Simple Markovian Queueing Systems

Abstract

Poisson arrivals and exponential service make queueing models Markovian that are easy to analyze and get useable results. Historically, these are also the models used in the early stages of queueing theory to help decision-making in the telephone industry. The underlying Markov process representing the number of customers in such systems is known as a birth and death process, which is widely used in population models. The birth–death terminology is used to represent increase and decrease in the population size. The corresponding events in queueing systems are arrivals and departures. In this chapter we present some of the important models belonging to this class.