Server_Qlearning.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statistics as stat \n",
    "\n",
    "B = 512;C = 10000;W = 1.4 * pow(10,6)\n",
    "f_I = pow(10,9);f_M = pow(10,12)\n",
    "N_0 = pow(10,-16);P = 0.5 \n",
    "\n",
    "def arrival_and_departure_times(param1,param2,N):\n",
    "    a = []\n",
    "    d = []\n",
    "    s = 0\n",
    "    for i in range(N):\n",
    "        s = s + np.random.exponential(param1)\n",
    "        a.append(s)\n",
    "    for i in range(N):\n",
    "        d.append(a[i] + np.random.exponential(param2))\n",
    "    return (np.array(a),np.array(d))\n",
    "\n",
    "def local_cost():\n",
    "    return ((B*C)/f_I)\n",
    "\n",
    "def cloud_cost(n):\n",
    "    h_g_2 = np.random.exponential(1)\n",
    "    R = W * np.log2(1 + P*h_g_2/N_0)\n",
    "    #R = np.random.choice([R,R/5],p = [0.5,0.5])\n",
    "    return (B/R + B*C*n/f_M)\n",
    "\n",
    "def next_state(local_pos,cloud_pos,action):\n",
    "    if action == 0:\n",
    "        (new_local_pos,new_cloud_pos,reward) = (local_pos + 1,cloud_pos,-local_cost())\n",
    "    else:\n",
    "        (new_local_pos,new_cloud_pos,reward) = (local_pos,cloud_pos + 1,-cloud_cost(cloud_pos))\n",
    "    return  (new_local_pos,new_cloud_pos,reward)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Server_Q_learning(N):\n",
    "    gamma = 0.9\n",
    "    n = 50\n",
    "    reward_list = []\n",
    "    reward_sum_list = []\n",
    "    reward_sum_avg_list = np.array([0]*N)\n",
    "    runs = 1\n",
    "    mu = 1/20;lamda = 1\n",
    "    for ind in range(runs):\n",
    "        count = 0\n",
    "        Qa = np.zeros((n,n,2))\n",
    "        freq = np.ones((n,n))\n",
    "        freq_action = np.ones((n,n,2))\n",
    "        (arrivals,departures) = arrival_and_departure_times(mu,lamda,N)\n",
    "        local_pos = 0;cloud_pos = 0\n",
    "        local_actions = np.array([False]*N)\n",
    "        cloud_actions = np.array([False]*N)\n",
    "        reward_sum_list = []\n",
    "        reward_sum = 0\n",
    "        for i in range(N):\n",
    "            local_pos = ((departures > arrivals[i]) & (arrivals < arrivals[i]) & (local_actions)).sum()\n",
    "            cloud_pos = ((departures > arrivals[i]) & (arrivals < arrivals[i]) & (cloud_actions)).sum()\n",
    "            eps = 1/np.sqrt(freq[local_pos,cloud_pos])\n",
    "            action = np.random.choice([np.argmax(Qa[local_pos,cloud_pos]),np.random.choice([0,1])],p = [1 - eps,eps])\n",
    "            if local_pos == n:\n",
    "                action = 1\n",
    "            if cloud_pos == n:\n",
    "                action = 0        \n",
    "            if action == 0:\n",
    "                local_actions[i] = 1\n",
    "            if action == 1:\n",
    "                cloud_actions[i] = 1\n",
    "            (new_local_pos,new_cloud_pos,reward) = next_state(local_pos,cloud_pos,action)\n",
    "            reward_sum = reward_sum + reward\n",
    "            count = count + 1\n",
    "            alpha = 1/np.power(freq_action[local_pos,cloud_pos, action],0.8)\n",
    "            Qa[local_pos,cloud_pos,action] = Qa[local_pos,cloud_pos,action] + alpha*(reward + gamma*np.max(Qa[new_local_pos,new_cloud_pos]) - Qa[local_pos,cloud_pos,action])\n",
    "            freq[local_pos,cloud_pos] = freq[local_pos,cloud_pos] + 1\n",
    "            freq_action[local_pos,cloud_pos,action] = freq_action[local_pos,cloud_pos,action] + 1     \n",
    "            reward_list.append(reward)\n",
    "            reward_sum_list.append(reward_sum/count)\n",
    "        reward_sum_avg_list = reward_sum_avg_list + np.array(reward_sum_list)\n",
    "    return reward_list,reward_sum_list,reward_sum_avg_list/runs,local_actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x267991a5e10>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 5000\n",
    "r_list_q,r_sum_list_q,r_sum_avg_list_q,local_actions_q = Server_Q_learning(N)\n",
    "plt.plot(-r_sum_avg_list_q)\n"
   ]
  },
  {
   "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
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