_probs = np.zeros(13)\n",
    "gaps = np.zeros(13)\n",
    "for j in range(9):\n",
    "    print(i)\n",
    "    file_name = \"../probab_curve_50k/sim_paths_prob_curve\" + str(i) + '.pkl'\n",
    "    with open(file_name,'rb') as f:\n",
    "        M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "    Q_paths_M = M_res[\"Q_paths\"]\n",
    "    C_paths_M = M_res[\"C_paths\"]\n",
    "    Q_paths_B = B_res[\"Q_paths\"]\n",
    "    C_paths_B = B_res[\"C_paths\"]\n",
    "    zero_probs[i]  = np.dot(pmf_cust,pmf_serv)\n",
    "    # zero_probs[i] = round (np.sum(np.outer(pmf_cust,pmf_serv)*W), 3) \n",
    "    (average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "    (average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "    # [Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "    cM, qM, cB, qB = minmax(average_cost_M, average_queue_M, average_cost_B, average_queue_B)  \n",
    "    gaps[i] = cB - cM\n",
    "    i = i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n",
      "10\n",
      "11\n",
      "12\n"
     ]
    }
   ],
   "source": [
    "for j in range(4):\n",
    "    print(i)\n",
    "    file_name = \"../probab_curve_50k/sp_prob_curve_right_\" + str(j) + '.pkl'\n",
    "    with open(file_name,'rb') as f:\n",
    "        M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "    Q_paths_M = M_res[\"Q_paths\"]\n",
    "    C_paths_M = M_res[\"C_paths\"]\n",
    "    Q_paths_B = B_res[\"Q_paths\"]\n",
    "    C_paths_B = B_res[\"C_paths\"]\n",
    "    zero_probs[i]  = np.dot(pmf_cust,pmf_serv)\n",
    "    # zero_probs[i] = round (np.sum(np.outer(pmf_cust,pmf_serv)*W), 3) \n",
    "    (average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "    (average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "    # [Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "    cM, qM, cB, qB = minmax(average_cost_M, average_queue_M, average_cost_B, average_queue_B)  \n",
    "    gaps[i] = cB - cM\n",
    "    i = i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(zero_probs,gaps,linewidth=4)\n",
    "plt.plot(zero_probs,gaps,'rx', markersize = 10, markeredgewidth=2)\n",
    "plt.ylabel(\"Cost Gap\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Probability of arrival with zero cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"Maxweight vs Batching for different Probabilities\", weight='bold',fontsize=15)\n",
    "plt.savefig('../../plots_stash/cost-gap.jpg', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.4505, 0.424 , 0.3975, 0.371 , 0.3445, 0.318 , 0.2915, 0.265 ,\n",
       "       0.2385, 0.4745, 0.5635, 0.6525, 0.7415])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zero_probs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.13315724, 0.13622282, 0.13534796, 0.1364185 , 0.1282509 ,\n",
       "       0.12316989, 0.11224113, 0.0956178 , 0.08422555, 0.03976965,\n",
       "       0.04919262, 0.06533033, 0.08583871])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 0.433\n",
      "Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (win64)\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i7-8550U CPU @ 1.80GHz, instruction set [SSE2|AVX|AVX2]\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 8 rows, 16 columns and 32 nonzeros\n",
      "Model fingerprint: 0xb3b41879\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [1e+00, 1e+00]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [3e-02, 9e-01]\n",
      "Presolve removed 2 rows and 5 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 6 rows, 11 columns, 22 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    2.1970563e-01   2.000000e-01   0.000000e+00      0s\n",
      "       4    2.9041631e-01   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 4 iterations and 0.02 seconds (0.00 work units)\n",
      "Optimal objective  2.904163056e-01\n",
      "Objective Value: 0.29\n",
      "x:  [[0.7   0.    0.    0.   ]\n",
      " [0.025 0.025 0.    0.   ]\n",
      " [0.025 0.    0.025 0.   ]\n",
      " [0.17  0.    0.    0.03 ]]\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 = \"../probab_curve_50k/sp_prob_curve_right_2.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "    M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "cM, qM, cB, qB = minmax(average_cost_M, average_queue_M, average_cost_B, average_queue_B)\n",
    "plot(Ex,fluid_sol,average_queue_B,average_cost_B,average_queue_M,average_cost_M, cM, qM, cB, qB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 0.582\n",
      "Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (win64)\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i7-8550U CPU @ 1.80GHz, instruction set [SSE2|AVX|AVX2]\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 8 rows, 16 columns and 32 nonzeros\n",
      "Model fingerprint: 0x1aec452b\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [1e+00, 1e+00]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [1e-02, 8e-01]\n",
      "Presolve removed 1 rows and 1 columns\n",
      "Presolve time: 0.01s\n",
      "Presolved: 7 rows, 15 columns, 30 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    0.0000000e+00   5.389900e-01   0.000000e+00      0s\n",
      "       6    2.5000000e-01   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 6 iterations and 0.01 seconds (0.00 work units)\n",
      "Optimal objective  2.500000000e-01\n",
      "Objective Value: 0.25\n",
      "x:  [[0.01 0.   0.04 0.  ]\n",
      " [0.   0.1  0.   0.  ]\n",
      " [0.   0.   0.1  0.  ]\n",
      " [0.   0.1  0.11 0.54]]\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 = \"../probab_curve_50k/sim_paths_prob_curve\" + str(0) + '.pkl'\n",
    "with open(file_name,'rb') as f:\n",
    "    M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "cM, qM, cB, qB = minmax(average_cost_M, average_queue_M, average_cost_B, average_queue_B)\n",
    "plot(Ex,fluid_sol,average_queue_B,average_cost_B,average_queue_M,average_cost_M, cM, qM, cB, qB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": 4
}