max-weight-no-diag.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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_weights(N_grid, is_spatial = 0):\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(\"Spatial\",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(\"Random\",rand_weights)\n",
    "        Weights = rand_weights\n",
    "    return(Weights)\n",
    "def max_weight( time_steps, N, cust_process, serv_process, W, alpha ):\n",
    "\n",
    "    cust_arrivals = cust_process.rvs( size = time_steps )\n",
    "    serv_arrivals = serv_process.rvs( size = time_steps )\n",
    "\n",
    "    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 = [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( M[i,i] == 0)\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",
    "\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",
    "        \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",
    "        \n",
    "\n",
    "        print(\"-------------------------------------------------------------------\")\n",
    "        print(\"time step = \", k)\n",
    "        print(\"M=\", Mstar)\n",
    "        print(\"customer queue\",q )\n",
    "        print(\"server queue\", qtilde)\n",
    "        print(\"-------------------------------------------------------------------\")\n",
    "\n",
    "\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",
    "        \n",
    "        \n",
    "\n",
    "\n",
    "        total_queue.append(np.sum(q))\n",
    "        cost_path.append(matching_cost)\n",
    "    \n",
    "    return({\"QP\": total_queue, \"CP\": cost_path})\n",
    "\n",
    "def run_max_weight( time_steps, N, pmf_cust, pmf_serv, W, alpha_values, gurobi_flag = 1 ):\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))\n",
    "    \n",
    "    Q_paths = []\n",
    "    C_paths = []\n",
    "    for alpha in alpha_values:\n",
    "        res = max_weight( time_steps, N, cust_process, serv_process, W, alpha )\n",
    "        Q_paths.append(res[\"QP\"])\n",
    "        C_paths.append(res[\"CP\"])\n",
    "    return({\"Q_paths\": Q_paths,\"C_paths\":C_paths})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Spatial [[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",
      "-------------------------------------------------------------------\n",
      "time step =  1\n",
      "M= [[0. 1. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [1. 0. 0. 0.]\n",
      "server queue [0. 1. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  2\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [1. 0. 0. 0.]]\n",
      "customer queue [0. 0. 0. 1.]\n",
      "server queue [1. 0. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  3\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [1. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [0. 0. 1. 0.]\n",
      "server queue [1. 0. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  4\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 1. 0. 0.]]\n",
      "customer queue [0. 0. 0. 1.]\n",
      "server queue [0. 1. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  5\n",
      "M= [[0. 0. 0. 0.]\n",
      " [1. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [0. 1. 0. 0.]\n",
      "server queue [1. 0. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  6\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [1. 0. 0. 0.]]\n",
      "customer queue [0. 0. 0. 1.]\n",
      "server queue [1. 0. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  7\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [1. 0. 0. 0.]\n",
      "server queue [1. 0. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  8\n",
      "M= [[0. 0. 1. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [1. 0. 0. 0.]]\n",
      "customer queue [1. 0. 0. 1.]\n",
      "server queue [1. 0. 1. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  9\n",
      "M= [[0. 0. 0. 0.]\n",
      " [1. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [0. 1. 0. 0.]\n",
      "server queue [1. 0. 0. 0.]\n",
      "-------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "\n",
    "N = 2\n",
    "is_spatial = 1\n",
    "W = generate_weights(N,is_spatial)\n",
    "time_steps_M = 10\n",
    "\n",
    "\n",
    "alpha_values = np.asarray( [0] )\n",
    "\n",
    "\n",
    "if is_spatial == 1:\n",
    "    N = N*N\n",
    "\n",
    "pmf_cust = np.ones(N)*(1/N)\n",
    "pmf_serv = np.ones(N)*(1/N)\n",
    "\n",
    "print(pmf_cust,pmf_serv)\n",
    "\n",
    "M_res = run_max_weight( time_steps_M, N, pmf_cust, pmf_serv, W, alpha_values,0 )\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0, 1.0]]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_paths_M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Spatial [[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",
      "-------------------------------------------------------------------\n",
      "time step =  1\n",
      "M= [[0. 1. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [1. 0. 0. 0.]\n",
      "server queue [0. 1. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  2\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [1. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [0. 0. 1. 0.]\n",
      "server queue [1. 0. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  3\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [0. 0. 1. 0.]\n",
      "server queue [0. 0. 1. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  4\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 1.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [0. 0. 2. 0.]\n",
      "server queue [0. 0. 1. 1.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  5\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [1. 0. 0. 0.]\n",
      " [0. 0. 1. 0.]]\n",
      "customer queue [0. 0. 1. 1.]\n",
      "server queue [1. 0. 1. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  6\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [0. 0. 1. 0.]\n",
      "server queue [0. 1. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  7\n",
      "M= [[0. 1. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 1.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [1. 0. 1. 0.]\n",
      "server queue [0. 1. 0. 1.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  8\n",
      "M= [[0. 1. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [1. 0. 0. 0.]\n",
      "server queue [0. 1. 0. 0.]\n",
      "-------------------------------------------------------------------\n",
      "-------------------------------------------------------------------\n",
      "time step =  9\n",
      "M= [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "customer queue [0. 1. 0. 0.]\n",
      "server queue [0. 0. 1. 0.]\n",
      "-------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "\n",
    "N = 2\n",
    "is_spatial = 1\n",
    "W = generate_weights(N,is_spatial)\n",
    "time_steps_M = 10\n",
    "\n",
    "\n",
    "alpha_values = np.asarray( [0.6] )\n",
    "\n",
    "\n",
    "if is_spatial == 1:\n",
    "    N = N*N\n",
    "\n",
    "pmf_cust = np.ones(N)*(1/N)\n",
    "pmf_serv = np.ones(N)*(1/N)\n",
    "\n",
    "print(pmf_cust,pmf_serv)\n",
    "\n",
    "M_res = run_max_weight( time_steps_M, N, pmf_cust, pmf_serv, W, alpha_values,0 )\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import utils\n",
    "def fluid_solution(N, W, pmf_cust, pmf_serv):\n",
    "    x = cp.Variable((N,N)) # fraction of matchings from i to j\n",
    "    print(W)\n",
    "    constraints = []                          \n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "            constraints.append(x[i,j] >= 0)\n",
    "            constraints.append(x[i,j] <= 1)\n",
    "    # inequality to avoid round off, and violating equality is anyway penalised by objective\n",
    "    for i in range(N):\n",
    "        constraints.append(cp.sum(x[i,:]) == pmf_cust[i] ) \n",
    "        constraints.append( x[i,i] == 0 )\n",
    "    for j in range(N):\n",
    "        constraints.append(cp.sum(x[:,j]) == pmf_serv[j] ) \n",
    "                     \n",
    "\n",
    "    objective = cp.Minimize( cp.sum( cp.multiply( x , W ) ) )\n",
    "    problem = cp.Problem(objective, constraints)\n",
    "    problem.solve()  \n",
    "    print(problem)\n",
    "    return({\"X\": x.value, \"Cost\": problem.value })\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "\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 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",
    "\n",
    "    fluid_sol = fluid_solution(N, W, pmf_cust, pmf_serv)\n",
    "    print(\"\\nFluid Solution:\\n\")\n",
    "    print(fluid_sol)\n",
    "    \n",
    "    return(fluid_sol)\n",
    "\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": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_name = '../max_weight_no_diag_9.pkl'\n",
    "frac = 0\n",
    "with open(file_name,'rb') as f:\n",
    "    M_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",
    "(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",
    "(average_cost_B, average_queue_B) = (average_cost_M, average_queue_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.         1.         2.         1.         1.41421356 2.23606798\n",
      "  2.         2.23606798 2.82842712]\n",
      " [1.         0.         1.         1.41421356 1.         1.41421356\n",
      "  2.23606798 2.         2.23606798]\n",
      " [2.         1.         0.         2.23606798 1.41421356 1.\n",
      "  2.82842712 2.23606798 2.        ]\n",
      " [1.         1.41421356 2.23606798 0.         1.         2.\n",
      "  1.         1.41421356 2.23606798]\n",
      " [1.41421356 1.         1.41421356 1.         0.         1.\n",
      "  1.41421356 1.         1.41421356]\n",
      " [2.23606798 1.41421356 1.         2.         1.         0.\n",
      "  2.23606798 1.41421356 1.        ]\n",
      " [2.         2.23606798 2.82842712 1.         1.41421356 2.23606798\n",
      "  0.         1.         2.        ]\n",
      " [2.23606798 2.         2.23606798 1.41421356 1.         1.41421356\n",
      "  1.         0.         1.        ]\n",
      " [2.82842712 2.23606798 2.         2.23606798 1.41421356 1.\n",
      "  2.         1.         0.        ]]\n",
      "minimize Sum(var1823 @ [[0.         1.         2.         1.         1.41421356 2.23606798\n",
      "  2.         2.23606798 2.82842712]\n",
      " [1.         0.         1.         1.41421356 1.         1.41421356\n",
      "  2.23606798 2.         2.23606798]\n",
      " [2.         1.         0.         2.23606798 1.41421356 1.\n",
      "  2.82842712 2.23606798 2.        ]\n",
      " [1.         1.41421356 2.23606798 0.         1.         2.\n",
      "  1.         1.41421356 2.23606798]\n",
      " [1.41421356 1.         1.41421356 1.         0.         1.\n",
      "  1.41421356 1.         1.41421356]\n",
      " [2.23606798 1.41421356 1.         2.         1.         0.\n",
      "  2.23606798 1.41421356 1.        ]\n",
      " [2.         2.23606798 2.82842712 1.         1.41421356 2.23606798\n",
      "  0.         1.         2.        ]\n",
      " [2.23606798 2.         2.23606798 1.41421356 1.         1.41421356\n",
      "  1.         0.         1.        ]\n",
      " [2.82842712 2.23606798 2.         2.23606798 1.41421356 1.\n",
      "  2.         1.         0.        ]], None, False)\n",
      "subject to 0.0 <= var1823[0, 0]\n",
      "           var1823[0, 0] <= 1.0\n",
      "           0.0 <= var1823[0, 1]\n",
      "           var1823[0, 1] <= 1.0\n",
      "           0.0 <= var1823[0, 2]\n",
      "           var1823[0, 2] <= 1.0\n",
      "           0.0 <= var1823[0, 3]\n",
      "           var1823[0, 3] <= 1.0\n",
      "           0.0 <= var1823[0, 4]\n",
      "           var1823[0, 4] <= 1.0\n",
      "           0.0 <= var1823[0, 5]\n",
      "           var1823[0, 5] <= 1.0\n",
      "           0.0 <= var1823[0, 6]\n",
      "           var1823[0, 6] <= 1.0\n",
      "           0.0 <= var1823[0, 7]\n",
      "           var1823[0, 7] <= 1.0\n",
      "           0.0 <= var1823[0, 8]\n",
      "           var1823[0, 8] <= 1.0\n",
      "           0.0 <= var1823[1, 0]\n",
      "           var1823[1, 0] <= 1.0\n",
      "           0.0 <= var1823[1, 1]\n",
      "           var1823[1, 1] <= 1.0\n",
      "           0.0 <= var1823[1, 2]\n",
      "           var1823[1, 2] <= 1.0\n",
      "           0.0 <= var1823[1, 3]\n",
      "           var1823[1, 3] <= 1.0\n",
      "           0.0 <= var1823[1, 4]\n",
      "           var1823[1, 4] <= 1.0\n",
      "           0.0 <= var1823[1, 5]\n",
      "           var1823[1, 5] <= 1.0\n",
      "           0.0 <= var1823[1, 6]\n",
      "           var1823[1, 6] <= 1.0\n",
      "           0.0 <= var1823[1, 7]\n",
      "           var1823[1, 7] <= 1.0\n",
      "           0.0 <= var1823[1, 8]\n",
      "           var1823[1, 8] <= 1.0\n",
      "           0.0 <= var1823[2, 0]\n",
      "           var1823[2, 0] <= 1.0\n",
      "           0.0 <= var1823[2, 1]\n",
      "           var1823[2, 1] <= 1.0\n",
      "           0.0 <= var1823[2, 2]\n",
      "           var1823[2, 2] <= 1.0\n",
      "           0.0 <= var1823[2, 3]\n",
      "           var1823[2, 3] <= 1.0\n",
      "           0.0 <= var1823[2, 4]\n",
      "           var1823[2, 4] <= 1.0\n",
      "           0.0 <= var1823[2, 5]\n",
      "           var1823[2, 5] <= 1.0\n",
      "           0.0 <= var1823[2, 6]\n",
      "           var1823[2, 6] <= 1.0\n",
      "           0.0 <= var1823[2, 7]\n",
      "           var1823[2, 7] <= 1.0\n",
      "           0.0 <= var1823[2, 8]\n",
      "           var1823[2, 8] <= 1.0\n",
      "           0.0 <= var1823[3, 0]\n",
      "           var1823[3, 0] <= 1.0\n",
      "           0.0 <= var1823[3, 1]\n",
      "           var1823[3, 1] <= 1.0\n",
      "           0.0 <= var1823[3, 2]\n",
      "           var1823[3, 2] <= 1.0\n",
      "           0.0 <= var1823[3, 3]\n",
      "           var1823[3, 3] <= 1.0\n",
      "           0.0 <= var1823[3, 4]\n",
      "           var1823[3, 4] <= 1.0\n",
      "           0.0 <= var1823[3, 5]\n",
      "           var1823[3, 5] <= 1.0\n",
      "           0.0 <= var1823[3, 6]\n",
      "           var1823[3, 6] <= 1.0\n",
      "           0.0 <= var1823[3, 7]\n",
      "           var1823[3, 7] <= 1.0\n",
      "           0.0 <= var1823[3, 8]\n",
      "           var1823[3, 8] <= 1.0\n",
      "           0.0 <= var1823[4, 0]\n",
      "           var1823[4, 0] <= 1.0\n",
      "           0.0 <= var1823[4, 1]\n",
      "           var1823[4, 1] <= 1.0\n",
      "           0.0 <= var1823[4, 2]\n",
      "           var1823[4, 2] <= 1.0\n",
      "           0.0 <= var1823[4, 3]\n",
      "           var1823[4, 3] <= 1.0\n",
      "           0.0 <= var1823[4, 4]\n",
      "           var1823[4, 4] <= 1.0\n",
      "           0.0 <= var1823[4, 5]\n",
      "           var1823[4, 5] <= 1.0\n",
      "           0.0 <= var1823[4, 6]\n",
      "           var1823[4, 6] <= 1.0\n",
      "           0.0 <= var1823[4, 7]\n",
      "           var1823[4, 7] <= 1.0\n",
      "           0.0 <= var1823[4, 8]\n",
      "           var1823[4, 8] <= 1.0\n",
      "           0.0 <= var1823[5, 0]\n",
      "           var1823[5, 0] <= 1.0\n",
      "           0.0 <= var1823[5, 1]\n",
      "           var1823[5, 1] <= 1.0\n",
      "           0.0 <= var1823[5, 2]\n",
      "           var1823[5, 2] <= 1.0\n",
      "           0.0 <= var1823[5, 3]\n",
      "           var1823[5, 3] <= 1.0\n",
      "           0.0 <= var1823[5, 4]\n",
      "           var1823[5, 4] <= 1.0\n",
      "           0.0 <= var1823[5, 5]\n",
      "           var1823[5, 5] <= 1.0\n",
      "           0.0 <= var1823[5, 6]\n",
      "           var1823[5, 6] <= 1.0\n",
      "           0.0 <= var1823[5, 7]\n",
      "           var1823[5, 7] <= 1.0\n",
      "           0.0 <= var1823[5, 8]\n",
      "           var1823[5, 8] <= 1.0\n",
      "           0.0 <= var1823[6, 0]\n",
      "           var1823[6, 0] <= 1.0\n",
      "           0.0 <= var1823[6, 1]\n",
      "           var1823[6, 1] <= 1.0\n",
      "           0.0 <= var1823[6, 2]\n",
      "           var1823[6, 2] <= 1.0\n",
      "           0.0 <= var1823[6, 3]\n",
      "           var1823[6, 3] <= 1.0\n",
      "           0.0 <= var1823[6, 4]\n",
      "           var1823[6, 4] <= 1.0\n",
      "           0.0 <= var1823[6, 5]\n",
      "           var1823[6, 5] <= 1.0\n",
      "           0.0 <= var1823[6, 6]\n",
      "           var1823[6, 6] <= 1.0\n",
      "           0.0 <= var1823[6, 7]\n",
      "           var1823[6, 7] <= 1.0\n",
      "           0.0 <= var1823[6, 8]\n",
      "           var1823[6, 8] <= 1.0\n",
      "           0.0 <= var1823[7, 0]\n",
      "           var1823[7, 0] <= 1.0\n",
      "           0.0 <= var1823[7, 1]\n",
      "           var1823[7, 1] <= 1.0\n",
      "           0.0 <= var1823[7, 2]\n",
      "           var1823[7, 2] <= 1.0\n",
      "           0.0 <= var1823[7, 3]\n",
      "           var1823[7, 3] <= 1.0\n",
      "           0.0 <= var1823[7, 4]\n",
      "           var1823[7, 4] <= 1.0\n",
      "           0.0 <= var1823[7, 5]\n",
      "           var1823[7, 5] <= 1.0\n",
      "           0.0 <= var1823[7, 6]\n",
      "           var1823[7, 6] <= 1.0\n",
      "           0.0 <= var1823[7, 7]\n",
      "           var1823[7, 7] <= 1.0\n",
      "           0.0 <= var1823[7, 8]\n",
      "           var1823[7, 8] <= 1.0\n",
      "           0.0 <= var1823[8, 0]\n",
      "           var1823[8, 0] <= 1.0\n",
      "           0.0 <= var1823[8, 1]\n",
      "           var1823[8, 1] <= 1.0\n",
      "           0.0 <= var1823[8, 2]\n",
      "           var1823[8, 2] <= 1.0\n",
      "           0.0 <= var1823[8, 3]\n",
      "           var1823[8, 3] <= 1.0\n",
      "           0.0 <= var1823[8, 4]\n",
      "           var1823[8, 4] <= 1.0\n",
      "           0.0 <= var1823[8, 5]\n",
      "           var1823[8, 5] <= 1.0\n",
      "           0.0 <= var1823[8, 6]\n",
      "           var1823[8, 6] <= 1.0\n",
      "           0.0 <= var1823[8, 7]\n",
      "           var1823[8, 7] <= 1.0\n",
      "           0.0 <= var1823[8, 8]\n",
      "           var1823[8, 8] <= 1.0\n",
      "           Sum(var1823[0, 0:9], None, False) == 0.1111111111111111\n",
      "           var1823[0, 0] == 0.0\n",
      "           Sum(var1823[1, 0:9], None, False) == 0.1111111111111111\n",
      "           var1823[1, 1] == 0.0\n",
      "           Sum(var1823[2, 0:9], None, False) == 0.1111111111111111\n",
      "           var1823[2, 2] == 0.0\n",
      "           Sum(var1823[3, 0:9], None, False) == 0.1111111111111111\n",
      "           var1823[3, 3] == 0.0\n",
      "           Sum(var1823[4, 0:9], None, False) == 0.1111111111111111\n",
      "           var1823[4, 4] == 0.0\n",
      "           Sum(var1823[5, 0:9], None, False) == 0.1111111111111111\n",
      "           var1823[5, 5] == 0.0\n",
      "           Sum(var1823[6, 0:9], None, False) == 0.1111111111111111\n",
      "           var1823[6, 6] == 0.0\n",
      "           Sum(var1823[7, 0:9], None, False) == 0.1111111111111111\n",
      "           var1823[7, 7] == 0.0\n",
      "           Sum(var1823[8, 0:9], None, False) == 0.1111111111111111\n",
      "           var1823[8, 8] == 0.0\n",
      "           Sum(var1823[0:9, 0], None, False) == 0.1111111111111111\n",
      "           Sum(var1823[0:9, 1], None, False) == 0.1111111111111111\n",
      "           Sum(var1823[0:9, 2], None, False) == 0.1111111111111111\n",
      "           Sum(var1823[0:9, 3], None, False) == 0.1111111111111111\n",
      "           Sum(var1823[0:9, 4], None, False) == 0.1111111111111111\n",
      "           Sum(var1823[0:9, 5], None, False) == 0.1111111111111111\n",
      "           Sum(var1823[0:9, 6], None, False) == 0.1111111111111111\n",
      "           Sum(var1823[0:9, 7], None, False) == 0.1111111111111111\n",
      "           Sum(var1823[0:9, 8], None, False) == 0.1111111111111111\n",
      "\n",
      "Fluid Solution:\n",
      "\n",
      "{'X': array([[1.02485060e-14, 4.86111113e-02, 2.03717650e-11, 4.86111108e-02,\n",
      "        1.38888889e-02, 6.98281105e-12, 2.03717650e-11, 6.98281105e-12,\n",
      "        5.97704366e-12],\n",
      "       [4.86111114e-02, 1.89716850e-14, 4.86111107e-02, 1.48855041e-11,\n",
      "        1.38888889e-02, 1.48855041e-11, 6.98281105e-12, 3.99659493e-12,\n",
      "        6.98281105e-12],\n",
      "       [2.03717650e-11, 4.86111109e-02, 1.02485060e-14, 6.98281105e-12,\n",
      "        1.38888889e-02, 4.86111112e-02, 5.97704366e-12, 6.98281105e-12,\n",
      "        2.03717650e-11],\n",
      "       [4.86111107e-02, 1.48855041e-11, 6.98281105e-12, 1.89716851e-14,\n",
      "        1.38888889e-02, 3.99659493e-12, 4.86111115e-02, 1.48855041e-11,\n",
      "        6.98281105e-12],\n",
      "       [1.38888889e-02, 1.38888888e-02, 1.38888889e-02, 1.38888889e-02,\n",
      "        3.00729978e-14, 1.38888889e-02, 1.38888889e-02, 1.38888889e-02,\n",
      "        1.38888889e-02],\n",
      "       [6.98281105e-12, 1.48855041e-11, 4.86111114e-02, 3.99659493e-12,\n",
      "        1.38888889e-02, 1.89716850e-14, 6.98281105e-12, 1.48855041e-11,\n",
      "        4.86111107e-02],\n",
      "       [2.03717650e-11, 6.98281105e-12, 5.97704366e-12, 4.86111113e-02,\n",
      "        1.38888888e-02, 6.98281105e-12, 1.02485060e-14, 4.86111109e-02,\n",
      "        2.03717650e-11],\n",
      "       [6.98281105e-12, 3.99659493e-12, 6.98281105e-12, 1.48855041e-11,\n",
      "        1.38888889e-02, 1.48855041e-11, 4.86111107e-02, 1.89716851e-14,\n",
      "        4.86111114e-02],\n",
      "       [5.97704366e-12, 6.98281105e-12, 2.03717650e-11, 6.98281105e-12,\n",
      "        1.38888888e-02, 4.86111109e-02, 2.03717650e-11, 4.86111113e-02,\n",
      "        1.02485060e-14]]), 'Cost': 1.0460237295411163}\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": [
    "fluid_sol = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "\n",
    "plt.figure( figsize=(10,6) ) \n",
    "\n",
    "# C = 0 Case\n",
    "\n",
    "# C = Inf/Fluid Case\n",
    "ylim = max( max( average_queue_B ), max( average_queue_M ) )\n",
    "plt.plot([fluid_sol['Cost'],fluid_sol['Cost']],[0,ylim],linewidth = 3)\n",
    "# Batching data\n",
    "plt.plot(average_cost_B,average_queue_B,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "# Max Weight data\n",
    "plt.plot(average_cost_M, average_queue_M,'go',markersize = 8)\n",
    "# plt.plot([Ex],[1],'r*',markersize = 12, markeredgewidth=3)\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.legend(['Fluid', 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "# plt.legend([ 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "plt.grid(True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'X': array([[1.02485060e-14, 4.86111113e-02, 2.03717650e-11, 4.86111108e-02,\n",
       "         1.38888889e-02, 6.98281105e-12, 2.03717650e-11, 6.98281105e-12,\n",
       "         5.97704366e-12],\n",
       "        [4.86111114e-02, 1.89716850e-14, 4.86111107e-02, 1.48855041e-11,\n",
       "         1.38888889e-02, 1.48855041e-11, 6.98281105e-12, 3.99659493e-12,\n",
       "         6.98281105e-12],\n",
       "        [2.03717650e-11, 4.86111109e-02, 1.02485060e-14, 6.98281105e-12,\n",
       "         1.38888889e-02, 4.86111112e-02, 5.97704366e-12, 6.98281105e-12,\n",
       "         2.03717650e-11],\n",
       "        [4.86111107e-02, 1.48855041e-11, 6.98281105e-12, 1.89716851e-14,\n",
       "         1.38888889e-02, 3.99659493e-12, 4.86111115e-02, 1.48855041e-11,\n",
       "         6.98281105e-12],\n",
       "        [1.38888889e-02, 1.38888888e-02, 1.38888889e-02, 1.38888889e-02,\n",
       "         3.00729978e-14, 1.38888889e-02, 1.38888889e-02, 1.38888889e-02,\n",
       "         1.38888889e-02],\n",
       "        [6.98281105e-12, 1.48855041e-11, 4.86111114e-02, 3.99659493e-12,\n",
       "         1.38888889e-02, 1.89716850e-14, 6.98281105e-12, 1.48855041e-11,\n",
       "         4.86111107e-02],\n",
       "        [2.03717650e-11, 6.98281105e-12, 5.97704366e-12, 4.86111113e-02,\n",
       "         1.38888888e-02, 6.98281105e-12, 1.02485060e-14, 4.86111109e-02,\n",
       "         2.03717650e-11],\n",
       "        [6.98281105e-12, 3.99659493e-12, 6.98281105e-12, 1.48855041e-11,\n",
       "         1.38888889e-02, 1.48855041e-11, 4.86111107e-02, 1.89716851e-14,\n",
       "         4.86111114e-02],\n",
       "        [5.97704366e-12, 6.98281105e-12, 2.03717650e-11, 6.98281105e-12,\n",
       "         1.38888888e-02, 4.86111109e-02, 2.03717650e-11, 4.86111113e-02,\n",
       "         1.02485060e-14]]),\n",
       " 'Cost': 1.0460237295411163}"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fluid_sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}