Single server queue simulation

queue.py

import random
import numpy as np
# for graphing
from mpl_toolkits.mplot3d.axes3d import Axes3D
import matplotlib.pyplot as plt

if __name__ == "__main__":
    # setting up scatterplot
    Xa = []
    Ya = []
    Za = []
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    # iterate through various lambda variables
    for lambd_in in np.arange(0.2,2,0.1):
        for lambd_out in np.arange(0.2,2,0.1):
            #  define and initialize queue variables
            T = 1000            # 'closing' time
            t = 0               # time variable
            na = 0              # number of arrivals (by time t)
            nd = 0              # number of departures (by time t)
            n = 0               # number of customers in the system at time t
            td = float('inf')   # service completion time of the customer presently being served
            ta = random.expovariate(lambd_in)  # time of the next arrival (after t)
            D = []              # list of departure times
            A = []              # list of customer arrival times
            Tp = 0              # time past T that the last customer departs
            max_line_length = 0 # maximum line length

            while t < T or n > 0:
                # case 1 - arrival before next departure
                if ta <= td and ta <= T:
                    t = ta      # move along to time ta
                    na += 1     # one additional arrival
                    n += 1      # one additional customer
                    # generate time of next arrival
                    ta = random.expovariate(lambd_in) + t
                    # generate time of departure if queue has been empty
                    if n == 1:
                        Y = random.expovariate(lambd_out)
                        td = t + Y
                    A.append(t)
                    # print("Arrival ", na, "at time ", t)

                #case 2 - departure before next arrival
                elif td < ta and td <= T:
                    # advance time to next departure
                    t = td
                    # one less person in line
                    n -= 1
                    # one more person served
                    nd += 1
                    # if queue is empty, infinite time of next departure
                    if n == 0:
                        td = float('inf')
                    # if queue isn't empty, generate next time of departure
                    else:
                        Y = random.expovariate(lambd_out)
                        td = t + Y
                    D.append(t)
                    # print("Departure ", nd, "at time ", t)

                # case 3 - next arrival/departure happens after closing time and there are people still in queue
                elif min(ta, td) > T and n > 0:
                    # advance time to next departure
                    t = td
                    # one less person in line
                    n -= 1
                    # one more person served
                    nd += 1
                    # if line isn't empty, generate time of next departure
                    if n > 0:
                        Y = random.expovariate(lambd_out)
                        td = t + Y
                    D.append(t)
                    # print("Departure ", nd, "at time ", t)

                # case 4 - next arrival/departure happens after closing time and there is nobody left in the queue
                elif min(ta, td) > T and n == 0:
                    # calculate overtime
                    Tp = max(t-T, 0)
                    break
                # update max_line_length
                if n > max_line_length:
                    max_line_length = n
            # save statistics to be graphed later
            Xa.append(lambd_in)
            Ya.append(lambd_out)
            Za.append(max_line_length)
    # display graph
    ax.scatter(Xa, Ya, Za, c='r', marker='o')
    ax.set_xlabel('Arrival Lambda')
    ax.set_ylabel('Departure Lambda')
    ax.set_zlabel('Maximum Line Length')
    plt.show()