single-path-run.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 as gp\n",
    "from gurobipy import GRB\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)\n",
    "    \n",
    "def generate_weights(N_grid, is_spatial = 1):\n",
    "    Weights = np.zeros(shape=(N_grid,N_grid))\n",
    "    if is_spatial:\n",
    "        X = np.arange(0.5,N_grid,1)\n",
    "        Y = np.arange(0.5,N_grid,1)\n",
    "        cell_locs = []\n",
    "        for i in range(N_grid):\n",
    "            for j in range(N_grid):\n",
    "                cell_locs.append([X[i],Y[j]])\n",
    "        N_cells = N_grid*N_grid\n",
    "        Weights = np.zeros(shape=(N_cells,N_cells))\n",
    "\n",
    "        for i in range(N_cells):\n",
    "            for j in range(N_cells):\n",
    "                Weights[i,j] = np.sqrt((cell_locs[i][0] - cell_locs[j][0])**2 + (cell_locs[i][1] - cell_locs[j][1])**2)\n",
    "        print(Weights)\n",
    "    else:\n",
    "        rand_weights = np.random.rand(N_grid, N_grid)\n",
    "        N_cells = N_grid*N_grid\n",
    "        for counter in range(N_cells):\n",
    "            for i in range(N_grid):\n",
    "                for j in range(N_grid):\n",
    "                    for k in range(N_grid):\n",
    "                        rand_weights[i,j] = min(rand_weights[i,j],rand_weights[i,k] + rand_weights[k,j] )\n",
    "        print(rand_weights)\n",
    "        Weights = rand_weights\n",
    "    return(Weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 0.854\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-03\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: 0x1e0e9b1b\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-01, 3e-01]\n",
      "Presolve time: 0.05s\n",
      "Presolved: 8 rows, 16 columns, 32 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    0.0000000e+00   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 0 iterations and 0.17 seconds (0.00 work units)\n",
      "Optimal objective  0.000000000e+00\n",
      "Objective Value: 0.00\n",
      "x:  [[0.25 0.   0.   0.  ]\n",
      " [0.   0.25 0.   0.  ]\n",
      " [0.   0.   0.25 0.  ]\n",
      " [0.   0.   0.   0.25]]\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_spatial_uniform_4.pkl'\n",
    "plot_from_sim_paths(file_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_values = alpha_values = np.asarray( [0, 0.2, 0.25, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.675, 0.7, 0.725, 0.75, 0.8, 0.825, 0.85, 0.875,  0.9, 0.925, 0.95] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21,)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_values.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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.        ]]\n",
      "[0.25 0.25 0.25 0.25] [0.25 0.25 0.25 0.25]\n"
     ]
    }
   ],
   "source": [
    "N = 2\n",
    "\n",
    "is_spatial = 1\n",
    "W = generate_weights(N,is_spatial)\n",
    "\n",
    "time_steps = 10000\n",
    "\n",
    "\n",
    "if is_spatial:\n",
    "    N = N*N\n",
    "    \n",
    "pmf_cust = np.ones(N)*(1/N)\n",
    "pmf_serv = np.ones(N)*(1/N)\n",
    "print(pmf_cust,pmf_serv)\n",
    "\n",
    "arrival_ids = np.arange(0,N,1)\n",
    "cust_process = rv_discrete(name='cust_arr', values=(arrival_ids, pmf_cust))\n",
    "serv_process = rv_discrete(name='serv_arr', values=(arrival_ids, pmf_serv))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "cust_arrivals = cust_process.rvs( size = time_steps )\n",
    "serv_arrivals = serv_process.rvs( size = time_steps )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.9\n",
    "Q_mw = []\n",
    "Qtilde_mw = []\n",
    "Mstars_mw = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "q = np.zeros(N)\n",
    "q[cust_arrivals[0]] = 1\n",
    "qtilde = np.zeros(N)\n",
    "qtilde[serv_arrivals[0]] = 1\n",
    "\n",
    "cost_path_mw = [0]\n",
    "total_queue = []\n",
    "total_queue.append(np.sum(q))\n",
    "\n",
    "for k in range(1,time_steps):\n",
    "    # Maxweight Matching\n",
    "    M = cp.Variable((N,N),integer=True)\n",
    "    constraints = []\n",
    "    for i in range(N):\n",
    "        constraints.append( cp.sum(M[i,:]) <= q[i] )\n",
    "        constraints.append( cp.sum(M[:,i]) <= qtilde[i] )\n",
    "    constraints.append( M[:,:]>=0 )\n",
    "\n",
    "    objective = cp.Maximize( cp.sum( (1-alpha)*( cp.multiply( q, cp.sum(M, axis=1) ) + cp.multiply( qtilde, cp.sum(M, axis=0) ) ) )\n",
    "                            - cp.sum( alpha*cp.multiply( W,M  ) ) )\n",
    "    problem  = cp.Problem(objective, constraints)         \n",
    "    problem.solve(solver=\"GLPK_MI\")\n",
    "    # print(\"q=\",q)\n",
    "    # print(\"qtilde=\",qtilde)\n",
    "    # print(problem)\n",
    "\n",
    "\n",
    "    # Check arrivals\n",
    "    a = np.zeros(N)\n",
    "    atilde = np.zeros(N)\n",
    "\n",
    "    a[cust_arrivals[k]] = 1\n",
    "    atilde[serv_arrivals[k]] = 1\n",
    "    # State Update\n",
    "    Mstar = M.value\n",
    "    # print(\"M=\", Mstar)\n",
    "    matching_cost = np.sum(np.multiply(Mstar,W)) \n",
    "    q = q + a - np.sum(Mstar, 1)\n",
    "    qtilde = qtilde + atilde - np.sum(Mstar,0)\n",
    "    Q_mw.append(q)\n",
    "    Qtilde_mw.append(qtilde)\n",
    "    Mstars_mw.append(Mstar)\n",
    "    total_queue.append(np.sum(q))\n",
    "    cost_path_mw.append(matching_cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.11806467529817258\n",
      "4.7633\n"
     ]
    }
   ],
   "source": [
    "average_cost_mw = np.average(cost_path_mw)\n",
    "print(average_cost_mw)\n",
    "average_queue_mw = np.average(total_queue)\n",
    "print(average_queue_mw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 9\n",
    "Q_b = []\n",
    "Qtilde_b = []\n",
    "Mstars_b = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = np.zeros(N)\n",
    "q[cust_arrivals[0]] = 1\n",
    "qtilde = np.zeros(N)\n",
    "qtilde[serv_arrivals[0]] = 1\n",
    "\n",
    "running_cost = 0\n",
    "cost_path = [0]\n",
    "total_queue = [] \n",
    "total_queue.append(np.sum(q))\n",
    "\n",
    "for k in range(1,time_steps):\n",
    "    # Check arrivals\n",
    "    a = np.zeros(N)\n",
    "    atilde = np.zeros(N)\n",
    "\n",
    "    a[cust_arrivals[k]] = 1\n",
    "    atilde[serv_arrivals[k]] = 1\n",
    "    # State Update\n",
    "    Mstar = np.zeros(shape=(N,N))\n",
    "\n",
    "    # Matching is done every T time steps \n",
    "    if(k%T==0):\n",
    "        constraints = []\n",
    "        M = cp.Variable((N,N),integer=True)\n",
    "        constraints = []\n",
    "        for i in range(N):\n",
    "            constraints.append( cp.sum(M[i,:]) == q[i] )\n",
    "            constraints.append( cp.sum(M[:,i]) == qtilde[i] )\n",
    "        constraints.append( M[:,:]>=0 )\n",
    "\n",
    "        objective = cp.Minimize( cp.sum( cp.multiply( W, M ) ) )\n",
    "        problem  = cp.Problem(objective, constraints)         \n",
    "        problem.solve(solver=\"GLPK_MI\")\n",
    "        Mstar = M.value\n",
    "\n",
    "    running_cost += np.sum(np.multiply(Mstar,W))\n",
    "    q = q + a - np.sum(Mstar, 1)\n",
    "    if q[0] < 0:\n",
    "        print(q-a+np.sum(Mstar, 1))\n",
    "        print(Mstar, k)\n",
    "        print(constraints)\n",
    "        break\n",
    "    qtilde = qtilde + atilde - np.sum(Mstar,0)\n",
    "    Q_b.append(q)\n",
    "    Qtilde_b.append(qtilde)\n",
    "    Mstars_b.append(Mstar)\n",
    "    total_queue.append(np.sum(q))\n",
    "    cost_path.append(np.sum(np.multiply(Mstar,W)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.34715129855222066\n",
      "4.9996\n"
     ]
    }
   ],
   "source": [
    "average_cost_b = np.average(cost_path)\n",
    "print(average_cost_b)\n",
    "average_queue_b = np.average(total_queue)\n",
    "print(average_queue_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"../single_path_run.pkl\", 'wb') as f:\n",
    "    pickle.dump([Q_mw, Qtilde_mw, Mstars_mw, Q_b, Qtilde_b, Mstars_b ],f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"../single_path_run.pkl\", 'rb') as f:\n",
    "    Q_mw, Qtilde_mw, Mstars_mw, Q_b, Qtilde_b, Mstars_b = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_mw = np.asarray(Q_mw,dtype='int64')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_mw = np.asarray(Q_mw)\n",
    "Qtilde_mw = np.asarray(Qtilde_mw)\n",
    "Mstars_mw = np.asarray(Mstars_mw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_b = np.asarray(Q_b)\n",
    "Qtilde_b = np.asarray(Qtilde_b)\n",
    "Mstars_b = np.asarray(Mstars_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 0.854\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: 0x1e0e9b1b\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-01, 3e-01]\n",
      "Presolve time: 0.01s\n",
      "Presolved: 8 rows, 16 columns, 32 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    0.0000000e+00   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 0 iterations and 0.02 seconds (0.00 work units)\n",
      "Optimal objective  0.000000000e+00\n",
      "Objective Value: 0.00\n",
      "x:  [[0.25 0.   0.   0.  ]\n",
      " [0.   0.25 0.   0.  ]\n",
      " [0.   0.   0.25 0.  ]\n",
      " [0.   0.   0.   0.25]]\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_spatial_uniform_4.pkl'\n",
    "plot_from_sim_paths(file_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "Mstars_b = np.asarray(Mstars_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(12,6) )\n",
    "plot_length = 200\n",
    "plt.step(np.arange(0,plot_length,1), Q_mw[:plot_length,0],linewidth=2)\n",
    "plt.step(np.arange(0,plot_length,1), Qtilde_mw[:plot_length,0],linewidth=2)\n",
    "plt.ylabel(\"Queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Time\", weight='bold',fontsize=12)\n",
    "plt.title(\"Queue lengths vs time - Maxweight\", weight='bold',fontsize=15)\n",
    "plt.legend(['Customer Queue length', 'Server Queue length'])\n",
    "plt.savefig('../../plots_stash/single-path-mw.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H3nvvzVVXXdWxbrvJkydz3HHHATB37lwOO+wwRo4cyciRI7n77rsBaGtr48ILL+xYZ8iQIcyePbtsfKVMmTKFD3/4wwwfPpwjjjiCRYsWAdkvMp9zzjkMHz6cXXfdlccff7wjpn333Zfhw4dz4oknss022zBv3jzOOOMMnn76aYYNG8Zpp50GwKJFizj88MPZcccdOeaYY0gplY2lEvW86sUPgT+llA6PiHWA99axbUmStBpoOePGmtQ7+/wDSj736KOPMmLEiKrqe/XVV7nuuut4/PHHiQjmz5/PRhttxIQJEzjwwAM5/PDDARg6dCg/+tGPGD16NGeffTbf+MY3+MEPfgDAOuusw5133skPf/hDDj74YKZNm8Ymm2zC9ttvz6mnnsrLL7/MNddcw913302fPn34/Oc/z1VXXcW//Mu/8MYbbzBkyBDOPffcFeJ6/fXXeeONN9h+++1XKG9tbe3yTPcpp5zCqaeeyp577smzzz7L+PHjmTVrVsnlZ82aVTK+PPPmzeO8887j5ptvZr311uM73/kO3//+9zn77LMBGDBgANOnT+fHP/4xF154IT/72c/4xje+wT777MOZZ57Jn/70JyZOnAjA+eefz6OPPsqMGTOAbOrFQw89xGOPPcYWW2zBHnvswd13382ee+5Zdpu7UpdEOSI2APYGjgNIKb0DvFOPtiWpW646Ap6a0vVyg8bBMb+tfTySmsoGG2xAv379+MxnPsMBBxyQOz92wYIFzJ8/n9GjRwNw7LHHcsQRR3Q8P2HCBAB23XVXdtllFzbffHMAtttuO/7xj39w1113MW3aNEaOHAnAW2+9xfve9z4AevXqxWGHHVZxvJWcXb355ptXSKZff/11Fi5cWHL5W265pWR8ee677z5mzpzJHnvsAcA777zDhz+8fILBoYceCsCIESO49tprAbjrrru47rrrANhvv/3YeOONS9Y/atQottxySyD7RGD27NmrR6IMbAfMBS6PiN2AacApKaUVJstExAnACQBbb711nUKTpByVJMnVLCepIuXO/NbKLrvswuTJk3Of6927N8uWLet43H55sd69e/PAAw9wyy23cPXVV3PxxRdz6623VtVu3759AXjPe97Tcb/98dKlS0kpceyxx/Kf//mfK63br18/evXqtVL5BhtswHrrrcczzzzDdttt11E+ffp0xo0bB6x49Yfiy6UtW7aMe++9l3XXXbeiPigXX56UEvvuuy+//vWvc59v74NevXqxdOnSjnUqVdyHxXWsinrNUe4NDAd+klLaHXgDOKPzQimliSml1pRS68CBA+sUmiSV0bag9E3SGmGfffZh8eLF/PSnP+0oe/DBB7njjjvYZpttmDlzJosXL2bBggXccsstQDYfdsGCBey///784Ac/6JgCsP7663echd1www3ZeOON+fOf/wzAL3/5y46zy5X4yEc+wuTJk3n55ZeBbLrH3//+9y7XO+200/jSl77EW2+9BWRnih977LGO6SCbbbYZs2bNYtmyZR1nayGby3zxxRd3PG7fppaWFqZPnw5kCfff/va3bsX3oQ99iLvvvpu//vWvALz55ptdXllkzz335De/+Q2QzW9un+Nd3M+1VK8zynOAOSml+wuPJ5OTKEuSJNVbRHDdddfx5S9/mfPPP59+/frR0tLCD37wA7baais+8YlPMHToUAYNGsTuu+8OwMKFCzn44IN5++23SSnxX//1XwAcddRRfPazn+Wiiy5i8uTJXHHFFZx00km8+eabbLfddlx++eUVx7Xzzjtz3nnnMW7cOJYtW0afPn245JJL2Gabbcqu98UvfpH58+czdOhQlixZwjvvvMOjjz5Kv379gGx+74EHHshWW23FkCFDOr5Qd9FFF3HyySczdOhQli5dyt57782ll17KYYcdxi9+8QuGDRvGyJEj2WGHHboV38CBA5k0aRJHH300ixcvBuC8887rqC/POeecw9FHH80111zD6NGj2XzzzVl//fXp27cve+yxB0OGDOFjH/sYBxxQm08ioie+EVhRQxF/Bj6TUnoiItqA9VJKp5VavrW1NfX0NfckqWJtGxb+ljlzXMkykro0a9Ysdtppp0aHsUZatGgRhxxyCCNHjuTb3/52o8Op2uLFi+nVqxe9e/fm3nvv5XOf+1zHme7uyBtrETEtpdSat3w9r3rxReCqwhUvngGOr2PbkiRJa53+/ftz0003NTqMbnv22Wf5xCc+wbJly1hnnXVWmB5TD3VLlFNKM4DcbF2SJEnqbNCgQTz00EMNa99f5pMkSZJymChLkiRJOUyUJUmSpBwmypIkSVIOE2VJkrTW+9a3vsUuu+zC0KFDGTZsGPfff3/XK9XQXXfdxahRo9hxxx0ZPHgwl1xyScNimTRpEl/4whdqUu/zzz/f8bilpYV58+b1eDurop6Xh5MkSWo69957LzfccAPTp0+nb9++zJs3j3feeafi9ZcuXUrv3t1PqTqv/+KLL/LJT36S3//+9wwfPpx58+Yxfvx4tthiCw455JBut9NsJk2axJAhQ9hiiy0aHUpJnlGWJElrtRdeeIEBAwbQt29fAAYMGNCRvE2bNo3Ro0czYsQIxo8fzwsvvADAmDFj+NrXvsbo0aP51re+RUtLC8uWLQOyn2beaqutWLJkCU8//TT77bcfI0aMYK+99uLxxx8H4LjjjuMrX/kKY8eO5fTTT18hnksuuYTjjjuO4cOHd8Tz3e9+lwsuuKBj3cmTJ3cs379//477F1xwASNHjmTo0KGcc845AMyePZshQ4Z0LHPhhRfS1tYGUDK+UubOncthhx3GyJEjGTlyJHfffTcAbW1tfPrTn2bMmDFst912XHTRRR3rfPOb32THHXdk33335eijj+bCCy9k8uTJTJ06lWOOOYZhw4Z1/Nz2j370I4YPH86uu+7aZSz14BllSZLUPNp/8bLH6y39C5rjxo3j3HPPZYcdduCjH/0oRx55JKNHj2bJkiV88Ytf5Prrr2fgwIFcc801nHXWWVx22WUAzJ8/nzvuuAOA6dOnc8cddzB27Fj++Mc/Mn78ePr06cMJJ5zApZdeyqBBg7j//vv5/Oc/z6233grAk08+yc0330yvXr1WiOexxx7j2GOPXaGstbWVmTNnlt3EKVOm8NRTT/HAAw+QUmLChAnceeedbL311iXXKRdfnlNOOYVTTz2VPffck2effZbx48cza9YsAB5//HFuu+02Fi5cyODBg/nc5z7Hww8/zO9+9zseeughli5dyvDhwxkxYgSHH344F198MRdeeCGtrct/ZmPAgAFMnz6dH//4x1x44YX87Gc/K7vNtWaiLEmS1mr9+/dn2rRp/PnPf+a2227jyCOP5Pzzz6e1tZVHH32UfffdF4B3332XzTffvGO9I488coX711xzDWPHjuXqq6/m85//PIsWLeKee+7hiCOO6Fhu8eLFHfePOOKIlZJkgJQSEVH1dkyZMoUpU6aw++67A9nPVz/11FMlE+Wu4stz8803r5Cwv/766yxcuBCAAw44gL59+9K3b1/e97738dJLL3HXXXdx8MEHs+666wJw0EEHla3/0EMPBWDEiBFce+21XWxx7ZkoS5Kk5lHmzG8t9erVizFjxjBmzBh23XVXrrjiCkaMGMEuu+zCvffem7vOeuut13F/woQJnHnmmbz66qtMmzaNffbZhzfeeIONNtqIGTNmdLl+sV122YWpU6cyYcKEjrJp06Z1nHnt3bt3xzSPlFLHfOqUEmeeeSYnnnjiCvXNmTOnY3mAt99+G4Bly5aVjS/PsmXLuPfeezsS32LtU1cg68+lS5eSUqq47uI62tdvNOcoS5KktdoTTzzBU0891fF4xowZbLPNNgwePJi5c+d2JMpLlizhsccey62jf//+jBo1ilNOOYUDDzyQXr16scEGG7Dtttvy29/+FsgS2YcffrjLeE4++WQmTZrUkcC+8sornHXWWfzHf/wHkF0dYtq0aQBcf/31LFmyBIDx48dz2WWXsWjRIgCee+45Xn75ZTbbbDNefvllXnnlFRYvXswNN9wA0K34xo0bx8UXX7xCX5Wz55578sc//pG3336bRYsWceONN3Y8t/7663ecjW5WJsqSJGmttmjRIo499lh23nlnhg4dysyZM2lra2OdddZh8uTJnH766ey2224MGzaMe+65p2Q9Rx55JFdeeeUKUzKuuuoqfv7zn7Pbbruxyy67cP3113cZz+abb86VV17JCSecwODBg9liiy340pe+xOjRowH47Gc/yx133MGoUaO4//77O85Mjxs3jk9+8pN8+MMfZtddd+Xwww9n4cKF9OnTh7PPPpsPfvCDHHjggey4447dju+iiy5i6tSpDB06lJ133plLL7207PIjR45kwoQJ7Lbbbhx66KG0tray4YbZPPTjjjuOk046aYUv8zWbqPaUeL20tramqVOnNjoMSWur9i8UlfsYuJJlJHVp1qxZ7LTTTo0Oo2ldcsklXHrppdx5551svPHGjQ6naosWLaJ///68+eab7L333kycOLHjih71ljfWImJaSqk1b3nPKEuSJDWxk08+mb/85S+rZZIM2ZU1hg0bxvDhwznssMMaliR3h1/mkyRJUs386le/anQI3eYZZUmSJCmHibIkSWq4Zv3OlNYc3RljJsqSJKmh+vXrxyuvvGKyrJpJKfHKK6/Qr1+/qtZzjrIkSWqoLbfckjlz5jB37txGh6I1WL9+/dhyyy2rWsdEWZIkNVSfPn3YdtttGx2GtBKnXkiSJEk5TJQlSZKkHCbKkiRJUg4TZUmSJCmHibIkSZKUw0RZkiRJymGiLEmSJOUwUZYkSZJymChLkiRJOUyUJUmSpBwmypIkSVIOE2VJkiQph4myJEmSlMNEWZIkScphoixJkiTlMFGWJEmScpgoS5IkSTlMlCVJkqQcJsqSJElSDhNlSZIkKUfvejUUEbOBhcC7wNKUUmu92pYkSZKqVbdEuWBsSmlenduUJEmSqubUC0mSJClHPc8oJ2BKRCTgv1NKE+vYtiR17aoj4KkpjY5CktQk6pko75FSej4i3gfcFBGPp5TuLF4gIk4ATgDYeuut6xiaJLFykjxoXGPikCQ1hbolyiml5wt/X46I64BRwJ2dlpkITARobW1N9YpNklbQtqDREUiSmkBd5ihHxHoRsX77fWAc8Gg92pYkSZK6o15nlDcDrouI9jZ/lVL6U53aliRJkqpWl0Q5pfQMsFs92pIkSZJ6gpeHkyRJknKYKEuSJEk5TJQlSZKkHCbKkiRJUg4TZUmSJCmHibIkSZKUw0RZkiRJymGiLEmSJOUwUZYkSZJymChLkiRJOUyUJUmSpBwmypIkSVIOE2VJkiQph4myJEmSlMNEWZIkScphoixJkiTlMFGWJEmScpgoS5IkSTlMlCVJkqQcJsqSJElSDhNlSZIkKYeJsiRJkpTDRFmSJEnKYaIsSZIk5TBRliRJknKYKEuSJEk5TJQlSZKkHCbKkiRJUg4TZUmSJCmHibIkSZKUw0RZkiRJymGiLEmSJOUwUZYkSZJymChLkiRJOUyUJUmSpBwmypIkSVIOE2VJkiQph4myJEmSlMNEWZIkScphoixJkiTlMFGWJEmSctQ1UY6IXhHxUETcUM92JUmSpGrV+4zyKcCsOrcpSZIkVa13vRqKiC2BA4BvAV+pV7uNcPzlD3DbE3M7Ho8dPJDLjx/VwIgq0znuStRk2646Ap6akv/coHFwzG97tr16qsG2dWe/weozLmuu3D5RTa2ux0pJa496nlH+AfDvwLJSC0TECRExNSKmzp1b/Rt/s+ictHQniWmE7sRZk20rl7Ss7glNDbatu/tgdRmXNde53weNa0wca6HV9Vgpae1RlzPKEXEg8HJKaVpEjCm1XEppIjARoLW1NdUjtlqaff4BtJxxY6PDqNrs8w+oaLmab1vbgk6PN6xte/VUg22rdL9BHfbd6qjzPlHdrK7HSklrvnqdUd4DmBARs4GrgX0i4so6tS1JkiRVrS6JckrpzJTSlimlFuAo4NaU0j/Xo21JkiSpO7yOsiRJkpSjble9aJdSuh24vd7tSpIkSdWoOFGOiO2B3YD+xeUppV/0dFCSJElSo1WUKEfEV4Hzgch52kRZkiRJa5xKzyifRjaf+VlgPrDaX7pNkiRJKqfSRHkZcG1K6fBaBiNJkiQ1i0qvevFdYMeIGFjLYCRJkqRmUfKMckQ806loa+C5iHgRWFooSyml7WsVnCRJktQo5aZetOSUvQfYsuixc5UlSZK0RiqXKI+tWxSSJElSkymZKKeU7mi/HxFnA/ellKYUle0KDKpteJIkSVJjVPplvjZgv05lnwZ+26PRSJIkSU2i7OXhIuJfih7uXPT4PWRTM5auvJYkSZK0+uvqOsqTyL6wl4B9C7d2ATxcm7AkSZKkxuoqUb6TLEkeDTwH/LVQ/i7wD+B7tQtNkiRJapyyiXJKaQxARNwO/DaldEkdYpIkSZIartKfsJ4AEBEbdCp/J6X0ds+GJEmSJDVepVe9eK3E7Y2I+HtEfKVG8UmSJEkNUWmiHGVuWwEXRMRnaxKhJEmS1ACVJsonAi8BhwI7AocALwJfAo4BXgc+V4sAJUmSpEaodI7yvwM3ppR+X3j8ZEQcBHwppbRDRIwAPKMsSZKkNUalifKmwCGFq188TvbT1R8nm3oBsKTHI5MkSZIaqNJE+Rqy6RdXFJUF8JOI6E02FePRHo5NkiRJaphKE+UvAS8DnwTeT/bjI1cC3wb6AEcCr9QiQEmSJKkRKkqUU0pLgHMKt86W4E9ZS5IkaQ1T6RllImIssDvQv7g8pXRuTwclSZIkNVpFiXJEfB84pXMxkAATZUmSJK1xKj2jfBxZUnwXML9wX5IkSVpjVZooLyS7jvKnahmMJEmS1Cwq/WW+NmCviBgeEZWuI0mSJK22Kj2j/HOy6RYPAkS0/84IKaVU8RcCJUmSpNVFNUluVFgmSZIkrfYqTZS3rWkUkiRJUpOp9AdH/g4QETsAH0gp/U9No5IkSZIarKIv5kXEJhFxMzAL+ENEtETE0oj4Zm3DkyRJkhqj0itYXADsA7wDREppNnAfcGCN4pIkSZIaqtJEeT/gduDSorKZwHY9HZAkSZLUDCpNlNcFXuhUNoDsDLMkSZK0xqk0UX6EbJrFBwEi4gLgIODhGsUlSZIkNVSlifLXgb7Ah8iunfxvwDKyX+yTJEmS1jiVXh7urohoBT4HbAPMBiamlB6pYWySJElSw1T8y3wppUeBk2sYiyRJktQ0SibKEXFrBeunlNJHulooIvoBd5JN3+gNTE4pnVNxlJIkSVKdlTujPKaC9VOF7SwG9kkpLYqIPsBdEfG/KaX7KlxfkiRJqqtyifLxPdVISikBiwoP+xRulSbZkiRJUt2VTJRTSlf0ZEMR0QuYBnwAuCSldH9P1l8vD39nX3Z764Gyy8zuV7jTlt2/9d1hwAE1jqx7jr/8AW57Yu7KT1x1BDw1pey6q7xtFbSxSnqi/kHj4Jjf1iSO4r7vGDNllNxXa6sy+/fhdUex2+k3dWvdNVZ3trknxj+lx+5lfb7LPr1mrBbHSi3XeX+OHTyQy48ftdq31aO6e4zpoddcu3LvG132ZQ8fJ7s8LjepSi8Pt8pSSu+mlIYBWwKjImJI52Ui4oSImBoRU+fObc6EoKskOc8+vWb0fCA9pPMLaOzggdmdCl8cq7Rt5doYNK779VZSfyPrKGxbtUlvueU79tvapMy+6fJ1WmKfrNG6M5Z76E2y1NjtfPxo5mOlluu8P2v5D3w92+pR3X3t9PA/8OX6q8u+7OFYupM/NYOKr3rRU1JK8yPidrKfxX6003MTgYkAra2tzT01o21BhcttWNs4esjs80ucxSm3nT21bZX2Zb3r7+l9VyKO2ecfUNUVyUvuq7VV2wJazrgRaO/LKvZbrcdeM2rgsWulsdvW/nfBanOs1HKzzz+g47W3JrXVo6o5xtTwNdD5tVdVX1a4DSsch1eqY/V9fdfljHJEDIyIjQr31wU+Cjxej7YlSZKk7qjXGeXNgSsK85TfA/wmpXRDndqWJEmSqlZxohwRnyL7Zb7tgZFkH5pdk1L6v67WLfyC3+7djFGSJEmqu4oS5Yj4DPDfQJBd7e3ZiBgDbAZ0mShLkiRJq5tK5yifCswB/lhUdj8wvMcjkiRJkppApYnyNsAtwDNFZQuBDXo8IkmSJKkJVJooPwt8CFgfICJ2AQ4C/lajuCRJkqSGqjRRvhzYkeU/a/0I8D5gUg1ikiRJkhqu0qtefB/YBDgZ6A+8AVwC/KA2YUmSJEmNVVGinFJ6FzgTODMiBqSU5tU2LEmSJKmxKr083L90etxxP6X0ix6OSZIkSWq4SqdeTAJSiedMlCVJkrTGqTRRvpPliXIvYAeyL/PdW4ugJEmSpEardI7ymOLHEdEHuAH4aw1ikiRJkhqu0svDrSCltAR4ETisZ8ORJEmSmkOlX+Z7plPR+mSXi3u+xyOSJEmSmkClc5RbcsreBM7ouVAkSZKk5lFpojy20+M3gCdTSq/3cDySJElSU6j0y3x3AETEDsAH2h9LkiRJa6qKvswXEZtExM3ALOAPEdESEUsj4pu1DU+SJElqjEqvenEBsA/wDhAppdnAfcCBNYpLkiRJaqhKE+X9gNuBS4vKZgLb9XRAkiRJUjOoNFFeF3ihU9kAsjPMkiRJ0hqn0kT5EbJpFh8EiIgLgIOAh2sUlyRJktRQlSbKXwf6Ah8CAvg3YBnQVpuwJEmSpMaq9PJwd0VEK/A5YBtgNjAxpfRIDWOTJEmSGqbSHxwhpfQocHINY5EkSZKaRkWJckTcWuKplFL6SA/GI0mSJDWFSs8ojylRnnooDkmSJKmpVJooH190vxewK9l85R/1eESSJElSE6j0y3xXdC6LiABG9XhEkiRJUhOodI7y3p2KNgDGAtv2eESSJElSE6h06sXtrDwfOYB7ejQaSZIkqUlUmig/y4qJ8hvAQ2Q/RCJJkiStcSqdo9xS4zgkSZKkplLNHOVxwKbAC8AfU0oP1TIwSZIkqZHKJsoR8R7gKuATnZ46JyImppQ+FxGbA3unlK6pVZCSJElSvXV1RvlU4MjC/b+TnU3+f0ALcEJEzCs8f2WtApQkSZIa4T1dPH8s8CawX0pp25TSP6WUtgPGA28BXwM2B26pbZiSJElSfXWVKH8AuC6lNKW4MKV0E3Bd4eFHU0p31yI4SZIkqVG6SpSXABuXeG4jYGFK6f4ejUiSJElqAl0lyjOAj0XENyJiq4joHRHvj4j/APYHptc8QkmSJKkBuvoy34XAXmQ/LJL34yLf6/GIJEmSpCZQ9oxySumPwMnAIrKfrG6/LQK+kFK6seYRSpIkSQ3Q5Q+OpJR+EhG/BP4JGADMA+5JKS2qtJGI2Ar4Bdml5ZYBE1NKP+xeyJIkSVLtVfoT1ouAKV0uWNpS4N9SStMjYn1gWkTclFKauQp1SpIkSTVTUaK8qlJKL5D9WAkppYURMQt4P7BaJMoPf2dfdnvrgUaHsaKrjoCn8v93eXjdUex2+k0lVz3+8ge47Ym5AFzW57vs02sGtNUgxjxl4l4t6l/FNor7flWWaahubH/emCy1nR1jskItZ1Q4A6zKuCvZD7P7VVxdY5TY5lXZtkrHZ/F+7KirrcvV1GC57w+dFO/P2f3g1neHAQesUlurqqfq6rzNXb2friDn9Vbx8YlVO56U2m+lXnsl91sNjpOru66uetHjIqIF2B1Y6bJyEXFCREyNiKlz5zZPx3dOkh9ed1SDIilSZiB3ldQXD+qyCcmgcdVG1bXOcfd0G7WuP6+NShTi6HxAGTt44EqLljvo5C1fd93Y/rwxWWo7q0mSswN9psu+qXJsrBEH/xLbvCrbVum6Fe/HWrxG1W0Vvz8UqeY1W6qtcio57vXU67XztlR1kqzT6634+FRrPbbfVvE42RTvUT2sLmeU20VEf+B3wJdTSq93fj6lNBGYCNDa2prqGVtF2hYAsFuDw1hB24KO/1hnn38AtG1Y8arZ8svrqatat1eP7VmFNmaf3/XZl0qWaahO27/COFxhufJjcuXl8+vPsw8wu8ulOqlyv5XdD23VNt4gJbZ5Vbaty/HZvn69jy3qERW/P1TxnlO2rR6yynW1tf9d0P1t6/y+XG3bq6DH9ltPHidXc3U7oxwRfciS5KtSStfWq11JkiSpO+qSKEdEAD8HZqWUvl+PNiVJkqRVUa8zynsAnwL2iYgZhdv+dWpbkiRJqlq9rnpxF9kPlUiSJEmrhbpf9UKSJElaHZgoS5IkSTlMlCVJkqQcJsqSJElSDhNlSZIkKYeJsiRJkpTDRFmSJEnKYaIsSZIk5TBRliRJknKYKEuSJEk5TJQlSZKkHCbKkiRJUg4TZUmSJCmHibIkSZKUw0RZkiRJymGiLEmSJOUwUZYkSZJymChLkiRJOUyUJUmSpBwmypIkSVIOE2VJkiQph4myJEmSlMNEWZIkScphoixJkiTlMFGWJEmScpgoS5IkSTlMlCVJkqQcJsqSJElSDhNlSZIkKYeJsiRJkpTDRFmSJEnKYaIsSZIk5TBRliRJknKYKEuSJEk5TJQlSZKkHCbKkiRJUg4TZUmSJCmHibIkSZKUw0RZkiRJymGiLEmSJOWoS6IcEZdFxMsR8Wg92pMkSZJWVb3OKE8C9qtTW5IkSdIqq0uinFK6E3i1Hm1JkiRJPaF3owNoKm0b1rT64y9/gNuemNvlcpf1+S779JpRUZ0tZ9xYdXsd9bdV1ETXathvxdswu1/RE1cdAU9NqXjd7uhor8T2lev77qpFnVWpoF/bVRtryxk3rjC2l/dvVdVUro77bSVV9GO1Hl53FLudflNN91W31u3BbV7V124lxg4eyOXHj6o4hmqOy3k69luxGo2TVWmr1q/LqvdtUdyz+8Gt7w4DDqi8np7o4yrf41b1GFPp+j1yPK1w2+rxmmxWTfVlvog4ISKmRsTUuXOba4c8vG7pA2qlKh1klR6MswNGZuzggRW3t1L9g8ZV1F659qtSRXsl+6zcga9Q/6q+qMttX7e3nfx91Z1laqLCN5RS299V3BUnGt0ck9Cz+63b+6FGSTLAbm89UFUb3d1X5eSumxdPN/djPd6Qu2qj8/OrkiRD0X4rVqNx0qNtrcJrMU/nfu1yHHaKu30/5O2/isdlVwrb3J33/a7el3tS2THZxX4reyzMWbfc66Vh71d10lRnlFNKE4GJAK2tranuAbQt6Ljb/h/d7PMPAGC3Hmymvc7ScawcT559gNndaa/C+rvy6SX/Dksq2J4eMPv8A/L/U65gG7ofX+n1Ku37atWjLytSpl87vzYqtcI+XMWxV06pcdnduFdJT/dj3tmftgVl61rVsVp1f/Xgvq3VvqrmjF9HDG2Fgu5sX1dn7Sqss6IxU2FbDXk9FOnWuMrZtorr6cZ+W+msfAV64r2h8m1q/1v9tnX3/btp3qPqqKnOKEuSJEnNol6Xh/s1cC8wOCLmRMS/1qNdSZIkqbvqMvUipXR0PdqRJEmSeopTLyRJkqQcJsqSJElSDhNlSZIkKYeJsiRJkpTDRFmSJEnKYaIsSZIk5TBRliRJknKYKEuSJEk5TJQlSZKkHCbKkiRJUg4TZUmSJCmHibIkSZKUw0RZkiRJymGiLEmSJOUwUZYkSZJymChLkiRJOUyUJUmSpBwmypIkSVIOE2VJkiQph4myJEmSlMNEWZIkScphoixJkiTlMFGWJEmScpgoS5IkSTlMlCVJkqQcJsqSJElSDhNlSZIkKYeJsiRJkpTDRFmSJEnKYaIsSZIk5TBRliRJknKYKEuSJEk5TJQlSZKkHCbKkiRJUg4TZUmSJCmHibIkSZKUw0RZkiRJymGiLEmSJOUwUZYkSZJymChLkiRJOUyUJUmSpBx1S5QjYr+IeCIi/hoRZ9SrXUmSJKk76pIoR0Qv4BLgY8DOwNERsXM92pYkSZK6o3ed2hkF/DWl9AxARFwNHAzMrFP7FWk548baVd62IbP7td+vXTONaK+m/ZanbcPGtV1rRdtWS12NjZr0a522rV1dx0aJbatZDPV8DdR5v9Xj2FVJ/TWJoZ7jpIFjspwe6dd6v5/WWx1fc418/y69zILax1GFek29eD/wj6LHcwplK4iIEyJiakRMnTt3bp1CK23s4IGrXMfD647q3oqDxtW2vW7WX6wn+qeadjpv263vDqt43abXA/ujp/R4v3bethpva7nYeno8lHu91WJ8lnsN9PhY785+WoV92+1jZT3V4LhcyTgp1tV+rqathr7HVaPQ7/V+P627Or7murPvV2W8rBav7xIipVT7RiKOAManlD5TePwpYFRK6Yul1mltbU1Tp06teWySJElae0XEtJRSa95z9TqjPAfYqujxlsDzdWpbkiRJqlq9EuUHgUERsW1ErAMcBfyhTm1LkiRJVavLl/lSSksj4gvA/wG9gMtSSo/Vo21JkiSpO+p11QtSSv8D/E+92pMkSZJWhb/MJ0mSJOUwUZYkSZJymChLkiRJOUyUJUmSpBwmypIkSVIOE2VJkiQph4myJEmSlMNEWZIkScphoixJkiTliJRSo2PIFRFzgb83oOkBwLwGtLu6sr+qZ59Vx/6qnn1WHfurevZZdeyv6tWzz7ZJKQ3Me6JpE+VGiYipKaXWRsexurC/qmefVcf+qp59Vh37q3r2WXXsr+o1S5859UKSJEnKYaIsSZIk5TBRXtnERgewmrG/qmefVcf+qp59Vh37q3r2WXXsr+o1RZ85R1mSJEnK4RllSZIkKYeJckFE7BcRT0TEXyPijEbH04wiYquIuC0iZkXEYxFxSqG8LSKei4gZhdv+jY61WUTE7Ij4S6FfphbKNomImyLiqcLfjRsdZ7OIiMFF42hGRLweEV92jC0XEZdFxMsR8WhRWckxFRFnFo5rT0TE+MZE3Vgl+uyCiHg8Ih6JiOsiYqNCeUtEvFU01i5tWOANUqK/Sr4GHWMl++yaov6aHREzCuWOsdL5RNMdy5x6AUREL+BJYF9gDvAgcHRKaWZDA2syEbE5sHlKaXpErA9MAz4OfAJYlFK6sJHxNaOImA20ppTmFZV9F3g1pXR+4Z+yjVNKpzcqxmZVeF0+B3wQOB7HGAARsTewCPhFSmlIoSx3TEXEzsCvgVHAFsDNwA4ppXcbFH5DlOizccCtKaWlEfEdgEKftQA3tC+3NirRX23kvAYdY5m8Puv0/PeABSmlcx1jZfOJ42iyY5lnlDOjgL+mlJ5JKb0DXA0c3OCYmk5K6YWU0vTC/YXALOD9jY1qtXQwcEXh/hVkBwet7CPA0ymlRvzwUNNKKd0JvNqpuNSYOhi4OqW0OKX0N+CvZMe7tUpen6WUpqSUlhYe3gdsWffAmlSJMVaKY4zyfRYRQXZC6dd1DaqJlcknmu5YZqKceT/wj6LHczABLKvwH/HuwP2Foi8UPsK8zKkEK0jAlIiYFhEnFMo2Sym9ANnBAnhfw6Jrbkex4huLY6y0UmPKY1tlPg38b9HjbSPioYi4IyL2alRQTSjvNegY69pewEsppaeKyhxjBZ3yiaY7lpkoZyKnzDkpJUREf+B3wJdTSq8DPwG2B4YBLwDfa1x0TWePlNJw4GPAyYWP59SFiFgHmAD8tlDkGOsej21diIizgKXAVYWiF4CtU0q7A18BfhURGzQqviZS6jXoGOva0az4T79jrCAnnyi5aE5ZXcaZiXJmDrBV0eMtgecbFEtTi4g+ZIP6qpTStQAppZdSSu+mlJYBP2Ut/NitlJTS84W/LwPXkfXNS4X5We3ztF5uXIRN62PA9JTSS+AYq0CpMeWxrYyIOBY4EDgmFb6wU/ho95XC/WnA08AOjYuyOZR5DTrGyoiI3sChwDXtZY6xTF4+QRMey0yUMw8CgyJi28KZrKOAPzQ4pqZTmGf1c2BWSun7ReWbFy12CPBo53XXRhGxXuFLCkTEesA4sr75A3BsYbFjgesbE2FTW+EMjGOsS6XG1B+AoyKib0RsCwwCHmhAfE0nIvYDTgcmpJTeLCofWPgiKRGxHVmfPdOYKJtHmdegY6y8jwKPp5TmtBc4xkrnEzThsax3PRppdoVvPX8B+D+gF3BZSumxBofVjPYAPgX8pf0yN8DXgKMjYhjZxyCzgRMbEVwT2gy4Ljse0Bv4VUrpTxHxIPCbiPhX4FngiAbG2HQi4r1kV6ApHkffdYxlIuLXwBhgQETMAc4BzidnTKWUHouI3wAzyaYXnLy2XY0ASvbZmUBf4KbCa/S+lNJJwN7AuRGxFHgXOCmlVOkX29YIJfprTN5r0DGWyeuzlNLPWfm7FuAYg9L5RNMdy7w8nCRJkpTDqReSJElSDhNlSZIkKYeJsiRJkpTDRFmSJEnKYaIsSZIk5TBRlqTVRERMiogUEW2NjkWS1gZeR1mSmkREzAa2KbPIMcB84L56xCNJazsTZUlqHpcBmxTufw5Yh+wnXtt/1euBlNKvGhGYJK2NnHohSU0ipXRuSunLKaUvA28Vii8uKvt68dSLiGgrPP7fiLgyIt6MiAci4gMRMTEiFkXEoxExvL2NiNg6Iq6OiOciYn5ETImIIfXeVklaHZgoS9LqbzywKdlPvo4EpgK7A48AuwAXQcfPg98KfKLw3E1kP7t7W0QMqHvUktTkTJQlafX3NLA/cH7h8XuBjwInFh4PK/w9ANgeeB54AniOLLkeABxep1glabXhHGVJWv09nlJKETG/8PillNKCiFhYeLxe4W9L4e/7gVM61fGB2oYoSasfE2VJWv2928XjdrMLf6cBI1NKCSAiNgKiJpFJ0mrMqReStPb4H+AZYARwd0RcGhH/QzYVY7eGRiZJTchEWZLWEimlN4CPAL8GtgaOBQYDV5LNWZYkFYnCJ2+SJEmSinhGWZIkScphoixJkiTlMFGWJEmScpgoS5IkSTlMlCVJkqQcJsqSJElSDhNlSZIkKYeJsiRJkpTDRFmSJEnK8f8BLPXqi+EiV/IAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(12,6) )\n",
    "plot_length = 200\n",
    "plt.step(np.arange(0,plot_length,1), Q_b[:plot_length,0],linewidth=2)\n",
    "plt.step(np.arange(0,plot_length,1), Qtilde_b[:plot_length,0],linewidth=2)\n",
    "plt.ylabel(\"Queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Time\", weight='bold',fontsize=12)\n",
    "plt.title(\"Queue lengths vs time - Batching\", weight='bold',fontsize=15)\n",
    "plt.legend(['Customer Queue length', 'Server Queue length'])\n",
    "plt.savefig('../../plots_stash/single-path-B.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x29aca890908>]"
      ]
     },
     "execution_count": 29,
     "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": [
    "\n",
    "plot_length = 100\n",
    "plt.step(np.arange(0,plot_length,1), Q_mw[:plot_length,1])\n",
    "plt.step(np.arange(0,plot_length,1), Qtilde_mw[:plot_length,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(12,6) )\n",
    "plot_length = 200\n",
    "plt.step(np.arange(0,plot_length,1), Q_mw[:plot_length,2],linewidth=2)\n",
    "plt.step(np.arange(0,plot_length,1), Qtilde_mw[:plot_length,1],linewidth=2)\n",
    "plt.ylabel(\"Queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Time\", weight='bold',fontsize=12)\n",
    "plt.title(\"Queue lengths vs time - Maxweight\", weight='bold',fontsize=15)\n",
    "plt.legend(['Customer Queue length', 'Server Queue length'])\n",
    "plt.savefig('../../plots_stash/single-path-mw-1.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x29ac9229780>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWoAAAD4CAYAAADFAawfAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/d3fzzAAAACXBIWXMAAAsTAAALEwEAmpwYAAAWV0lEQVR4nO3dfXBU133G8ednIYGFEAnFQRoCFjA0E1E1kNFEJZC0djKJbZKotLhOaDMemg7utHlrzLR5maEp0zJ9mWT6T6cBT6xk2pDQkDBKY6eNQ0lTbKJUOHKEhFMZIcCyAAFThIpBoJz+sXdXd1f37t4V2t1j+/uZ0bB799xzf+fcs4+uVivWnHMCAPjrjkoXAADIj6AGAM8R1ADgOYIaADxHUAOA5+aUotPFixe7pqamUnQNAK9Kx44du+icuyvqsZIEdVNTk7q7u0vRNQC8KpnZ6bjHeOkDADxHUAOA5whqAPAcQQ0AniOoAcBzid71YWZDkq5KmpR0yznXWsqiAABTinl73j3OuYslqwQAEKkk76MGZsu+rjPq7BlW+9ql2tq2vNLlvGKl51ESc/kKlPQ1aifp+2Z2zMy2RzUws+1m1m1m3aOjo7NXIV7TOnuG1XXqciZkMDOdPcPqHxlT/8gYc/kKlPSKeoNz7iUze4Okp8zseefcj8INnHN7Je2VpNbWVj6NAPBMc2N9pUvADCW6onbOvRT8e0HSQUlvK2VRAIApBYPazOab2YL0bUnvkXS81IUBAFKSvPSxRNJBM0u33+ec+7eSVgUAyCgY1M65QUlvKUMtAIAI/GUiAHiOoAYAzxHUAOA5ghoAPEdQA4DnCGoA8BxBDQCeI6gBwHMENQB4jqAGAM8R1ADgOYIaADxHUAOA5whqAPAcQQ0AniOoAcBzBDUAeI6gBgDPEdQA4DmCGgA8R1ADgOcIagDwHEENAJ4jqAHAcwQ1AHiOoAYAzxHUAOA5ghoAPEdQA4DnCGoA8BxBDQCeSxzUZlZlZj81s++WsiAAQLZirqg/IelEqQoBAESbk6SRmb1R0iZJfyXpUyWtyBfdHVLvgan7LVuk1m2VqyfHvq4z6uwZztrWvnaptrYtL7qPYvcrlagx9Y+MVagaD81wTe7rOqOuU5fVtmJRCYtDKSW9ov57SX8q6RdxDcxsu5l1m1n36OjobNRWWb0HpHO9qdvnerOfIB7o7BnOCrH+kbFpIZekj65Tl4ver1RyxyRJzY31FarGQzNck+nz2752aakqQ4kVvKI2s/dJuuCcO2ZmvxHXzjm3V9JeSWptbXWzVWBFNbRI256QOjZVupJIzY312v/IeknSQ3uOVria2REeU9qrZWyzYoZrsm3FIm1tW+7NN2UUJ8kV9QZJHzCzIUnfkHSvmf1zSasCAGQUDGrn3Gecc290zjVJ+qCk/3DO/V7JKwMASOJ91ADgvUTv+khzzv1Q0g9LUgkAIBJX1ADgOYIaADxHUAOA5whqAPAcQQ0AniOoAcBzBDUAeI6gBgDPEdQA4DmCGgA8R1ADgOcIagDwHEENAJ4jqAHAcwQ1AHiOoAYAzxHUAOA5ghoAPEdQA4DnCGoA8BxBDQCeI6gBwHMENQB4jqAGAM8R1ADgOYIaADxHUAOA5whqAPAcQQ0AniOoAcBzBYPazOaZ2U/M7Dkz6zOzvyhHYQCAlDkJ2tyQdK9zbtzMqiUdMbPvOed+XOLaAABKENTOOSdpPLhbHXy5UhZVEt0dUu8BqWWL1LotfxtJOtcrNbRoX9cZvWXkihbXzdUSSfu6zqizZzjxYdvXLtXWtuUF2+X2G7VfuE3/yJiaG+sT1xHXR1HC8yPln8sZ1NV16rLaViwqer985yPp/JdybJH9h+UeK65tsCaTmI21krT/tHdde1IbXj48re346s1qe/DRvP11ffMLqhs4WNQ+ryWJXqM2syoz65F0QdJTzrmuiDbbzazbzLpHR0dnucxZ0HtAOn0k/smSbnOuN3W7oUVq2aLOnmFdvX5LF8dvSJI6e4YTB1z/yFjiUA/3G7dfuE1zY73a1y5N1He+PooSnp9zvfnncgZ1SSp6TPnORzHzX8qxTes/LOpYcW2DNZnEbKyVpP2nbXj5sJpuDmZtWzZxMiuA49QNHNSyiZNF7fNakuSlDznnJiWtNbPXSTpoZr/inDue02avpL2S1Nra+sq74k5raJG2PTF1/9jRaU2aG+u1/5H1Bbt6aM/0ffNJ95tvv6THTnKcmdSYmZ+OTbdVQ5S2FYuSXf3miJsTn8aW1X9Y3LGi2hZpNtZKUf13LJS0TmtCdfft3pi4v7M1q7Tms0eK2ue1oqh3fTjn/lfSDyXdV4piAADTJXnXx13BlbTM7E5J75b0fInrAgAEkrz00Sjpq2ZWpVSw/4tz7rulLQsAkJbkXR8/k7SuDLUAACLwl4kA4DmCGgA8R1ADgOcIagDwHEENAJ4jqAHAcwQ1AHiOoAYAzxHUAOA5ghoAPEdQA4DnCGoA8BxBDQCeI6gBwHMENQB4jqAGAM8R1ADgOYIaADxHUAOA5whqAPAcQQ0AniOoAcBzBDUAeI6gBgDPEdQA4DmCGgA8R1ADgOcIagDwHEENAJ4jqAHAcwQ1AHiuYFCb2TIzO2xmJ8ysz8w+UY7CAAApcxK0uSXpUefcs2a2QNIxM3vKOddf4toAAEoQ1M65EUkjwe2rZnZC0lJJsx7U+7rOaPyZx7Th5cMF246v3qy2Bx+NfrC7Q+o9IEk6f/W6Lo7fUNPNQc0P7i/JaZNxrlfn56/Wx/cczWzqHxnLqq/r1GW1rVhU5Mim29d1Rp09w1nHaW6sz9suro26O7Tz0pf19J33SN3PZ40rPf60HROTqq2pkjoWSpJ2XroSuV9YeA6Hqldq156j2nnpihbXzU3NZYKxhs/r4epf13/Vvy+rTezY8vTZ2TOs/pExfWzhEanjL6e1yYxN66c2Rp13KevcFzO2RLo7pNNHpLs3Tjvv044VahseZ9TYomoMz0sx85lVa8w66Kq7V1+8/HZJOecrvc+5XqmhJdFhctfEsomTOluzqvh6c+tu2SK1bpt5P4qf8yjta5dqa9vyqeM3tEj3//VtHT9KUa9Rm1mTpHWSuiIe225m3WbWPTo6OqNiOnuGte7KD9R0czBvu2UTJ1U3cDC+QXrRSLo4fkPXJiY1VL0ycz+3TUZDizon354VzuHFnj557WuXJh1SrPSTKXycqH7D7eLaqPeA1kz0phZ9zrjS40+rranS4rq5mftNNwcj9wsLz2Eq+KRrE5NZ3wAKjTV9XpdNnFTr1UNZY887tjx9psOiveqZyNozYwuLG2fo3BcztkTSwdeyZdp5n3asUFtp+jqJ3S+QNS8zWadx83OuV3UDB6PXYjikg7oLyX2un61ZpfHVm4uvN1z36SOx32SKETfnufpHxqYCPX38Ekny0ockyczqJH1L0iedc9NG4ZzbK2mvJLW2trqZFlRbU6X5jeu0ZtsTsW36dm8s3FFDi7TtCe0Kro73P7J++n5Bm7BDe46quTbVfup4U9PUtmJR6jvoLGhurM86zu22ywiNKzz+KEPhOYmYj9w+1kjaLqlvd1XyejR1XvtGrkjXbxU/pgiZPjrmSQum1z4Ut05ixpk+97WXihtbIndvTF3pHTuaNfbIeUy3DUTNVb75v+25jZqfjk3SyJX4vmPmNJ8kz/VKSTKHD4V+8paUOm8luJqWEl5Rm1m1UiH9Nefct0tSCQAgUpJ3fZikL0s64Zz7YulLAgCEJbmi3iDpw5LuNbOe4OuBEtcFAAgkedfHEUlWhloAABH4y0QA8BxBDQCeI6gBwHMENQB4jqAGAM8R1ADgOYIaADxHUAOA5whqAPAcQQ0AniOoAcBzBDUAeI6gBgDPEdQA4DmCGgA8R1ADgOcIagDwHEENAJ4jqAHAcwQ1AHiOoAYAzxHUAOA5ghoAPEdQA4DnCGoA8BxBDQCeI6gBwHMENQB4jqAGAM8R1ADguYJBbWaPm9kFMztejoIAANmSXFF/RdJ9Ja4DABBjTqEGzrkfmVlTGWrRw1e+pDUTvZI2Frdjd4fUeyBzd2L4OQ3c0aRde46qf2RMzY31mceWTZxU3+6Naro5qKHqldq152hWV7nt065NTGY/lnPMKDsvXdGBifV6aI/0rmtPasPLhzOP7ZiYVG1NldSxMHK/yevj6ttdl7ddxrleSVLTzUHp3Bydn79aHw/GFTeesKabg5oYviMzZ7mS9BGl65tfUN3AQe2YmFSTnZa0rug+cu3rOqPOnuGpmro7pNNHpLuj10zTzUGpY9PUhnO9WfMTVmic6WNL089n2vjqzWp78FHt6zqj8Wce04aXD2ettahjZNV4rldqaMkcr+vUZbWtWJRobOevXtefXPw/LZg3J3a97Lx0JXUjbj2Fjh92/up1Xb1+K3Und+3H7JOWfs6FzWRN5Jv/ppuDmh/UuWQG/bWvXaqtbcuz57zAc3znpSu6ev2W+nbPyZzjA//apz9//5rEY0pq1l6jNrPtZtZtZt2jo6Mz6mNRXY2G6tZJLVuK27H3QCasJGngjiYdmFgvSWpurFf72qWSUk+iszWrJElD1Sv19J33TOsq3D5tcd1c1dZUZT+Wc8woq38xpC01qUBIP2HTamuqtLhubuR+TTcH9at3nNKyiZN522U0tOhk9WoNVa+UGlrUOfl29Y+MxY4n7Ok779FQ9cqsOctVqI84dQMHM2MYf/2bpZYtWlw3VwvmzZlRf5KyQrp97dKpJ1LEmkmPLUvO/IQVGmf62NL08ymlAqlu4GCm7borP8g8gdNrLfcY02psaMmMJRwiScZ2cfyGJBVeL/mEjh/Vd2bOw2s/Zh8p+zkXFl4TSeWb//RcpOsspr/+kbHMXGfNeYLnuJS6iIvLk9lS8Io6KefcXkl7Jam1tdXNpI9f+6PHZl5AQ4u07QlJylwV7n8kO3jaHnxU0qOZ+2skbU/Q9ZIF87RkwTzt35YTZKFjRqnp2KQ1Umq/joWS1mlNnvZpQ7s3as1Er87WrNKazx5JUKH02fSYt63XoT1H1Vw7ffxRDtU+oEO1D2TuJ9mnGLljWNJ7QEsWzNOatuUz7rO5sX6qzn6lrqZbt01rlx5b7nkrND99hxIcO+J85l411tZUaX5jqk3cWourMa1txSJtjZirqP3i1n3YrtA6KdaCeXNStfSr4NpPy33O3a5i5j9pf7kyc15gnLv2HM1cfe9/ZL1m/zp6Cu/6AADPEdQA4Lkkb8/7uqSjkt5kZi+a2UdKXxYAIC3Juz4+VI5CAADReOkDADxHUAOA5whqAPAcQQ0AniOoAcBzBDUAeI6gBgDPEdQA4DmCGgA8R1ADgOcIagDwHEENAJ4jqAHAcwQ1AHiOoAYAzxHUAOA5ghoAPEdQA4DnCGoA8BxBDQCeI6gBwHMENQB4jqAGAM8R1ADgOYIaADxHUAOA5whqAPAcQQ0AniOoAcBzBDUAeI6gBgDPJQpqM7vPzH5uZi+Y2adLXRQAYErBoDazKkn/IOl+Sc2SPmRmzaUuDACQMidBm7dJesE5NyhJZvYNSe2S+ktZWCHLJk6qb/dGSVLTzUENVa/Urj1HJUn9I2Nqbqyf3QOe65U6NmXfb2hJvl/S9rehf2RMD+05WvT4+0fGJKnoOQufg7jHz9asmv5A7lwWsPPSFV2bmFTf7irtmJhUbU2V1LFwqq8885qek9xthcYaNbasY8ccN73fjolJNdlpSesKji+qxiR15u6X9LzHHS+fHROTarbTZVvLtzv/SWT6k6LXVxnGmVSSoF4q6Wzo/ouS2nIbmdl2Sdslafny5bNSXJzx1Zt1duBg5v5Q9Uo9fec9mfvNjfVqX7t09g7YsmX6toaW6O1x+yVpHxhfvVl9A6l/kwqPt5jxh9sVM2e55yDK2ZpV08eQcA7CFtfN1cXxG5Kk2poqLa6bO/VgnnmNG0+h+YkbW9axI44b3q+2pkrjdW/W/ALjzVdHvjqjtic57zN9Xvx04bu1vOoZzZeKWsszMRvzn0S4v8j1VWCc6bmc1ayJYc65/A3MHpT0XufcHwT3Pyzpbc65j8Xt09ra6rq7u2e1UAB4NTOzY8651qjHkvwy8UVJy0L33yjppdkoDABQWJKg/m9Jq81shZnVSPqgpO+UtiwAQFrB16idc7fM7KOS/l1SlaTHnXN9Ja8MACAp2S8T5Zx7UtKTJa4FABCBv0wEAM8R1ADgOYIaADxHUAOA5wr+wcuMOjUblXR6hrsvlnRxFsuZLdRVPF9ro67iUFfxZlLb3c65u6IeKElQ3w4z647765xKoq7i+VobdRWHuoo327Xx0gcAeI6gBgDP+RjUeytdQAzqKp6vtVFXcaireLNam3evUQMAsvl4RQ0ACCGoAcBz3gS1Lx+ga2bLzOywmZ0wsz4z+0Sw/fNmNmxmPcHXAxWqb8jMeoMauoNti8zsKTMbCP59fZlrelNoXnrMbMzMPlmJOTOzx83sgpkdD22LnR8z+0yw5n5uZu+tQG1/Z2bPm9nPzOygmb0u2N5kZi+H5u5LZa4r9tyVa85i6tofqmnIzHqC7eWcr7iMKN06c85V/Eup/z71pKSVkmokPSepuUK1NEp6a3B7gaT/UepDfT8vaYcHczUkaXHOtr+V9Ong9qcl/U2Fz+U5SXdXYs4kvVPSWyUdLzQ/wXl9TtJcSSuCNVhV5treI2lOcPtvQrU1hdtVYM4iz1055yyqrpzHvyBpZwXmKy4jSrbOfLmiznyArnNuQlL6A3TLzjk34px7Nrh9VdIJpT430mftkr4a3P6qpN+sXCl6l6STzrmZ/mXqbXHO/UjS5ZzNcfPTLukbzrkbzrlTkl5Qai2WrTbn3Pedc7eCuz9W6hOUyipmzuKUbc7y1WVmJul3JH29FMfOJ09GlGyd+RLUUR+gW/FwNLMmpT5GuivY9NHgR9THy/3yQoiT9H0zOxZ8oLAkLXHOjUipRSTpDRWqTUp9AlD4yePDnMXNj2/r7vclfS90f4WZ/dTM/tPM3lGBeqLOnS9z9g5J551zA6FtZZ+vnIwo2TrzJagtYltF3zdoZnWSviXpk865MUn/KGmVpLWSRpT6sasSNjjn3irpfkl/bGbvrFAd01jqo9o+IOmbwSZf5iyON+vOzD4n6ZakrwWbRiQtd86tk/QpSfvMrL6MJcWdO1/m7EPKviAo+3xFZERs04htRc2ZL0Ht1Qfomlm1Uifga865b0uSc+68c27SOfcLSY+phD8i5+Oceyn494Kkg0Ed582sMai9UdKFStSm1DePZ51z54MavZgzxc+PF+vOzB6W9D5Jv+uCFzWDH5MvBbePKfW65i+Xq6Y8567ic2ZmcyT9lqT96W3lnq+ojFAJ15kvQe3NB+gGr319WdIJ59wXQ9sbQ802Szqeu28ZaptvZgvSt5X6RdRxpebq4aDZw5I6y11bIOsqx4c5C8TNz3ckfdDM5prZCkmrJf2knIWZ2X2S/kzSB5xz10Lb7zKzquD2yqC2wTLWFXfuKj5nkt4t6Xnn3IvpDeWcr7iMUCnXWTl+S5rwN6kPKPXb05OSPlfBOjYq9WPJzyT1BF8PSPonSb3B9u9IaqxAbSuV+u3xc5L60vMk6ZckHZI0EPy7qAK11Uq6JGlhaFvZ50ypbxQjkm4qdSXzkXzzI+lzwZr7uaT7K1DbC0q9fplea18K2v52cI6fk/SspPeXua7Yc1euOYuqK9j+FUl/mNO2nPMVlxElW2f8CTkAeM6Xlz4AADEIagDwHEENAJ4jqAHAcwQ1AHiOoAYAzxHUAOC5/wed1HUCFc5w3QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Tplot_length = 100\n",
    "plt.step(np.arange(0,plot_length,1), Q_b[:plot_length,1])\n",
    "plt.step(np.arange(0,plot_length,1), Qtilde_b[:plot_length,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(12,6) )\n",
    "plot_length = 200\n",
    "plt.step(np.arange(0,plot_length,1), Q_b[:plot_length,1],linewidth=2)\n",
    "plt.step(np.arange(0,plot_length,1), Qtilde_b[:plot_length,1],linewidth=2)\n",
    "plt.ylabel(\"Queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Time\", weight='bold',fontsize=12)\n",
    "plt.title(\"Queue lengths vs time - Batching\", weight='bold',fontsize=15)\n",
    "plt.legend(['Customer Queue length', 'Server Queue length'])\n",
    "plt.savefig('../../plots_stash/single-path-B-1.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = int( len(Mstars_mw) )\n",
    "cost_path_mw = np.zeros(N)\n",
    "cost_path_b  = np.zeros(N)\n",
    "for i in range(N):\n",
    "    cost_path_mw[i] = np.sum( np.multiply(Mstars_mw[i],W) )\n",
    "    cost_path_b[i] = np.sum( np.multiply(Mstars_b[i],W) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.multiply(Mstars_mw[i],W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(12,6) )\n",
    "plot_length = 1000\n",
    "plt.step(np.arange(0,plot_length,1), cost_path_mw[:plot_length],linewidth=2)\n",
    "plt.ylabel(\"Cost\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Time\", weight='bold',fontsize=12)\n",
    "plt.title(\"Cost Path - Maxweight\", weight='bold',fontsize=15)\n",
    "plt.savefig('../../plots_stash/cost-path-MW.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5f/fMLYfxv88b+lA+3CxcW37+mzu6WdvUXnA1kiSNXIvXt5ISdJcSDRtbiy5nQHL7X3NK6bu9yxFxPPAl4PmUD8fobXM1cHVEpLzqkiRJkrLkEpQj4iXA94BxlT4/DLQBs/LoX5IkSRqsvGaUNwB7A98GDgDmAP+bUlqVU/+SJEnSoOQSlFNKq4G35NGXJEmSVAt+M58kSZKUwaAsZbjh4WV85vrpzFrROOR9LV7fwudueISf37toyPuSJEkDZ1CWMnx97Cz+Mms110xcPOR93TJtBX+euYqLxs3bdtpASZJUPIOy1IeO7p4h76O7p7RtuafkmRElSaoXBmVJkiQpg0FZkiRJymBQliRJkjIYlCVJkqQMBmVJkiQpg0FZkiRJymBQliRJkjIYlCVJkqQMBmVJkiQpg0FZkiRJymBQliRJkjIYlCVJkqQMBmVJkiQpg0FZkiRJymBQliRJkjIYlDWsjZ2+gnPGTOWhxRuLLqXuPLaqkU/9dhq/nrSk6FK0h9Y0tvOFGx/he3+dS0qp6HI0QPc+vp6zx0xl3KzVu3X/1o5uvvb7R/n62Edp6+zps21Texfn3jKT//njLDq6+26r+lYqJS68fQ5fvGkG65raiy5n1Nun6AKkPfGlm2cCsKWti5s/eXLB1dSX6x9axrjZaxg3ew0fO+W5RZejPTBu9mr+NGMVAO876Qied+iBBVekgfjWnx9j8YZW7nt8PW9+yWGDvv/kxRu5aepyAN74omdx2nHP2GXb+xds4JZpKwB460ufzclHP333ilbhFq1v4Zf3lyc4TjjyYD508lHFFjTKOaOsEaG1o7voEupOT48zjyNFTyllLqu+bd7aCUBHd2m37t89iHEfTFvVt+qx7HYsC2dQliRJkjIYlCVJkqQMBmVJkiQpg0FZkiRJymBQliRJI0KplJixfIunVVPNGJQlSdKI8JvJS3n7lZN4zcXjPZ+0asKgLEmSRoRVjW1A+ZR8WzsMytpzBmVJkiQpg0FZkiRJymBQliRJkjIYlCVJkqQMBmVJkiQpg0FZkiRJypBrUI6I/SNifkSkiLgiz74lSZKkwch7Rvl84Dk59ylJkiQNWm5BOSJeCnwRuCCvPuvBI8s284n/m8qYBxuKLkWqaxMXrOfj103h1hkrC6vhr7NW8/+um8Lf560trAbVh55S4ht/ms0XbnyEjS0dNdtue1cPX/v9o3z55pk0t3fVbLuqnR/f9Tif+u00Fq9vKbqUHTy0eCOf+L8p3Dx1eU23O2H+Oj5+3RRum7mqptsdKfbJo5OI2Au4FrgSmNJHu3OAc/KoKS+/mtTA3XPXcvfctXz45KOKLkeqW9//6zzmrG7innnreNvLDy+khq/cMpOtnT0sWNfM6S94ZiE1qD7MWdXEbyYvBeDVxxzCe048oibbndqwmZsqQecNL3omb3zRs2qyXdXGlq2dXHbPAgCOecaBfPkNxxVc0XaX3bOABxZt5O6562q2PwJcePscFq1v5d7H1/PWlz27ZtsdKfKaUf4YcBQwBuj9C3hQRBxa3SildHVK6cScaspFp981Lw1Ic0fxs2tbO8u/r5tbi69FxeoulbYt95RS3W9XtVE9Jt11Nj69r0+11tjWDdTf460XucwoA0cAhwIzq9b9J9ABfCKnGiRJkqQByyso3wzMriy/iPJxyncAV+XUvyRJkjQouQTllNIcYA5ARGyorF6UUpqWR/+SJEnSYOU1o7xNSmkCEHn3K0mSJA2G38ynmpu/ppkFa5t3+/5N7V08uGgj7V1+EFKDs2BtM/PX7P6+p/x195SY0rCJ9c21OwWbJNVK7jPKGtlmLN/C26+cBMC4z7+Gfz7sHwa9jQ9e8xCzVjby1pc9m8vff3ytS9QINW9NE2/6yUQA/vjpV3P8kf9YcEUaiCvGL+Qndy/goCfvy4zzX0+E/3CUVD+cUVZNrWlsq1pu361tzFrZCMCM5ZtrUpNGh9VV+9vu7nvKX+9YNbZ5Sj5J9cegLEmSJGUwKEuSJEkZDMqSJElSBoOyJEmSlGHAQTkifhUR79tp3WkR8aXalyVJkiQVazAzyh8FXrHTurcDl9SqGEmSJKle9Hse5Yg4v+rmq6pu7wW8FegcisIkSZKkIg3kC0cuAFLl8srKpVcAk2pfliRJklSsgQTlMZRD8keAucDDlfU9wHLgmqEpTZIkSSpOv0E5pfRRoPdrRf+WUrpxiGuSJEmSCjeYD/N9H1gVZS+MiGsi4uKIOGioipMkSZKKMpBDL3r9AjgipXRMRPwBOI7yIRnPBv5zKIqTJEmSijKYGeUXAZMj4nDKIfkHwKPAmUNRmCRJklSkwQTlpwJNwAspzyRfSfmMFwfXvixJkiSpWIM59GIl8B/AycDGlNKKiHgGsGFIKpMkSZIKNJgZ5SuAQ4GXAT+NiL2AU4FpQ1GYRr6UErNWNPL42uaab/eRZZtZtL6lptuthTWN7UxevJHunlLRpQxrWzu7uX/BBprau4ouZbellJixfEtd7qf1YNnGrUxt2ESplLat6+wu8cDCDaxv7iiwMtWLtU3tPLjI19PBWLC2mVkrGkkp9d9YwCBmlFNKP4mI24B9U0rzony+uFdSPhxDGrTJizfx/msmA3DPl1/L0YceWJPt3jlnLZ/8Tfn920P/cwbP/If9a7LdPdVTSrzuhxNo6+rh3Dcex2ded0zRJQ1bn7vhEe6eu44TjjyYsZ8+pehydstdc9ZyTh3up/Wgub2LUy8ZD8DF//FS3nPSEQBceud8fnHfYg458ElMPc+Px4xmpVLi9B9OoLWzhy+//vl89oxjiy6p7jVsaOX1P74PgOs/8UpOOeaQgisaHgYzowzlwyz+NSIuBD4ONKaUNte+LI0Ga5vaM5drud16mnnq6inR1tUD1PbxjkZTGsovO9OXbSm2kD1Qr/tpPWhs2/6fgjVVz9OKzW0AbGjx+RrtelKitbP8errG19MBqX7NWdPoczZQA55RjojnA+OBZ1Wt/lZEnJ5Sml/zyiRJkqQCDWZG+YfAYcBM4CZgRuX2xbUvS5IkSSrWYM568SrgzpTSm3pXRMQ4ymfBkCRJkkaUwcwoB9C507rOynpJkiRpRBnMjPI04KyIuAeYC7wAeB1w51AUJkmSJBVpMEH5q8C9lMPxaZRnkhuB/659WZIkSVKx+g3KEbEPcAAwB/hn4EPAUcBSYAx+M58kSZJGoIEco/wjYD1wREppTUrpkpTSZ4AbgSXApUNZoCRJklSEgQTltwATUkpLqlemlJYB91R+LkmSJI0oAwnKhwMNu/jZSuA5NatGkiRJqhMDCcqtwEk7r4yIAF5R+bkkSZI0ogwkKD8IvCwirouIYyNiv4g4FrgOeGnl55IkSdKIMpDTw10EvIny2S4+tNPPSsAPal2UJEmSVLR+Z5RTSpMoB+TNlM+d3HvZAnwkpXT/QDqKiIciojkitkbE1Ig4dffLliRJkobWgL5wJKV0Y0TcCpwCPANYBzyQUto6iL4eAH4OPAu4ELgWeP7gypUkSZLyMZBjlAFIKbWllO5OKf2ucj2YkAzwJeA2yqeU66B82IaqtHf1cN/j69nQ0pFLf3NXNzFz+RZSSv22nb2ykVkrGgfUVsNPR3cPExesZ11Te9GlPMHc1U3MGOB+OhRSSsxcvoU5q5oG1PaRZZuZv6Y5h8qGzqotbUxauIGuntq+TC/buJXJizfSU6rtWC5e38KUhk2UBrDdheuambZ0k69lBSuVEg8v2cSSDSPvfAAd3T3cv2BDXb6e7qnm9i4mzF9HU3tX0aXkZjBfYb2nDqL8xSVQPmzjEzn2PSx867Y53PDwMp7zj0/m/q+dPqR9LVzXwpsvmwjADWe/ipOPfvou2z62qpF/u7x8hM3YT7+aE478xyGtTfn74d/mc83EJRxy4H5MPe/1RZezzaL12/fT3539Sl599CG51/DQkk287+rJANz9pVM55hlP3WXb+xZs4CO/eri8fO7rOPLpB+RSYy2VSokzLr2Xtq4evvz65/PZM46tyXbbOns49ZLxAHz7bS/iwycfVZPtbm7t5PRL7wXgJ+99OW8//vBdtl3X1M6ZP7oPgKs+eAJvfslhNalBgzf2kZV85ZaZAMw8/w0cdMC+BVdUOz+683F+cd9invaU/Zj+jfp5Pa2FT18/nYkLNvCK5z6Nmz95ctHl5GLAM8o10AK8AfgcsD/w7Z0bRMQ5ETE1x5rqyuL1LQCs2Nw25H1Vv9Nd19z3u951TR1VyyPvHbK273MbWjoLrmRHa6v306Z8/tPSVw1r+6mhuu36luH5u9JdSrR19QCwtp/XhsFo6ejetry2hq8jm7Zu32f72271/l3LGjR41c//lrb6et3ZUyu3lF9PN7WOrMcFMHnxRgAeXrKp4Eryk1tQTil1p5TuSildDjwMvC4iDtmpzdUppRPzqkmSJEnalVwOvYiINwLvofyBviOAVwNrgY159C9JkiQNVl7HKG8CXgl8gPIH+e4Hvpr8NIUkSZLqVC5BOaU0BXhxHn1JkiRJtZDnh/kkSZKkYcOgLEnSAN06YyVv+PG9/PzeRUWXMiJ95/Y5vOkn93H/gg1FlyIBBmVJkgbsZ+MX8fjaFi4aN6/oUkaka+9fwrw1zYx9ZEXRpUiAQVmSpAHrrPG3FWoX/Ki/6oRBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIyGJQlSZKkDAblYeq2mas449IJXH7PgqJLUY4mL97Im35yH//zx1mF1fC3x9Zw5o/u5Yd/m19YDcPN5fcs4IxLJ3DbzFVFl7KDWSsaectlE/nsDY+QUuqz7fRlm3nzZRP50s0zdmh77i0zedNP7mPa0k3b1j1U2U+/Pra4/VSqpQcWbuCNP76P82+dvW1dqZT4zPXTOeunE3lsVWOB1T3RrTNWcsalE7hy/MLCarhu0hJOv3QCNzy8rLAaasGgPExdO3Exi9a3culdjxddinI0btZq5q1p5ncPLaO9q6eQGn47eSkL17VwRYEvwMPNpXc9zqL1rVw7cXHRpezgrrlrmbO6idtmrmJ9c0efbf/22Brmrm5i7PSVNLV1A9DS0c0t01Ywb00z42at2dZ23Ow1zFvTzA0PF7efSrV0+6zVzF/bzJgHl9JTKr9RXNPUzl9mreaxVU3cM3ddwRXu6KoJi1i0vpVLCpzQuPAvc1lccA21YFAepjp7+p790chUD6Ne6mfmUbtWd7+3VWPZb2WpejFV7p59//5mp6XhJmuXTv38vEidPaWiS9j2hmJrZ3fBlewZg7IkSZKUwaAsSZIkZTAoS5IkSRkMypIkSVIGg7IkSZKUwaAsSZIkZTAoS5IkSRkMypIkSVIGg7IkSZKUwaAsSZIkZTAoS5IkSRkMypIkSVIGg7IkSZKUIZegHBHHRsT4iNgYEc0RcVdEHJ1H35IkSdLuyGtG+fBKX98Efg2cCVybU9+SJEnSoOUVlB9IKb02pXRFSulzwCbgRTn1rUH43UPLOO2S8Vw7cXHRpdTcD+6Yx+t+OIFxs1YXXUq/Ukp84cZHeP2P7mVqw6aabbdUSpw9Zipv+sl9PLaqsc+23T0lPvbrh3nzZRN5fG1zzWpo6+zh/VdP5q2X38/yTVtrtt28/WzCQk67ZDy3TF1eWA3fuX0Op/9wAnfPWdtv2/Nvnc3pl05gwvx1OVSmwRrzYAOvvWQ8v560pKbb7d1Pb67aT1ds3sq/X3E/7/3Fg2zt7O7z/g0bWvm3yyfywWsn09HdU9Pa8vSlm2fw+h/dy8NLtr+eTl68kTN/dC9fuWVmgZXtmfauHj5wzWT+7fKJLNtYzOvpxpYO3vmzSbzzZ5PY3Nq5W9u4asKi8n46pbjX013JJSinlLY9cxFxIvA04L6d20XEORExNY+alO3Hdz9Ow8atfOcvc4supeaumrCIJRtauf6hZUWX0q+m9m7+NGMVC9a18LfH1tRsuyu3tHHXnLXMW9PM3+f2HZgaNm5l/Pz1zF3dVNNwNWd1Ew8u3sislY08sGhDzbabt4vvmE/Dxq1cOX5hYTVce/8SFm9o5ZZp/f9xGfPgUhavb+X2R+v/jeJodMkd81m6cSvfHzevptvN2k8fXLSRR1c08tCSTTy2qqnP+9+/cAOzVzYxaeFG5q+p3RvmPLV0dDN2+koWrGvhjtnbX0/vmL2Gheta+P20Ff2+YahX89Y088Cijcxe2cT9C4t5PZ22dDPTl21h+rItTFu6ebe28YM75tGwcSuXj19Q4+r2XK4f5ouI44BbgQbgszv/PKV0dUrpxDxr0o7au4bvjMFA9ZRS0SVoBOnsLhVdAoPZpZO7f13aWnntHar9qaOr+P1U6k897qe5BeWIeCFwL9ANnJ5SclpDkiRJdSuvs14cAUwADgGuAl4ZEe/Lo29JkiRpd+yTUz9HA4dWlr9ftf7GnPqXJEmSBiWXoJxSmgBEHn1JkiRJteA380mSJEkZDMqSJElSBoOyJEmSlMGgLEmSJGUwKEuSJEkZDMqSJElSBoOyJEmSlMGgLEmSJGUwKEuSJEkZDMqSJElSBoOyJEmSlMGgLEmSJGUwKEuSJEkZDMqSJElSBoOyJEmSlMGgLEmSJGUwKEuSJEkZDMqSJElSBoNyPx5ctJGbpiyjtaN727rNrZ38dvJSZi7fUlxhyl1bZw83T13O/Qs2FF2KBmHZxq2MebCBZRu3Fl2KVBMNG1oZ82ADyzcVt0/PXd3Ebx5sYF1ze2E1aOiklBg3azV/nrmKnlIqupxC7VN0AfWsub2L918zubLczSde8zwArhy/kGvvXwJAw0VnFVaf8nXLtOWcf+tjAEz/xut52lP2K7giDcSnfzeN2SubeOFhy/nr519TdDnSHvvEmKksXNfC8Ueu5I+fPqWQGt511QO0dvYwpWEzP33/8YXUoKEzc0Ujn7p+OgD/eMC+vObYQwuuqDjOKPehrbNn23JjW1fmskaPpqpxr/4Pg+rbY6uaAJizuqngSqTaWLiuBYD5a5oLq6G18vdxTaMzyiNRk5lnG4OyJEmSlMGgLEmSJGUwKEuSJEkZDMqSJElSBoOyJEmSlMGgLEmSJGUwKEuSJEkZDMqSJElSBoOyJEmSlMGgLEmSJGUwKEuSJEkZDMqSJElSBoOyJEmSlCGXoBwRP42ItRGRIuL2PPqUJEmS9kSeM8o35tiXJEmStEdyCcoppc8BP86jryLd+/h6bnh4GVs7uwurYdys1fx+2go6u0tD3lfDhlZ+ef8SGja0Dnlf6tukhRu4/qGltHQUt+/dNWctN09ZTntXz7Z1axrb+fWkJcxd3VRYXaPN1s5ubnh4GRPmryu6lEKtay7ve7NXNvbbtnc/nbPK/XRPtHf1cNOUZdwzd+0O6x9dsYXrJi1hfXNHQZVJu2+fogsYKTa2dPCRXz0MQFdPiQ+ffFTuNTy+tplPXT8dgAOftDdvevFhQ9rfp66fztzVTfx+2grGff41Q9qXdq25vYsPXvsQAK0d3Zxz6tG517B801bOHjMVgH33Cd5x/HMA+Mats7lrzloOevK+zPzmG3KvazT6/bQVnH/rYwBMO+9Mnn7gkwquqBgX/XUeYx9ZyX5778Xj331zn20v+PNj3PHYGp66/z7MuuCNOVU48vx5xiq+9odZADz49dM57KAnA/C2KyeREsxd3cwP3vXSIkuUBq2uPswXEedExNSi69gdWzu3z6I1tXUVUkNz+/Z+m9qGfmaxd5bQ2cJitXVV73vFzCg37WLfW7WlDYDGgn4nRqPm9u3Pf2tHTx8tR7b1LeXZy86e/v+7trqxvJ9WP3cavOrXgernMqXy9cZWZ5Q1/NRVUE4pXZ1SOrHoOiRJkqS8znpxFvDeys0jIuITEXFsHn1LkiRJuyOvGeVzgYsqyy8FrgFOyalvSZIkadBy+TBfSum0PPqRJEmSaqWujlGWJEmS6oVBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIyGJQlSZKkDAZlSZIkKYNBWZIkScpgUJYkSZIy5BaUI+KUiHg0IjoiYnpEnJBX35IkSdJg7ZNHJxGxP/AHoA34IvC/wO8j4tiUUk8eNQxETynRXSptu93RvX25u5To6C6X2pNSVZuevttuX71tXWdPdttSxnar23b1VLUtZbTt3r6uq1Tatj4NYrtVTbet69pF22rb21bV0FN6QtuUBr7dUonMvrL0VD2P/dXQk7a37a56Hju7n1hDT1UN3Ts85wPfbm/b6ue8ut4da6i03eX+VNW2p0QEu27bz7jvartZ49N/2+znvL/t7rhPk9E2e7tZvytdVc9DV6nvfbo/peqx7NnxOX/Cflq1T+/QNmN/Ku1iP83e7i72kay2pV3V2zPw7Vb2veq6drX/Z+2nPbvc9yr76YD2p3726T3eTwf+u1L9PHT3t+/tap/OfD0d+D7dvUPbjP1ph/20uoaB709dGa9lO+7TfW+3+nWvJ2Mf2aHtrl7L+nk97al6cehtW/3cVD+2nozfqx330+zXp87uEnvvtevX6dJObffai11uN3sfqf696vtvedeuauhn3+ve4e8+GW3TLtr2s91+9unq/al6u7122J9Kfe9PnT0lekqJvfcK6kVUP0FD1knEO4CxwFdTSpdExLeBbwBnppTuyWifYMfBy8PY6Sv40s0zc+1TkiRJZT96z8t45wnPybXPiHIwTyk9IaHnMqMMPLdyvbJyvaJy/TxgW1COiHOAc3Kq6Qn2imC/vXc8GqX33eVA1metS6Rt7+L6a1tKads7s/7a9qS07d1wf227SqVt7y77a1v9brrothGw7159Hx3U23bvvYK9I56wPmu7++4dBLVvu7v7SD20Hcx+Opi29byfZqnFftpX28Hsp/vsFew1BPt0ve17g2lbD/tpd6m0bVat6NfIoWrrflqf++lgMsJw3k+r96d6kFdQ3lnvs7DDlHFK6Wrg6t4Z5by9/fjDefvxhxfRtSRJkupMXh/mW1K57p1LP3yn9ZIkSVJdyesY5f2BpcBW4GLgPKATOCbrw3xFHaMsSZKk0aWvY5RzmVFOKbUD7wZagMuAdcC76+mMF5IkSVK1XGaUB8sZZUmSJOWh8BllSZIkabgxKEuSJEkZDMqSJElSBoOyJEmSlMGgLEmSJGUwKEuSJEkZDMqSJElSBoOyJEmSlGGfogvoS+8JoCVJkqS8OaMsSZIkZajLr7AuWkRMTSmdWHQdGlqO88jnGI8OjvPo4DiPDvU2zs4oS5IkSRkMypIkSVIGg3K2q4suQLlwnEc+x3h0cJxHB8d5dKircfYYZUmSJCmDM8qSJElSBoNylYg4JSIejYiOiJgeEScUXZMGLyKOjYjxEbExIpoj4q6IOLrys12OseM//ETE/hExPyJSRFxRWecYjyARcXBEjImILRHREhH3VdY7ziNIRHwhIhoqY7YkIj5bWe84D2MR8dOIWFt5jb69av1ujWsRY25QroiI/YE/AE8Fvgg8E/h9ROxdaGHaHYdT3re/CfwaOBO4tq8xdvyHrfOB5/TecIxHpF8BHwR+CXwBWOg4jywRcSzwY6AEfAnYF/hpRByB4zwS3Fh9Y3d/fwsb85SSl/Jx2u8AEnBu5fa3K7fPKLo2L4Mey/12ur0RWNfXGDv+w+8CvBRoA86tjNUVjvHIugDPq4zRb4H9gL0r6x3nEXQBjquM0cTK8lSgHXi34zz8L8BRlbG5vXJ7t35/ixpzZ5S3e27lemXlekXl+nkF1KI9kFLq7F2OiBOBpwH30fcYO/7DSETsBVwLXAlMqfqRYzyyvLByfRLQCrRGxA9wnEeUlNJ84L+BU4B5wPHAOcARlSaO88iyu7+/hYy5QXnXonLtaUGGqYg4DrgVaAA+m9Wkcp01xo5/ffsY5VmKMZQPtQE4iPK/bKs5xsPbkyrXTwHeC0wCvgrss1M7x3kYi4hDKb9GzwDeDsyk/B+iA3duWrl2nEeW3R3XXMZ85xeb0WxJ5br3eMfDd1qvYSQiXgj8HegATk8prY6Ivsb4H/r4merPEcChlP+g9vpPYHFl2TEeGRoq1xNTSmMrgep0tv+BdJxHhtdRHqefp5RujYiXABcCcys/d5xHlt39W1zImHse5YrKQeJLga3AxcB5QCdwTEqpp8jaNDiVD4BMo3zIxXls/2P7J3YxxpRnIh3/YaLyRqj33/IvAi4A7gC+A4zFMR4RIiIovxl6FvC/wMeBE4GXA/fgOI8IlUPkpgDzgUuArwAvoDzOd+I4D1sRcRbwYuAi4FHgcuAh4G4GOa59/WxIx7zog7zr6QKcCsyqPPGPACcWXZOX3RrH0yj/K2aHS39j7PgPz0vVeF/hGI+8C+U3Qg9S/nDX48AHHOeRd6F8tosllXFeDHzGcR7+F2BCxt/jj+7uuBYx5s4oS5IkSRn8MJ8kSZKUwaAsSZIkZTAoS5IkSRkMypIkSVIGg7IkSZKUwaAsScNIRFwXESkiLii6Fkka6fxmPkmqIxHRAPxTH00+CGwBJudRjySNZgZlSaovv6L8rZIAnwL2A/4ArKisezil9LsiCpOk0cZDLySpjqSUvp1S+kJK6QtAW2X1FVXrzqs+9CIiLqjcHhcRv42IrRHxcEQcExFXR0RLRMyOiBN6+4iIIyPixohYGRFbIuLOiHhx3o9VkuqdQVmSRoY3Ak8HlgEnAVOB44FHKX8N9E8BIuIA4O/Aeyo/u4vy14CPj4hDcq9akuqYQVmSRoZFwFuAiyq3DwDOBD5Zuf3yyvVZwNHAKmA+sJJyuD4EeFdOtUrSsOAxypI0MsxLKaWI2FK5vTal1BgRzZXbT6lcH1W5Phz4/E7bOGZoS5Sk4cWgLEkjQ08/t3s1VK6nASellBJARBwMxJBUJknDlIdeSNLo8ldgMfAvwKSI+HlE/JXyoRgvK7QySaozBmVJGkVSSq3AGcANwJHAR4DjgN9SPmZZklQRlf+6SZIkSarijLIkSZKUwaAsSZIkZTAoS5IkSRkMypIkSVIGg7IkSZKUwaAsSZIkZTAoS5IkSRkMypIkSVIGg7IkSZKU4f8D6G1PzYO6nUwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(12,6) )\n",
    "plot_length = 1000\n",
    "plt.step(np.arange(0,plot_length,1), cost_path_b[:plot_length],linewidth=2)\n",
    "plt.ylabel(\"Cost\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Time\", weight='bold',fontsize=12)\n",
    "plt.title(\"Cost Path - Batching\", weight='bold',fontsize=15)\n",
    "plt.savefig('../../plots_stash/cost-path-B.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost_path_b = []\n",
    "for i in range(9999):\n",
    "    cost_path_b.append(np.sum(np.multiply(Mstars_b[i],W)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost_path_b = np.asarray(cost_path_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 1.        , 1.        , 1.41421356],\n",
       "       [1.        , 0.        , 1.41421356, 1.        ],\n",
       "       [1.        , 1.41421356, 0.        , 1.        ],\n",
       "       [1.41421356, 1.        , 1.        , 0.        ]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 4., 0., 0.]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mstars_mw[22]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2146.,  141.,  167.,   58.],\n",
       "       [ 152., 2210.,   33.,  161.],\n",
       "       [ 112.,   35., 2202.,  181.],\n",
       "       [  44.,   79.,  105., 2171.]])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(Mstars_mw,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "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",
    "new = [2146+2210+2202+2171, 9997-(2146+2210+2202+2171)-(44+35+33+58), 44+35+33+58]\n",
    "plt.bar([0,1,1.414],new,0.1)\n",
    "# plt.grid(True)\n",
    "# rc('axes', linewidth=2)\n",
    "# rc('font', weight='bold')\n",
    "plt.ylabel(\"Cost\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Time\", weight='bold',fontsize=12)\n",
    "plt.title(\"Cost Path - Maxweight\", weight='bold',fontsize=15)\n",
    "plt.savefig('../../plots_stash/cost-distribution-MW.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1756.,  368.,  254.,  203.],\n",
       "       [ 286., 1726.,  186.,  251.],\n",
       "       [ 239.,  226., 1718.,  349.],\n",
       "       [ 195.,  256.,  323., 1663.]])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(Mstars_b,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "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",
    "batching = [1702+1709+1703+1706, 9999-(1702+1709+1703+1706)-(158+194+210+190), 158+194+210+190]\n",
    "plt.bar([0,1,1.414],batching,0.1)\n",
    "plt.ylabel(\"Cost\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Time\", weight='bold',fontsize=12)\n",
    "plt.title(\"Cost Path - Batching\", weight='bold',fontsize=15)\n",
    "plt.savefig('../../plots_stash/cost-distribution-B.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8729, 1098, 170]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[6820, 2427, 752]"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "batching"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "    Q_mw.append(q)\n",
    "    Qtilde_mw.append(qtilde)\n",
    "    Mstars_mw.append(Mstar)\n",
    "    total_queue.append(np.sum(q))\n",
    "    cost_path_mw.append(matching_cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9999, 4)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_mw = np.asarray(Q_mw)\n",
    "Q_mw.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4098., 2566., 1296.,    0.,  923.,  569.,    0.,  376.,  144.,\n",
       "          27.]),\n",
       " array([0. , 0.7, 1.4, 2.1, 2.8, 3.5, 4.2, 4.9, 5.6, 6.3, 7. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 18,
     "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.hist(Q_mw[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counter({0.0: 4098, 1.0: 2566, 2.0: 1296, 3.0: 923, 4.0: 569, 5.0: 376, 6.0: 144, 7.0: 27})\n"
     ]
    },
    {
     "ename": "AttributeError",
     "evalue": "'Counter' object has no attribute '_keys'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-43-f2d6aeafb738>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mcounter\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcollections\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mCounter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mQ_mw\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[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcounter\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbar\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcounter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_keys\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mcounter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mv_alues\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m: 'Counter' object has no attribute '_keys'"
     ]
    }
   ],
   "source": [
    "import collections\n",
    "counter = collections.Counter(Q_mw[:,0])\n",
    "print(counter)\n",
    "plt.bar(counter._keys,counter.v_alues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gbuCVnb7jgB8m2ZDkhLZtn3a5vl3e0C733UqfJEnSkjbOAHc78GyaadSdgTPb9vOAFwEvpwl270myzzSPT7usUfqSnJjkym2oW5IkaVEZ2xRqVd0DXApcmuTXgaOSPLqq3jzYJsmhNFOt+9NMqwLs1S6Xt8vraKZQZ+obft7VwOok0wU/SZKk3hlLgEvyHJpRtsuBvYGnAbcAj03yAeBTbS3HAXcB1wK3ARuAk5JsBE4A1gFrgB1n6ZMkSVrSxjWFehtwBHAO8BrgC8DzgVuBZTTTqWcB1wPHVtWNVbUJWEUz9Xo2TWBbVVX3ztY3ptcjSZI0MWMZgauqLwMHzdD9vFketxY4eNQ+SZKkpcwrMUiSJPWMAU6SJKlnDHCSJEk9Y4CTJEnqGQOcJElSzxjgJEmSesYAJ0mS1DMGOEmSpJ4xwEmSJPWMAU6SJKlnDHCSJEk9Y4CTJEnqGQOcJElSzxjgJEmSesYAJ0mS1DMGOEmSpJ4xwEmSJPWMAU6SJKlnDHCSJEk9Y4CTJEnqGQOcJElSzxjgJEmSesYAJ0mS1DMGOEmSpJ4xwEmSJPWMAU6SJKlnDHCSJEk9Y4CTJEnqGQOcJElSzxjgJEmSesYAJ0mS1DNjC3BJrkiyMcmdSa5M8vS2/cgk1yTZnOSqJId1HjOvPkmSpKVsnCNwlwOvBt4IPAl4b5KdgYuAXYCTgT2AC5Msm2/fGF+PJEnSRIwzwJ0C/G/gMmAzcB9wNE34OreqzgXeB+wDrNyGPkmSpCVtnAFuN+A7wBXA3cAraUIXwPp2eUO73Hcb+iRJkpa0cQa424Fn00yj7gycOc02aZe1vfqSnJjkytFKlSRJWrzGFuCq6p6qurSq/hvwj8BRwLfb7r3a5fJ2eV17m0/f8POurqrDt/0VSJIkLQ47jONJkjwHeBHNFxn2Bp4G3AJcDGwATkqyETgBWAesAXacZ58kSdKSNq4RuNuAI4BzgNcAXwCeX1V3AatoplfPpgllq6rq3qraNJ++Mb0eSZKkiRnLCFxVfRk4aIa+tcDB27NPkiRpKfNKDJIkST1jgJMkSeoZA5wkSVLPGOAkSZJ6xgAnSZLUMwY4SZKknjHASZIk9YwBTpIkqWcMcJIkST1jgJMkSeoZA5wkSVLPGOAkSZJ6xgAnSZLUMwY4SZKknjHASZIk9YwBTpIkqWcMcJIkST1jgJMkSeoZA5wkSVLPGOAkSZJ6xgAnSZLUMwY4SZKknjHASZIk9YwBTpIkqWcMcJIkST1jgJMkSeoZA5wkSVLPGOAkSZJ6ZodJF6B+WnHaJZMuYV7WnXXMpEuQJGmbOQInSZLUMwY4SZKknhlLgEuyX5LPJfluko1JLk3y+LZvXZLq3K7uPO7IJNck2ZzkqiSHzaVPkiRpKRvXCNzy9rneAHwAeBbw3k7/WuAl7e11AEl2Bi4CdgFOBvYALkyybLa+sbwaSZKkCRrXlxgur6pnDO4keSlwYKf/OuCSqtrYaTuaJpidWlXnJtkTOB1YCew6S99lC/lCJEmSJm0sI3BVdfdgPcnhwCNpRt0GjgN+mGRDkhPatn3a5fp2eUO73HcrfZIkSUvaWL/EkOQJwCeBdcCr2ubzgBcBLwfuBt6TZJ/pHt4ua5S+JCcmuXIbypYkSVpUxnYeuCQHAH8HbAaeWVU3AVTVmzvbHAqcAuxPM60KsFe7XN4ur6OZQp2pbwtVtRpYnWS64CdJktQ7YwlwSfYG1tBMnb4eOCLJEcC/AG8BPtXWchxwF3AtcBuwATgpyUbgBJqRuzXAjrP0SZIkLWnjmkJ9PLA7sAx4K3BBe7u1bTsTOAu4Hji2qm6sqk3AKuB24GyawLaqqu6drW9Mr0eSJGlixjICV1VrmDpObdjzZnncWuDgUfskSZKWMq/EIEmS1DMGOEmSpJ4xwEmSJPWMAU6SJKlnDHCSJEk9Y4CTJEnqGQOcJElSzxjgJEmSesYAJ0mS1DMGOEmSpJ4xwEmSJPWMAU6SJKlnDHCSJEk9Y4CTJEnqmTkHuCTvT/LiobaVSU7Z/mVJkiRpJqOMwB0PPGWo7QXA27dXMZIkSdq6Hba2QZI/6dz9+c79BwHPB+5eiMIkSZI0va0GOOAMoNrbEe1tIMAXt39ZkiRJmslcAtwHacLbbwJfBf6xbb8X+DZw3sKUJkmSpOlsNcBV1fEASQA+U1UXLHBNkiRJmsVcRuAAqKpXJHlYksOAhw31rd3ulUmSJGlacw5wSV4CvAd46FBXjbIfSZIkbZtRgtfbaUbe7gXuoAlukiRJGrNRAtxDgc8Av1JV9yxQPZIkSdqKUU7k+wHg4TSnDpEkSdKEjDIC9+T2dmOSrwKDUbiqql/a7pVJkiRpWqMEuCPb5aOAX+i0eyycJEnSGI0S4F6xYFVIkiRpzkY5D9xfL2QhkiRJmptRzgP3/hm6qqpO2E71SJIkaStGmUI9nuZ4t8G3UAfrBRjgJEmSxmSU04j8KXBmu3wT8L9owttMI3M/lmS/JJ9L8t0kG5NcmuTxbd+RSa5JsjnJVe2lutiWPkmSpKVslGPg/nS4LclqYPkcHr6cJiy+AdgfeBXw3iRHAxcBdwEnA38MXJhkP2DH+fRV1b1zfU2SJEl9NMoxcI8batoVeALwxDk8/PKqekZnXy8FDgSOBvYATq2qc5PsCZwOrGz3P5++y+b6miRJkvpolGPgrpuh/dqtPbCq7h6sJzkceCTNCNo+bfP6dnlDu9wX2GWefQY4SZK0pI1yDFyGbncBl9N8uWFuO0ieAHwSWEczjTrdc8D0JweeV1+SE5NcOdcaJUmSFrtRjoEbJezdT5IDgL8DNgPPrKqbkgxG9fZql4Pj6a6jmSadT99w3auB1Um8YoQkSVoSRplCJcluwCrgp2hG0S6qqu/P4XF7A2topk5fDxyR5Ajgb4ANwElJNtKcjmRdu+2O8+yTJEla0uY8qpZkf+ArwHuAPwJWA//STotuzeOB3YFlwFuBC4ALqmoTTSC8HTibJpStqqp759s319cjSZLUV6OMwP058FjgauBfab6BeijwZ8B/mO2BVbWGqePUhvvWAgdvzz5JkqSlbJQA9/PAZ6rquYOGJJ8Cnrrdq5IkSdKMRv0W6t1DbXczw8iaJEmSFsYoI3D/FzgmyWXAV4GfAY4CPrMQhUmSJGl6owS4U4HP04S2lTQjbz8ATtv+ZUmSJGkmWw1wSXYAHkLzDdSfBV4OrACuBz4I3LqA9UmSJGnIXI6B+0vgO8DeVXVzVb29qn4X+AjNiXP/YiELlCRJ0pbmEuCeB6ypqi2uclBV36K57ujzFqIwSZIkTW8uAW45zVUOprOeqctZSZIkaQzmEuDuAJ483JgkwFPafkmSJI3JXALcl4AnJjk/yX5JdkqyH3A+cEjbL0mSpDGZy2lEzgKeS/Pt05cP9d0HvG17FyVJkqSZbXUErqq+SBPcvkdz7rfB7fvAb1bVFxayQEmSJG1pTifyraqPJPkkcCTwGGADcHlV3bmQxUmSJOn+5nwlhqq6C/jsAtYiSZKkORjlYvaSJElaBAxwkiRJPWOAkyRJ6hkDnCRJUs8Y4CRJknrGACdJktQzBjhJkqSeMcBJkiT1jAFOkiSpZwxwkiRJPWOAkyRJ6hkDnCRJUs8Y4CRJknrGACdJktQzBjhJkqSeMcBJkiT1jAFOkiSpZ8YS4JK8M8ktSSrJxZ32dW3b4HZ1p+/IJNck2ZzkqiSHzaVPkiRpqRvnCNxHZmhfC7ykvb0OIMnOwEXALsDJwB7AhUmWzda3sOVLkiQtDjuM40mq6tVJVgCvnqb7OuCSqtrYaTuaJpidWlXnJtkTOB1YCew6S99lC/YiJEmSFonFcAzcccAPk2xIckLbtk+7XN8ub2iX+26lT5IkacmbdIA7D3gR8HLgbuA9SfaZZru0yxqxjyQnJrlyWwuVJElaLMYyhTqTqnrzYD3JocApwP4006oAe7XL5e3yOpop1Jn6pnuO1cDqJNMGPEmSpL4ZS4BLcgxwUHt37ySvBK4A3gJ8qq3jOOAu4FrgNmADcFKSjcAJwDpgDbDjLH2SJElL3rimUF8LnNWuH0IzdforwDLgzLbveuDYqrqxqjYBq4DbgbNpAtuqqrp3tr4xvRZJkqSJGte3UFfO0PXWWR6zFjh41D5JkqSlbtJfYpAkSdKIDHCSJEk9Y4CTJEnqGQOcJElSzxjgJEmSesYAJ0mS1DMGOEmSpJ4xwEmSJPWMAU6SJKlnDHCSJEk9Y4CTJEnqmbFcC1XqqxWnXTLpEuZl3VnHTLoESdICcgROkiSpZwxwkiRJPWOAkyRJ6hkDnCRJUs8Y4CRJknrGACdJktQzBjhJkqSeMcBJkiT1jAFOkiSpZwxwkiRJPWOAkyRJ6hkDnCRJUs8Y4CRJknrGACdJktQzBjhJkqSeMcBJkiT1jAFOkiSpZwxwkiRJPWOAkyRJ6pmxBLgk70xyS5JKcnGn/cgk1yTZnOSqJIdta58kSdJSN84RuI907yTZGbgI2AU4GdgDuDDJsvn2je2VSJIkTdAO43iSqnp1khXAqzvNR9OEr1Or6twkewKnAyuBXefZd9k4Xo+0lKw47ZJJlzBv6846ZtIlSNJETPIYuH3a5fp2eUO73Hcb+iRJkpa8xfQlhrTL2o59JDkxyZXbWJskSdKiMckAd1273KtdLu+0z7fvfqpqdVUdvs3VSpIkLRJjOQYuyTHAQe3dvZO8ErgC2ACclGQjcAKwDlgD7DjPPkmSpCVvXCNwrwXOatcPAc4Dfg5YBdwOnE0TylZV1b1VtWk+fWN6LZIkSRM1rm+hrpyl++AZHrN2Pn2SJElL3WL6EoMkSZLmwAAnSZLUMwY4SZKknjHASZIk9YwBTpIkqWcMcJIkST1jgJMkSeoZA5wkSVLPGOAkSZJ6xgAnSZLUMwY4SZKknjHASZIk9YwBTpIkqWcMcJIkST1jgJMkSeoZA5wkSVLPGOAkSZJ6xgAnSZLUMwY4SZKknjHASZIk9YwBTpIkqWcMcJIkST1jgJMkSeqZHSZdgCSNw4rTLpl0CfOy7qxjJl2CpEXIEThJkqSeMcBJkiT1jAFOkiSpZwxwkiRJPWOAkyRJ6hkDnCRJUs8Y4CRJknpmUQS4JOuSVOd2ddt+ZJJrkmxOclWSwzqPmbFPkiRpKVsUAa61FnhJe3tdkp2Bi4BdgJOBPYALkyybrW8ilUuSJI3RYroSw3XAJVW1ESDJsTTB7NSqOjfJnsDpwEpg11n6LptA7ZIkSWOzmEbgjgN+mGRDkhOAfdr29e3yhna571b6JEmSlrTFEuDOA14EvBy4G3gPkKFtBvdrmsfP2JfkxCRXbqc6JUmSJm5RTKFW1ZsH60kOBU5halRtr3a5vF1eRzOFOlPf8L5XA6uTTBf8JEmSemfiAS7JwcBbgE/R1HMccBfw98AG4KQkG4ETgHXAGmDHWfokSZKWtMUwhXorsAw4EzgLuB44tqpuBFYBtwNn0wS2VVV1b1VtmqlvAvVLkiSN1cRH4KrqJuB5M/StBQ4etU+SJGkpWwwjcJIkSRqBAU6SJKlnDHCSJEk9M/Fj4CRJ28+K0y6ZdAnzsu6sYyZdgtQrjsBJkiT1jAFOkiSpZwxwkiRJPWOAkyRJ6hkDnCRJUs8Y4CRJknrGACdJktQzBjhJkqSeMcBJkiT1jAFOkiSpZwxwkiRJPWOAkyRJ6hkDnCRJUs8Y4CRJknrGACdJktQzBjhJkqSeMcBJkiT1jAFOkiSpZwxwkiRJPWOAkyRJ6hkDnCRJUs/sMOkCJEkaxYrTLpl0CfO27qxjJl2ClghH4CRJknrGACdJktQzBjhJkqSeMcBJkiT1jAFOkiSpZ3od4JIcmeSaJJuTXJXksEnXJEmStNB6G+CS7AxcBOwCnAzsAVyYZNlEC5MkSVpgfT4P3NE0oe3Uqjo3yZ7A6cBK4LJJFiZJ0rbq6/nuPNfdeKSqJl3DvCQ5BfgL4KVV9eEkJwLvAU6sqvOm2b6fL1SSJD1gVVWma+/tFOo0Bi9wi6CW5MQkV06gHkmSpAXR5ynU69rlXu1y+VA7AFW1Glg9rqIWWpIrq+rwSdehbed7uXT4Xi4dvpdLy1J+P/sc4D4FbABOSrIROAFYB6yZYE2SJEkLrrdTqFW1CVgF3A6cTRPmVlXVvRMtTJIkaYH1eQSOqloLHDzpOsZsyUwHy/dyCfG9XDp8L5eWJft+9vZbqJIkSQ9UvZ1ClSRJeqAywPWElw1bGpLsl+RzSb6bZGOSS5M8ftJ1af6S7Jzka0kqyTmTrkfzl+ThST6Y5PtJbk+ydtI1aX6SvCbJuvZv5nVJXjXpmrY3A1wPeNmwJWU5ze/dG4APAM8C3jvRirSt/oSp0xmp394PvBR4H/Aa4N8mWo3mJcl+wDuA+4BTgB2BdybZe6KFbWcGuH4YXDbs3Ko6l+Yfl31oLhumfrm8qp5RVedU1auB24ADJ12U5ifJITT/qTpjwqVoGyXZFzgWuAD4Q+ADVfVbk61K8zTINuuBzwI3A5uBTROraAEY4Pphn3a5vl3e0C73nUAt2gZVdfdgPcnhwCMBp2l6KMmDaEZP3wV8ecLlaNsd0C6fDNwB3JHkbROsR/NUVV8DTgOOBP4VOJTmMpvfmWhh25kBrp+mvWyY+iPJE4BP0px8eskdm/EA8QpgBfBBpq4Es1uS3SdWkbbFT7TLhwK/AXwRODXJsyZXkuaj/R18FXA18ALgn4BzkiypQx0McP0wp8uGqR+SHAB8HrgHeGZV3TThkjQ/ewO70/xx+FDb9jLgrROrSNtiXbv8+6r6OPCx9r5fMuqfo2j+Tn68qj4JfJzmGPKnTrSq7azXJ/J9APGyYUtEexDtGpqp09cDRyQ5oqo+MtHCNB8fA/65XT+Q5ji4TwPvnlRB2iZXAdcCv5TkP9GMsN5LMxKnfvn3dvmyJDfRfDEF4OsTqmdBeCLfnkjydJpjbZ4A/Avwn6rqyslWpVElWQl8bri9qnK/jdUbnff1XVX1e5OtRvOV5ECa4xoPBb4FnFFVH55sVZqPJKfQTKM+FrgR+Iuqetdkq9q+DHCSJEk94zFwkiRJPWOAkyRJ6hkDnCRJUs8Y4CRJknrGACdJktQzBjhJ2o6SHJ+kkqxZBLWsbGtZN+laJG1fBjhJi1KS5yf5fJIfJrkrybVJ/iDJsknXthglWdOGteMnXYukhWeAk7ToJDkJ+F/A04Ev0FwK5/HA2wFPrCrpAc8AJ2lRSbIL8Lb27pur6nlV9VLghW3bi9orH5BkXTvqNLh/v+nLJL/Qjk59L8mNSd6f5FFt3/2mGIdHspLskOS1Sb6a5I4kX2kvtTTKa5qthhXt81WS30ryrXa7d3Qev1OSd7ft30xyYucxD29f7zPazT/Qtp8xVMMpSW5OsiHJa0epX9LiY4CTtNg8jebC0wDnDRqr6tPA9e3dZ89lR0kOAi4Dfo7mOqVfp7nG5f9MMtfLl70R+DMgwP8EHgasTvKbC1DDGcDfA7sCr0nyS237HwO/3a5/Hjhz6HEXAuvb9UuBs4F/6PQ/DnglcDmwO/C2JPvNpX5Ji5MBTtJi8+jO+k1DfYP7j5rjvk4CdqK5fvAtwNXAZuAomusKz6oNWINrm14OfL/dx2Df27uGX2tHG7/Q3j+0XQ4uxv2aqvqt4eeuqnOAf2vvfriqXtMG3oH7gGdW1QtprvEZ4IlzrF/SIrTDpAuQpCG3dtb3AL7dub9nu7x5hscOf8FhRbs8or11/TRw+1b28WiaETdoRs2GHz8XW6vhnzv3/1+7/H67HDz38nb51Xb5lTk+98DNVTX4mX2fZkTuYTNvLmmxcwRO0mJzObCxXf+tQWOSX2YqDP3vdnlHu9y1XR40tK917fIvqyqDG7BvVV3cefwu7XPsCOzfefytnW0O6Tz+QcDhc3w9W6vhx6rqnsHq0D4G06ODac+fmeZ57m2X0/27fk9nfXjfknrIACdpUamqjcBp7d0zklyc5EPA37Rt51XVle36YMTqTUnOBn5naHergR8Bv5/kE0nOS/IF4Jtt/9eBO4FHJvkgcAnwmE4tBbyrvXtp+/gLgH+nOV5tLrZWw1x8qF2+M8n7gL+aZpvBSOXvJ/mvSZwilZYwA5ykRaeqzgV+leaA/afTHAP2EOAtTB3MD/B64EvAvsBhwDlD+/kn4FnA2nY/L6YZbTur7f9Bu78bgefShKruwf+D53gdcBvwMuCZwNeAj87xtcxawxy9hSa0PQhYCby103d3u/wL4BrgAOD3mRqtk7QEpfkPpiQtXkmeSvPtypuBZ1TV+q08ZElJ8hDgR1X1o/b+S2jOh3dDVe090eIkTYRfYpC06FXVl5IcDfwSzSjWBRMuadz2Bz6a5BM0/26/sm1/5+RKkjRJjsBJ0iKXZG/gY0x9SeObNFOqq6vqvokVJmliDHCSJEk945cYJEmSesYAJ0mS1DMGOEmSpJ4xwEmSJPWMAU6SJKlnDHCSJEk98/8B/Y1KMlRcfIkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) )\n",
    "\n",
    "Q_mw = Q_mw.astype('int64')\n",
    "plt.bar(np.unique(Q_mw[:,0]), np.bincount(Q_mw[:,0]) )\n",
    "\n",
    "plt.ylabel(\"Count\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Queue length\", weight='bold',fontsize=12)\n",
    "plt.title(\"Queue length distribution - MW\", weight='bold',fontsize=15)\n",
    "plt.savefig('../../plots_stash/queue-distribution-MW.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Queue length distribution - B')"
      ]
     },
     "execution_count": 14,
     "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": [
    "plt.figure(figsize=(10,6))\n",
    "Q_b = np.asarray(Q_b)\n",
    "Q_b = Q_b.astype('int64')\n",
    "i = 0\n",
    "plt.bar(np.unique(Q_b[:,i]), np.bincount(Q_b[:,i]) )\n",
    "plt.ylabel(\"Count\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Queue length\", weight='bold',fontsize=12)\n",
    "plt.title(\"Queue length distribution - B\", weight='bold',fontsize=15)\n",
    "# plt.savefig('../../plots_stash/queue-distribution-B.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([3.111e+03, 3.228e+03, 2.189e+03, 0.000e+00, 9.970e+02, 3.410e+02,\n",
       "        0.000e+00, 1.110e+02, 2.000e+01, 2.000e+00]),\n",
       " array([0. , 0.7, 1.4, 2.1, 2.8, 3.5, 4.2, 4.9, 5.6, 6.3, 7. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 35,
     "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": [
    "Q_b = np.asarray(Q_b)\n",
    "plt.hist(Q_b[:,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5., 6., 7.])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(Q_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.81236423])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.random(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution for Q_mw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### MLE geometric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8746501049685095\n"
     ]
    }
   ],
   "source": [
    "p = 9999/np.sum(Q_mw[:,1])\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "vals = np.unique(Q_mw[:,1])\n",
    "bincounts= np.bincount(Q_mw[:,1])\n",
    "probabs = bincounts/9999"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "geom_fit = [p, p*(1-p), p*((1-p)**2), p*((1-p)**3) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.51545155e-01 2.56125613e-01 1.20912091e-01 8.84088409e-02\n",
      " 4.87048705e-02 2.23022302e-02 1.04010401e-02 1.40014001e-03\n",
      " 2.00020002e-04]\n"
     ]
    }
   ],
   "source": [
    "print(probabs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.8746501049685095, 0.10963729884708483, 0.01374302390201824, 0.0017226866035332518]\n"
     ]
    }
   ],
   "source": [
    "print(geom_fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "can't be negative binomial because -ve binomial is not uniformly decreasing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 9 artists>"
      ]
     },
     "execution_count": 7,
     "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": [
    "#Q_mw = np.asarray(Q_mw)\n",
    "#Q_mw = Q_mw.astype('int64')\n",
    "plt.bar(np.unique(Q_mw[:,3]), np.bincount(Q_mw[:,3]) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9999, 4)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_mw.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 9 artists>"
      ]
     },
     "execution_count": 63,
     "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": [
    "Q_mw = Q_mw.astype('int64')\n",
    "plt.bar(np.unique(Q_mw[:,2]), np.bincount(Q_mw[:,2]) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 9 artists>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UvLUJSPJG4AvAh6rqZ5MezyQleQ9wpqqemPRYVpjVwO8B91bVdcB/A11fF0uyhvnZgg3Am4E3JHn/ZEdl6A8a6SciepPktcwH/mer6ouTHs8KcAPw3iQnmJ8CfFeSz0x2SCvCHDBXVb/6L8HPM/+PQM/eDTxbVWer6hfAF4E/nPCYDP0B/kTEAknC/Bztsar6+KTHsxJU1e6qmq6q9cz/GflmVU387G3Squo/gOeSvLWVbgSemuCQVoKTwJYkr29/l25kBVzcHvsTuSuVPxEx1A3AB4AjSZ5stY+1p6qlhT4IfLadNP0Q+NMJj2eiqurxJJ8Hvsv8nXDfYwU8nesTuZLUEad3JKkjhr4kdcTQl6SOGPqS1BFDX5I6YuhLUkcMfUnqiKEvSR35H/r6CwAVncBjAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q_mw = Q_mw.astype('int64')\n",
    "plt.bar(np.unique(Q_mw[:,3]), np.bincount(Q_mw[:,3]) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0pm0L9HokSZLGZvECPc8lpZQX9iaSvBbYBdiPJnwdUUo5McnWwHuBZcCma9h2wQK9JkmSpLFYkB64UspDvfEkewKbARcB27Wzb2yHN7TD7deiTZIkaZ22oBcxJNkZ+DKwEnjboEXaYZmrtiSHJLl8tEolSZIm14IFuCRPBy4EHgZeXEq5Gbiubd6mHS5ph9etRdtqSiknlVL2XOsXIEmSNCEW5By4JNsCK2gOnb4H2CvJXsCXgNuAQ5OsAg6i6Z1bAWy4hm2SJEnrtIXqgdsB2BJYBBwNnAGcUUp5ADgAuBc4liaUHVBKeWRN2xbo9UiSJI3NgvTAlVJWMHWeWn/bRcBuc9kmSZK0LvNODJIkSZUxwEmSJFXGACdJklQZA5wkSVJlDHCSJEmVMcBJkiRVxgAnSZJUGQOcJElSZQxwkiRJlTHASZIkVcYAJ0mSVBkDnCRJUmUMcJIkSZUxwEmSJFXGACdJklQZA5wkSVJlDHCSJEmVMcBJkiRVZvG4C5AkTY6lR54z7hLmzMpj9h93CdK8sQdOkiSpMgY4SZKkyhjgJEmSKmOAkyRJqowBTpIkqTIGOEmSpMoY4CRJkipjgJMkSaqMAU6SJKkyBjhJkqTKGOAkSZIqY4CTJEmqjAFOkiSpMgY4SZKkyhjgJEmSKmOAkyRJqowBTpIkqTIGOEmSpMoY4CRJkipjgJMkSaqMAU6SJKkyBjhJkqTKGOAkSZIqY4CTJEmqjAFOkiSpMgY4SZKkyhjgJEmSKmOAkyRJqowBTpIkqTIGOEmSpMoY4CRJkipjgJMkSaqMAU6SJKkyi8ddgKTRLD3ynHGXIEkaM3vgJEmSKmOAkyRJqowBTpIkqTIGOEmSpMoY4CRJkiqzIAEuyXFJbk1Skny1M39lO6/3uLLTtneSq5I8mOSKJM8apk2SJGldt5A9cGdOM/8i4DXt490ASTYGzgY2AQ4HtgLOSrJoprb5LV+SJGkyLMjvwJVS3p5kKfD2Ac3XAeeUUlZ15u1HE8yOKKWcmGRr4L3AMmDTGdoumLcXIUmSNCEm4Ry4NwD3JLktyUHtvO3a4Y3t8IZ2uP0sbZIkSeu8cQe4k4FXAa8HHgL+Nsl2A5ZLOywjtpHkkCSXr22hkiRJk2Kst9IqpXyoN55kD+CdwE40h1UBtmmHS9rhdTSHUKdrG/QcJwEnJRkY8CRJkmqzIAEuyf7Aru3ktkkOBi4DPgyc29bxBuB+4GrgTuA24NAkq4CDgJXACmDDGdokSZLWeQt1CPVdwDHt+O40h05fDiwCPtC2XQ+8spRyUynlAeAA4F7gWJrAdkAp5ZGZ2hbotUiSJI3VQl2FumyapqNnWOciYLdR2yRJktZ1476IQZIkSSMywEmSJFXGACdJklQZA5wkSVJlDHCSJEmVMcBJkiRVxgAnSZJUGQOcJElSZQxwkiRJlTHASZIkVcYAJ0mSVBkDnCRJUmUMcJIkSZUxwEmSJFVm6ACX5JQkr+6btyzJO+e+LEmSJE1nlB64A4Hf7pv3CuBjc1WMJEmSZrd4tgWSvK8z+Tud6Q2A3wMemo/CJEmSNNisAQ5YDpT2sVf76Alw8dyXJUmSpOkME+BOpwlvbwSuAf6tnf8I8BPg5PkpTZIkSYPMGuBKKQcCJAE4r5RyxjzXJEmSpBkM0wMHQCnlTUmekORZwBP62i6a88okSZI00NABLslrgL8FHt/XVEbZjiRJktbOKMHrYzQ9b48A99EEN0mSJC2wUQLc44HzgJeXUh6ep3okSZI0i1F+yPdU4Ek0Px0iSZKkMRmlB+457eOmJNcAvV64Ukp5yZxXJkmSpIFGCXB7t8PNged35nsunCRJ0gIaJcC9ad6qkCRJ0tBG+R24z85nIZIkSRrOKL8Dd8o0TaWUctAc1SNJkqRZjHII9UCa8916V6H2xgtggJMkSVogowS493fGFwG7Ab8PTNczJ0mSpHkwyjlw7++fl+QkYMmcViRJkqQZjXIO3FP6Zm0K7Aw8Y04rkiRJ0oxGOYR63TTzr56LQiRJkjScUW6llb7H/cAlNBc3SJIkaYGMcg7cKGFPkiRJ82SUQ6gkeSJwAPBUYCVwdinlrrkvS5IkSdMZ5SKGnYCvA1t3Zn8gyYtLKd+f88okSZI00CiHRf8a+A3g28DngSvb6Y/OfVmSJEmaziiHUH8HOK+Usm9vRpJzgefOeVWSJEma1qhXoT7UN+8hpm6tJUmSpAUwSg/cfwD7J7kAuAb4LeBFwHnzUZgkSZIGGyXAHQFcSBPaltH0vN0NHDn3ZUmSJGk6swa4JIuBxwHfA54GvB5YClwPnA7cPo/1SZIkqc8w58B9AvgpsG0p5ZZSysdKKX8GnElze62Pz2eBkiRJWt0wAe5lwIpSymr3Qi2l/Bi4oG2XJEnSAhkmwC2huevCIDcC28xZNZIkSZrVMAHuPuA5/TOTBPjttl2SJEkLZJgA9y3gGUlOS7Jjko2S7AicBuzetkuSJGmBDPMzIscA+9Jcffr6vrZfAh+Z66IkSZI0vVl74EopF9MEt5/R/PZb73EX8MZSyjfns0BJkiStbqgf8i2lnJnky8DewK8DtwGXlFJ+Pp/FSZIk6dGGvhNDKeV+4F/nsRZJkiQNYZSb2UuSJGkCGOAkSZIqY4CTJEmqjAFOkiSpMkNfxLA2khwH/DHNFaznlFJe3s7fG/g0sDPwXeDgUsoVa9MmSRLA0iPPGXcJc2LlMfuPuwRNoIXsgTuzO5FkY+BsYBPgcGAr4Kwki9a0bcFeiSRJ0hgtSIArpbwd+GTf7P1owteJpZQTgc8A2wHL1qJNkiRpnTfOc+C2a4c3tsMb2uH2a9H2KEkOSXL5WlcrSZI0ISbpIoa0wzKHbZRSTiql7LmWtUmSJE2MBbmIYRrXtcNt2uGSzvxN17BNkiRpnbdQV6HuD+zaTm6b5GDgMpp7qh6aZBVwELASWAFsuIZtkiRJ67yFOoT6LuCYdnx34GTg2cABwL3AsTSh7IBSyiOllAfWpG2BXoskSdJYLUgPXCll2QzNu02zzkVr0iZJkrSum6SLGCRJkjQEA5wkSVJlDHCSJEmVMcBJkiRVxgAnSZJUGQOcJElSZQxwkiRJlTHASZIkVcYAJ0mSVBkDnCRJUmUMcJIkSZUxwEmSJFXGACdJklQZA5wkSVJlDHCSJEmVMcBJkiRVxgAnSZJUGQOcJElSZQxwkiRJlTHASZIkVcYAJ0mSVBkDnCRJUmUMcJIkSZUxwEmSJFXGACdJklQZA5wkSVJlDHCSJEmVMcBJkiRVxgAnSZJUGQOcJElSZQxwkiRJlTHASZIkVcYAJ0mSVBkDnCRJUmUMcJIkSZUxwEmSJFXGACdJklQZA5wkSVJlDHCSJEmVMcBJkiRVxgAnSZJUGQOcJElSZQxwkiRJlTHASZIkVcYAJ0mSVBkDnCRJUmUMcJIkSZUxwEmSJFXGACdJklQZA5wkSVJlFo+7AGkhLD3ynHGXIEnSnLEHTpIkqTIGOEmSpMoY4CRJkipjgJMkSaqMAU6SJKkyBjhJkqTKGOAkSZIqMxEBLsnKJKXzuLKdv3eSq5I8mOSKJM/qrDNtmyRJ0rpsIgJc6yLgNe3j3Uk2Bs4GNgEOB7YCzkqyaKa2sVQuSZK0gCbpTgzXAeeUUlYBJHklTTA7opRyYpKtgfcCy4BNZ2i7YAy1S5IkLZhJ6oF7A3BPktuSHARs186/sR3e0A63n6VtNUkOSXL5PNQrSZI0FpMS4E4GXgW8HngI+Fsgfcv0psuA9adtK6WcVErZc47qlCRJGruJOIRaSvlQbzzJHsA7mepV26YdLmmH19EcQp2uTZIkaZ029gCXZDfgw8C5NPW8Abgf+AZwG3BoklXAQcBKYAWw4QxtkiRJ67RJOIR6O7AI+ABwDHA98MpSyk3AAcC9wLE0ge2AUsojpZQHpmsbQ/2SJEkLauw9cKWUm4GXTdN2EbDbqG2SJEnrsknogZMkSdIIDHCSJEmVMcBJkiRVxgAnSZJUGQOcJElSZQxwkiRJlTHASZIkVcYAJ0mSVBkDnCRJUmUMcJIkSZUxwEmSJFXGACdJklQZA5wkSVJlDHCSJEmVMcBJkiRVxgAnSZJUGQOcJElSZQxwkiRJlTHASZIkVcYAJ0mSVJnF4y5AkiRNb+mR54y7hDmz8pj9x13COsMeOEmSpMoY4CRJkipjgJMkSaqMAU6SJKkyBjhJkqTKGOAkSZIqY4CTJEmqjAFOkiSpMgY4SZKkyhjgJEmSKmOAkyRJqowBTpIkqTIGOEmSpMoY4CRJkipjgJMkSaqMAU6SJKkyBjhJkqTKGOAkSZIqY4CTJEmqjAFOkiSpMgY4SZKkyhjgJEmSKmOAkyRJqowBTpIkqTIGOEmSpMoY4CRJkipjgJMkSaqMAU6SJKkyBjhJkqTKGOAkSZIqY4CTJEmqjAFOkiSpMovHXYAm19Ijzxl3CZIkaQADnCRJWhDrUsfAymP2H+vzewhVkiSpMgY4SZKkylQd4JLsneSqJA8muSLJs8ZdkyRJ0nyrNsAl2Rg4G9gEOBzYCjgryaKxFiZJkjTPqg1wwH40oe3EUsqJwGeA7YBl4yxKkiRpvtV8Fep27fDGdnhDO9weuGC6lZLMZ02SJGk9kI+M9/lr7oHr10tmZbWZySFJLh9DPZIkSfOi5h6469rhNu1wSd98AEopJwEnLVRRAEkuL6XsuZDPqZm5TyaP+2QyuV8mj/tkMo17v9Qc4M4FbgMOTbIKOAhYCawYY02SJEnzrtpDqKWUB4ADgHuBY2nC3AGllEfGWpgkSdI8q7kHjlLKRcBu465jgAU9ZKuhuE8mj/tkMrlfJo/7ZDKNdb+klDL7UpIkSZoY1R5ClSRJWl8Z4OaQt/aaLEl2TPL1JHckWZXk/CQ7jLsuNXdSSfL9JCXJ8eOuR5DkSUlOT3JXknuTXDTumgRJDkuysv1euS7J28Zd0/omyXFJbm3/v/pqZ/5Yv/MNcHPEW3tNpCU0n/GjgFOBfYC/G2tF6nkfUz8BpMlwCvBamrvaHAb891irEUl2BD4J/BJ4J7AhcFySbcda2PrpzO7EJHznG+Dmjrf2mjyXlFJeWEo5vpTyduBOYJdxF7W+S7I7zX94y8dcilpJtgdeCZwB/AVwainlzeOtSkx9R98I/CtwC/Ag8MDYKloPtd8fn+ybPfbvfAPc3Jnp1l4ag1LKQ73xJHsCmwEeFhqjJBvQ9IKeAPz7mMvRlKe3w+cA9wH3JeO+UZBKKd8HjgT2Bq4F9gAOKaX8dKyFCSbgO98AN38G3tpLCy/JzsCXaX7o2fNHxutNwFLgdKbunvLEJFuOrSIBPKYdPh74Y+Bi4Igk+4yvJLX/Lt4GXAm8Avg2cHwSTz+YPAv+nW+AmztD3dpLCyvJ04ELgYeBF5dSbh5zSeu7bYEtab6IPtfOex1w9NgqEjR/3AB8o5TyT8AX2mkv+hmvF9F8l/xTKeXLwD/RnHP13LFWJZiA7/yqf8h3wnhrrwnTnui7gubQ6XuAvZLsVUo5c8YVNZ++AHynHd+F5jy4rwGfHldBAuAK4GrgJUneQtNT+ghNT5zG50ft8HVJbqa5yATgB2OqZ72UZH9g13Zy2yQHA5cx5u98f8h3DiV5Ac25PTsD3wXeUkq5fLxVrb+SLAO+3j+/lJJHLawF19k/J5RS3jreapRkF5rzE/cAfgwsL6X8w3irUpJ30hxG/Q3gJuDjpZQTxlvV+iXJCuCFfbPfRBOwx/adb4CTJEmqjOfASZIkVcYAJ0mSVBkDnCRJUmUMcJIkSZUxwEmSJFXGACdJcyjJgUlK+9MD465lWVvLynHXImluGeAkTaQkv5fkwiT3JLk/ydVJ/jzJonHXNomSrGjD2oHjrkXS/DPASZo4SQ4FvgK8APgmzS2EdgA+BvjjspLWewY4SRMlySbAR9rJD5VSXlZKeS3wB+28V7V3cSDJyrbXqTf9qMOXSZ7f9k79LMlNSU5Jsnnb9qhDjP09WUkWJ3lXkmuS3Jfke+3tpkZ5TTPVsLR9vpLkzUl+3C73yc76GyX5dDv/h0kO6azzpL5fij+1nb+8r4Z3JrklyW1J3jVK/ZImjwFO0qR5Hs0NuwFO7s0spXwNuL6d/N1hNpRkV+AC4Nk091z9Ac0tcP4xybC3VPsg8FEgwD8CTwBOSvLGeahhOfANYFPgsCQvaef/FfAn7fiFwAf61jsLuLEdPx84Fri00/4U4GDgEmBL4CNJdhymfkmTyQAnadJs0Rm/ua+tN735kNs6FNiI5j6FtwJXAg8CL6K5f+GM2oDVu0/rJcBd7TZ6257rGv6w7W38Zju9Rzvs3cT8sFLKm/ufu5RyPPDf7eQ/lFIOawNvzy+BF5dS/oDmPqcBnjFk/ZIm0OJxFyBJfW7vjG8F/KQzvXU7vGWadfsvcFjaDvdqH12/Cdw7yza2oOlxg6bXrH/9YcxWw3c60//ZDu9qh73nXtIOr2mH3xvyuXtuKaX03rO7aHrknjD94pImnT1wkibNJcCqdvzNvZlJ/idTYeif2+F97XDTdrhr37ZWtsNPlFLSewDbl1K+2ll/k/Y5NgR26qx/e2eZ3TvrbwDsOeTrma2GXymlPNwb7dtG7/Bo77Dnbw14nkfa4aD/1x/ujPdvW1KFDHCSJkopZRVwZDu5PMlXk3wO+FI77+RSyuXteK/H6v8kORb4077NnQT8AnhHki8mOTnJN4Eftu0/AH4ObJbkdOAc4Nc7tRTghHby/Hb9M4Af0ZyvNozZahjG59rhcUk+A/zNgGV6PZXvSPKpJB4ildZhBjhJE6eUciLw+zQn7L+A5hywxwEfZupkfoD3AN8CtgeeBRzft51vA/sAF7XbeTVNb9sxbfvd7fZuAvalCVXdk/97z/Fu4E7gdcCLge8Dnx/ytcxYw5A+TBPaNgCWAUd32h5qhx8HrgKeDryDqd46SeugNH9gStLkSvJcmqsrbwFeWEq5cZZV1ilJHgf8opTyi3b6NTS/h3dDKWXbsRYnaSy8iEHSxCulfCvJfsBLaHqxzhhzSQttJ+DzSb5I8//2we3848ZXkqRxsgdOkiZckm2BLzB1kcYPaQ6pnlRK+eXYCpM0NgY4SZKkyngRgyRJUmUMcJIkSZUxwEmSJFXGACdJklQZA5wkSVJlDHCSJEmV+f/qckNbuPs2ygAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.hist(np.sum(Q_mw,axis=1), bins = np.arange(0,11,1))\n",
    "plt.ylabel(\"Count\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Queue length\", weight='bold',fontsize=12)\n",
    "plt.title(\"Total Queue length distribution - MW\", weight='bold',fontsize=15)\n",
    "plt.savefig('../../plots_stash/total-queue-distribution-MW.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "scrolled": true
   },
   "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.hist(np.sum(Q_b,axis=1), bins = np.arange(0,11,1))\n",
    "plt.ylabel(\"Count\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Queue length\", weight='bold',fontsize=12)\n",
    "plt.title(\"Total Queue length distribution - Batching\", weight='bold',fontsize=15)\n",
    "plt.savefig('../../plots_stash/total-queue-distribution-B.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "bins = np.arange(0,10,1)\n",
    "print(bins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_name = '../sim_paths_spatial_uniform_4.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\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_paths_M = np.asarray(Q_paths_M,dtype='int64')\n",
    "Q_paths_B = np.asarray(Q_paths_B,dtype='int64')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([    0., 24295., 67282.,  8423.,     0.,     0.,     0.,     0.,\n",
       "            0.,     0.]),\n",
       " array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 10,
     "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.hist(Q_paths_M[15,:], bins = np.arange(0,11,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(25, 100000)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_paths_M.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savetxt( \"../full_queue.txt\", np.sum(Q_mw,axis=1) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9999,)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_mw[:,0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 8 artists>"
      ]
     },
     "execution_count": 18,
     "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": [
    "Q_b = np.asarray(Q_b, dtype='int64')\n",
    "plt.bar(np.unique(Q_b[:,3]), np.bincount(Q_b[:,3]) )"
   ]
  },
  {
   "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
}