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    "########################################################################\n",
    "########################################################################\n",
    "#\n",
    "# Queue.py\n",
    "# Simulate a queue where people arrive randomly with an average time of\n",
    "# X seconds between people and are dealt with in Y seconds on average\n",
    "# Use a loop with a 1 second step in the simulation\n",
    "#\n",
    "# Print the maximum wait that any one of 1000 simulated people had\n",
    "# Note this solution uses numpy to generate distrubibutions, you can\n",
    "# also \"math\" functions and \"random\" functions (import math,random)\n",
    "#\n",
    "########################################################################\n",
    "########################################################################\n",
    "\n",
    "X = 10 # starting value, can be adjusted\n",
    "Y = 7  # starting value, can be adjusted\n",
    "nPerson = 1000 # number of people to simulate, stop when all dealt with\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "def timeToNext(beta):\n",
    "    \"\"\"Return time to next person, input is beta = 1/(average arrival rate)\"\"\"\n",
    "    # functional form of time to next person if ac is the average arrival time\n",
    "    # is p(t) = 1/beta * exp(- t / beta )\n",
    "    # where beta = beta\n",
    "    # np.random.exponential uses scale = beta\n",
    "    # https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.random.exponential.html\n",
    "    ranExp = np.random.exponential(scale = beta, size=1)\n",
    "    return int(ranExp) # note forcing integer times here to simplify\n",
    "\n",
    "def addAPerson(t,q):\n",
    "    \"\"\" Function to add a person to the queue with average time between people = X\"\"\"\n",
    "    # t = time added\n",
    "    # q = your queue\n",
    "    pass # write your function here\n",
    "\n",
    "def removeAPerson(t,q):\n",
    "    \"\"\"Function to remove a person how has been dealt with, return time they waited\"\"\"\n",
    "    # t = time removed\n",
    "    # q = your queue\n",
    "    return 0 #your function here, return time waited\n",
    "\n",
    "def arriveTimesArray(n,dt):\n",
    "    \"\"\"Return a numpy array of integers, which are the times each person will arrive\"\"\"    \n",
    "    return 0 # return the array here\n",
    "\n",
    "def timerLoop(X,Y):\n",
    "    \"\"\"Run a loop to add and remove people as required\"\"\"\n",
    "    arriveTimes = arriveTimesArray(nPerson,X)\n",
    "    # queue\n",
    "    q = []\n",
    "    # waied times\n",
    "    wait = []\n",
    "    ## loop over the times from 0 -> ... in steps of 1s \n",
    "    ## until there are no people to arrive and noone in the queue\n",
    "    ## store the time each person waited in the \"wait\" array as an integer\n",
    "    #\n",
    "    # np.max is the maximum of an array, np.mean is the average\n",
    "    print(\"Max time waited was {}s average {}s\".format(np.max(wait),np.mean(wait)))\n",
    "\n",
    "timerLoop(X,Y)\n",
    "print(\"\\nOnce this works try rerunning with different arrival times and processing times\\ntimerLoop(10,7) # default values\")\n",
    "\n",
    "\n"
   ]
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