Queueing Theory

Abstract

In this chapter, we will consider continuous-time and discrete-state stochastic processes, X(t), t ≥ 0, where X(t) represents the number of persons in a queueing system at time t. We suppose that the customers who arrive in the system come to receive some service or to perform a certain task (for example, to withdraw money from an automated teller machine). There can be one or many servers or service stations. The process X(t),t ≥ 0 is a model for a queue or a queueing phenomenon. If we want to be precise, the queue should designate the customers who are waiting to be served, that is, who are queueing, while the queueing system includes all the customers in the system. Since queue is the standard expression for this type of process, we will use these two expressions interchangeably. Moreover, it is clear that the queueing models do not apply only to the case when we are interested in the number of persons who are waiting in line. The customers in the system may be, for example, airplanes that are landing or are waiting for the landing authorization, or machines that have been sent to a repair shop, etc.