There are many examples of single queue systems in daily life. The ATM machine in the shopping mall is such an example. The ATM machine acts as a single server serving a single queue. A single line of people waiting to get money may form in front of the machine. If people are well-behaved, they will use the ATM machine on a First Come First Serve (FCFS) basis, patiently waiting in line to receive service. This is an example of a single server, single queue system, with a FCFS queuing discipline.
This chapter explores some important classical analytic results for single queue systems. These results are shown to be useful in modern computer system situations. The term queuing station is used broadly here to indicate a collection of one or more waiting lines along with a server or collection of servers that provide service to these waiting lines. Examples of queuing stations discussed in this chapter include: 1) a single waiting line and a single server, 2) multiple waiting lines (arranged by priority) and a single server, and 3) a single waiting line and multiple servers. When the context is clear, the terms "queue" and "queuing station" are used interchangeably. All results presented in this chapter assume that FCFS is the queuing discipline in all waiting lines. The following chapters deal with situations in which queuing stations are connected to one another to form a Queuing Network.
The results discussed in this chapter are implemented in the Ch11-SingleQueues.XLS MS Excel workbook. This chapter is not intended to provide a comprehensive treatment of single queue systems. More comprehensive surveys and results appear elsewhere [1, 2, 3, 4]. The goal here is to summarize and apply the key results of single queue systems to performance design issues.