Markov, Poisson, and Queueing Processes
Charles Therrien, Murali Tummala · 2018
It is seen that many types of random variables encountered earlier are related to this process. The chapter then moves on to develop the discrete form of Markov chain first introduced in Chapter 8. This process is characterized by “states” which determine its future probabilistic behavior, and is a useful model for many physical processes that evolve in time. The Markov and Poisson models are then combined in the continuoustime Markov chain. This random process is also characterized by states, but state transitions may occur randomly at any time (i.e., not at just discrete epochs of time) according to the Poisson model. This combined model is what is necessary to represent the computer and network problems cited above. With these tools and concepts firmly established, the chapter moves on with an introduction to queueing theory. This branch of probability and statistics deals with analysis of these combined systems. Among other things, queueing models provide ways to describe message traffic in a system, to estimate service times and predict delays, and to estimate needed resources (or predict catastrophe) under various operating conditions. The study of modern computer networks requires at least a basic understanding of these types of systems.