ABSTRACT
So far we have only considered single-stage queues. However, in practice, there are several systems where customers go from one station (or stage) to other stations. For example, in a theme park, the various rides are the different stations and customers wait in lines at each station, get served (i.e., go on a ride), and randomly move to other stations. Several engineering systems such as production, computer-communication, and transportation systems can also be modeled as networks of multistage queues. Such networks, which have a queue at each node, are called queueing networks. Just like the single-station case, the analysis of queueing networks also has several nuances to consider, such as multiple classes, scheduling disciplines, and capacity constraints, to name a few. However, as one would expect, the most general case that captures all the nuances is intractable in terms of analytical modeling. To that end, we divide the analysis into two groups, one where exact results are derivable, which is the focus of this chapter, and the other where we rely on approximations (that may or may not be asymptotically exact), which we consider in the next chapter. In addition, for each group, we start with the most basic model and develop some of the generalized classifications.
