notebooks/Getting Started with Discrete Event Simulation.ipynb

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     "source": [
      "The latest version of this IPython notebook is available at [http://github.com/jckantor/ESTM60203](http://github.com/jckantor/ESTM60203)  for noncommercial use under terms of the [Creative Commons Attribution Noncommericial ShareAlike License (CC BY-NC-SA 4.0)](http://creativecommons.org/licenses/by-nc-sa/4.0/)."
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      "J.C. Kantor (Kantor.1@nd.edu)"
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     "metadata": {},
     "source": [
      "Getting Started with Discrete Event Simulation"
     ]
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    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This [IPython notebook](http://ipython.org/notebook.html) demonstrates elementary use of the [SimPy](http://simpy.readthedocs.org/en/latest/) package for discrete event simulation."
     ]
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    {
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     "source": [
      "Initializations"
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     "metadata": {},
     "source": [
      "SimPy Installation"
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    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!pip install simpy\n",
      "import simpy as simpy\n",
      "#simpy.test()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Requirement already satisfied (use --upgrade to upgrade): simpy in /Users/jeff/anaconda/lib/python2.7/site-packages\r\n",
        "Cleaning up...\r\n"
       ]
      }
     ],
     "prompt_number": 2
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    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Introduction to Modeling with SimPy"
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    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "A Minimal SimPy Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A typical simpy model consists of an environment, processes that create events for the environment to process, and resources. We'll start by setting up an environment and running a simulation. This won't do anything, but it is valid (if useless) simulation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import simpy\n",
      "\n",
      "# create the simulation environment\n",
      "env = simpy.Environment()\n",
      "\n",
      "# run the simulation\n",
      "env.run()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
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    {
     "cell_type": "heading",
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     "metadata": {},
     "source": [
      "Adding a Process"
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An example of a process is a clock that ticks at regular intervals, and at each tick prints a message showing the current time. \n",
      "\n",
      "The clock is a regular python function that executes until it encounters the  `yield env.timeout(tick)` statement. At that point a new event is scheduled for tick time units in the future after which execution will continue.\n",
      "\n",
      "The `env.process(clock(env, 2.0))` statement adds a clock to the simulation environment. The `env.run(until=10)` statement processes the environment 10 simulated time units."
     ]
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     "cell_type": "code",
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     "input": [
      "import simpy\n",
      "\n",
      "# define a clock process\n",
      "def clock(env,tick):\n",
      "    while True:\n",
      "        print \"Time = {:8.6f} minutes\".format(env.now)\n",
      "        yield env.timeout(tick)\n",
      "\n",
      "# create the simulation environment\n",
      "env = simpy.Environment()\n",
      "\n",
      "# add the clock process to the environment. Set the tick interval.\n",
      "env.process(clock(env, 2.0))\n",
      "\n",
      "# run the simulation for a fixed period of time\n",
      "env.run(until=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time = 0.000000 minutes\n",
        "Time = 2.000000 minutes\n",
        "Time = 4.000000 minutes\n",
        "Time = 6.000000 minutes\n",
        "Time = 8.000000 minutes\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Mutliple Instances of a Process"
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     "cell_type": "markdown",
     "metadata": {},
     "source": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import simpy\n",
      "\n",
      "# define a clock process\n",
      "def clock(env,name,tick):\n",
      "    while True:\n",
      "        print \"Clock {:s} ticks. Time = {:8.6f} minutes\".format(name, env.now)\n",
      "        yield env.timeout(tick)\n",
      "\n",
      "# create the simulation environment\n",
      "env = simpy.Environment()\n",
      "\n",
      "# add the clock process to the environment. Set the tick interval.\n",
      "env.process(clock(env, \"A\", 2.0))\n",
      "env.process(clock(env, \"B\", 1.3))\n",
      "\n",
      "# run the simulation for a fixed period of time\n",
      "env.run(until=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Clock A ticks. Time = 0.000000 minutes\n",
        "Clock B ticks. Time = 0.000000 minutes\n",
        "Clock B ticks. Time = 1.300000 minutes\n",
        "Clock A ticks. Time = 2.000000 minutes\n",
        "Clock B ticks. Time = 2.600000 minutes\n",
        "Clock B ticks. Time = 3.900000 minutes\n",
        "Clock A ticks. Time = 4.000000 minutes\n",
        "Clock B ticks. Time = 5.200000 minutes\n",
        "Clock A ticks. Time = 6.000000 minutes\n",
        "Clock B ticks. Time = 6.500000 minutes\n",
        "Clock B ticks. Time = 7.800000 minutes\n",
        "Clock A ticks. Time = 8.000000 minutes\n",
        "Clock B ticks. Time = 9.100000 minutes\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Processes Manage their own State"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import simpy\n",
      "\n",
      "# define a clock process\n",
      "def clock(env,name,tick):\n",
      "    nTicks = 0\n",
      "    while True:\n",
      "        nTicks += 1\n",
      "        print \"Clock {:s}, tick number {:d}. Time = {:8.6f} minutes\".format(name, nTicks, env.now)\n",
      "        yield env.timeout(tick)\n",
      "\n",
      "# create the simulation environment\n",
      "env = simpy.Environment()\n",
      "\n",
      "# add the clock process to the environment. Set the tick interval.\n",
      "env.process(clock(env, \"A\", 2.0))\n",
      "env.process(clock(env, \"B\", 1.3))\n",
      "\n",
      "# run the simulation for a fixed period of time\n",
      "env.run(until=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Clock A, tick number 1. Time = 0.000000 minutes\n",
        "Clock B, tick number 1. Time = 0.000000 minutes\n",
        "Clock B, tick number 2. Time = 1.300000 minutes\n",
        "Clock A, tick number 2. Time = 2.000000 minutes\n",
        "Clock B, tick number 3. Time = 2.600000 minutes\n",
        "Clock B, tick number 4. Time = 3.900000 minutes\n",
        "Clock A, tick number 3. Time = 4.000000 minutes\n",
        "Clock B, tick number 5. Time = 5.200000 minutes\n",
        "Clock A, tick number 4. Time = 6.000000 minutes\n",
        "Clock B, tick number 6. Time = 6.500000 minutes\n",
        "Clock B, tick number 7. Time = 7.800000 minutes\n",
        "Clock A, tick number 5. Time = 8.000000 minutes\n",
        "Clock B, tick number 8. Time = 9.100000 minutes\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Application Examples"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Geometric Brownian Motion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import simpy\n",
      "import random        \n",
      "\n",
      "# geometric brownian motion\n",
      "def gbm(env,name,tick,P,mu,sigma):\n",
      "    t = 0;\n",
      "    while True:\n",
      "        Plog.append(P)\n",
      "        tlog.append(t)\n",
      "        yield env.timeout(tick)\n",
      "        P += P*(mu*tick + sigma*random.normalvariate(0,1)*sqrt(tick))\n",
      "        t += tick\n",
      "    \n",
      "# create the simulation environment\n",
      "env = simpy.Environment()\n",
      "\n",
      "# add the clock process to the environment. Set the tick interval.\n",
      "env.process(gbm_old(env, \"A\", sqrt(1.0/252), 80.0, 0, .3))\n",
      "\n",
      "# run the simulation for a fixed period of time\n",
      "    \n",
      "Plog = []\n",
      "tlog = []\n",
      "env.run(until=10)\n",
      "\n",
      "plot(tlog,Plog)\n",
      "xlabel('Date')\n",
      "ylabel('Price')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 'gbm_old' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-17-bd3b196fecc8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m \u001b[0;31m# add the clock process to the environment. Set the tick interval.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m \u001b[0menv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprocess\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgbm_old\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0menv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"A\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m252\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m80.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m.3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m \u001b[0;31m# run the simulation for a fixed period of time\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mNameError\u001b[0m: name 'gbm_old' is not defined"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import simpy\n",
      "import random\n",
      "\n",
      "class gbm(object):\n",
      "    def __init__(self,env,name,tick,val,mu,sigma):\n",
      "        self.env = env\n",
      "        self.name = name\n",
      "        self.tick = tick\n",
      "        self.val = val\n",
      "        self.mu = mu\n",
      "        self.sigma = sigma\n",
      "        self.t = 0\n",
      "        \n",
      "    def process(self):\n",
      "        while True:\n",
      "            yield self.env.timeout(self.tick)\n",
      "            self.t += self.tick\n",
      "            self.val += self.val*(self.mu*self.tick + self.sigma*random.normalvariate(0,1)*sqrt(self.tick))\n",
      "\n",
      "def reporter(env,tick,gbm):\n",
      "    t = 0\n",
      "    while True:\n",
      "        yield env.timeout(tick)\n",
      "        t += tick\n",
      "        print t, gbm.val\n",
      "\n",
      "env = simpy.Environment()\n",
      "a = gbm(env,'A',1.0/sqrt(12.0),80.0,0,0.30)\n",
      "env.process(a.process())\n",
      "env.process(reporter(env,1.0,a))\n",
      "env.run(until=5)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 'sqrt' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-18-d079aa585dfd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     27\u001b[0m \u001b[0menv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msimpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mEnvironment\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 28\u001b[0;31m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgbm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0menv\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'A'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m12.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m80.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.30\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     29\u001b[0m \u001b[0menv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprocess\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprocess\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[0menv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprocess\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mreporter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0menv\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mNameError\u001b[0m: name 'sqrt' is not defined"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Application"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Setting up a class provides a means of modeling more complex behaviors. Here we'll consider a Roomba cleaning robot that can be either in a running mode or a charging mode."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "class Roomba(object):\n",
      "    def __init__(self,env,name,charge_duration,clean_duration):\n",
      "        self.env = env\n",
      "        self.name = name\n",
      "        self.charge_duration = charge_duration\n",
      "        self.clean_duration = clean_duration\n",
      "        self.proc = env.process(self.run())\n",
      "\n",
      "    def run(self):\n",
      "        while True:\n",
      "            yield env.process(self.charge())\n",
      "            yield env.process(self.clean())\n",
      "    \n",
      "    def clean(self):\n",
      "        print \"{:<3s} start charging at {:4.1f}\".format(self.name,env.now)\n",
      "        yield env.timeout(self.clean_duration)\n",
      "    \n",
      "    def charge(self):\n",
      "        print \"{:<3s} start cleaning at {:4.1f}\".format(self.name,env.now)\n",
      "        yield env.timeout(self.charge_duration)\n",
      "\n",
      "import simpy\n",
      "env = simpy.Environment()\n",
      "\n",
      "A = Roomba(env,'A',1.1,2.3)\n",
      "B = Roomba(env,'B',0.9,3.1)\n",
      "\n",
      "# start processes\n",
      "env.run(until=6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A   start cleaning at  0.0\n",
        "B   start cleaning at  0.0\n",
        "B   start charging at  0.9\n",
        "A   start charging at  1.1\n",
        "A   start cleaning at  3.4\n",
        "B   start cleaning at  4.0\n",
        "A   start charging at  4.5\n",
        "B   start charging at  4.9\n"
       ]
      }
     ],
     "prompt_number": 64
    }
   ],
   "metadata": {}
  }
 ]
}