{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from heapq import heappush, heappop\n",
    "import random\n",
    "from scipy.special import factorial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Stats:\n",
    "    def __init__(self, sim):\n",
    "        self.sim = sim\n",
    "        self.waiting_time = 0.0\n",
    "        self.servicing_time = 0.0\n",
    "        \n",
    "    def avg_wait_time(self):\n",
    "        return self.waiting_time / self.sim.t\n",
    "    \n",
    "    def avg_service_time(self):\n",
    "        return self.servicing_time / self.sim.t\n",
    "    \n",
    "    def avg_system_time(self):\n",
    "        return (self.waiting_time + self.servicing_time) / self.sim.t\n",
    "    \n",
    "    def prb_empty(self):\n",
    "        c = self.sim.servers\n",
    "        rho = self.sim.arrival_rate / self.sim.service_rate\n",
    "        if self.sim.servers == 1:\n",
    "            return 1.0 - rho\n",
    "        return 1 / (sum(rho**n/factorial(n) for n in range(0, c)) +\n",
    "                    rho**c/factorial(c) * 1/(1-rho/c))\n",
    "    \n",
    "    def exp_wait_time(self):\n",
    "        c = self.sim.servers\n",
    "        if c == 1:\n",
    "            return self.exp_system_time() - self.exp_service_time()\n",
    "        rho = self.sim.arrival_rate / self.sim.service_rate\n",
    "        return self.prb_empty()*rho**(c+1) / (factorial(c-1)*(c-rho)**2)\n",
    "    \n",
    "    def exp_service_time(self):\n",
    "        c = self.sim.servers\n",
    "        rho = self.sim.arrival_rate / self.sim.service_rate\n",
    "        if c == 1:\n",
    "            return rho\n",
    "        return self.exp_system_time() - self.exp_wait_time()\n",
    "    \n",
    "    def exp_system_time(self):\n",
    "        c = self.sim.servers\n",
    "        rho = self.sim.arrival_rate / self.sim.service_rate\n",
    "        if c == 1:\n",
    "            return rho / (1 - rho)\n",
    "        return self.exp_wait_time() + rho\n",
    "    \n",
    "    def show(self):\n",
    "        summaries = [\n",
    "            'avg_wait_time',\n",
    "            'exp_wait_time',\n",
    "            'avg_service_time',\n",
    "            'exp_service_time',\n",
    "            'avg_system_time',\n",
    "            'exp_system_time',\n",
    "        ]\n",
    "        for s in summaries:\n",
    "            print('{} {:.2f}'.format(s, getattr(self, s)()))\n",
    "\n",
    "class Sim:\n",
    "    def __init__(self, arrival_rate, service_rate, servers, debug=False):\n",
    "        self.arrival_rate = arrival_rate\n",
    "        self.service_rate = service_rate\n",
    "        self.servers = servers\n",
    "        self.debug = debug\n",
    "        \n",
    "        self.t = 0.0\n",
    "        self.events = []\n",
    "        self.waiting = 0\n",
    "        self.servicing = 0\n",
    "        \n",
    "        self.stats = Stats(self)\n",
    "        \n",
    "    def schedule_arrival(self):\n",
    "        delay = random.expovariate(self.arrival_rate)\n",
    "        heappush(self.events, (self.t + delay, 'arrival'))\n",
    "        \n",
    "    def service(self):\n",
    "        assert self.waiting > 0\n",
    "        self.waiting -= 1\n",
    "        self.servicing += 1\n",
    "        delay = random.expovariate(self.service_rate)\n",
    "        heappush(self.events, (self.t + delay, 'serviced'))\n",
    "        \n",
    "    def process_event(self):\n",
    "        t, event = heappop(self.events)\n",
    "        if self.debug:\n",
    "            print(t, event)\n",
    "        self.stats.waiting_time += (t - self.t) * self.waiting\n",
    "        self.stats.servicing_time += (t - self.t) * self.servicing\n",
    "        self.t = t\n",
    "        if event == 'arrival':\n",
    "            self.waiting += 1\n",
    "            self.schedule_arrival()\n",
    "            if self.servicing < self.servers:\n",
    "                self.service()\n",
    "        elif event == 'serviced':\n",
    "            assert self.servicing > 0\n",
    "            self.servicing -= 1\n",
    "            if self.waiting > 0:\n",
    "                self.service()\n",
    "                \n",
    "    def simulate(self, duration):\n",
    "        self.schedule_arrival()\n",
    "        while self.t < duration:\n",
    "            self.process_event()\n",
    "        return self.stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "avg_wait_time 0.90\n",
      "exp_wait_time 0.90\n",
      "avg_service_time 0.60\n",
      "exp_service_time 0.60\n",
      "avg_system_time 1.50\n",
      "exp_system_time 1.50\n"
     ]
    }
   ],
   "source": [
    "Sim(arrival_rate=0.6, service_rate=1.0, servers=1).simulate(1e6).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "avg_wait_time 0.09\n",
      "exp_wait_time 0.09\n",
      "avg_service_time 1.20\n",
      "exp_service_time 1.20\n",
      "avg_system_time 1.29\n",
      "exp_system_time 1.29\n"
     ]
    }
   ],
   "source": [
    "Sim(arrival_rate=0.6, service_rate=0.5, servers=3).simulate(1e6).show()"
   ]
  }
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