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Simulate Different Types of Queues

    
Simulate an M/M/1 queue in which customers arrive at the rate of three per hour and are served at the rate of five per hour:
Wolfram Language code: data = RandomFunction[QueueingProcess[3, 5], {0, 20}]
Since the arrival rate is less than the service rate, the system reaches a steady state:
Wolfram Language code: ListLinePlot[data, InterpolationOrder -> 0, Filling -> Axis]
If the arrival rate is greater than the service rate, then the system does not reach a steady state:
Wolfram Language code: data = RandomFunction[QueueingProcess[5, 3], {0, 150}];
Wolfram Language code: ListLinePlot[data, Filling -> Axis]
Simulate a queueing system that can hold only 12 customers:
Wolfram Language code: data = RandomFunction[QueueingProcess[6, 6.1, 1, 12], {0, 150}];
Wolfram Language code: ListLinePlot[data, Filling -> Axis]
Simulate a queue with 20 customers in the initial state:
Wolfram Language code: data = RandomFunction[QueueingProcess[2, 3, 1, ∞, 20], {0, 80}];
Wolfram Language code: ListLinePlot[data, InterpolationOrder -> 0, Filling -> Axis, PlotRange -> All]