Introduction to Stochastic Processes and Simulation

11Simulation of a Queueing Process

CONCEPTS DISCUSSED IN THIS CHAPTER.– We will begin by defining what is needed to perform simulations of a queueing process, in particular, a list of parameters to consider.

We will then describe the simulation method used for an M/M/1 queue and for an M/M/S queue. We will examine the results obtained by comparing them to the theoretical results.

Recommended reading [PHE 77].

11.1. General provisions

To simulate a queueing process, it is necessary to define the probability laws governing the arrivals of elements and the departures of elements, as well as the number of service stations. We will assume here and in the theoretical part that there is only one queue, regardless of the number of service stations.

The probability distributions are used to calculate the theoretical mean values of the arrival rate λ. For “departure rates” or inverse service times, it is assumed that they are identical for all stations (and also that the same probability distribution applies to stations).

We will then obtain, with the corresponding probability law, the average theoretical service time, 1/μ.

In addition, using a computer requires the use of discrete values for time, not continuous values. For time management, two attitudes are possible:

• – varying the time with regular steps and examining the events that may occur between two consecutive instants;
• – basing the time on the next event and therefore proceeding in stages based on the events.

In what follows, ...