Basic Terminology of Queueing Theory

Terminology for study of queueing systems tends to be fairly standard. Some variation sometimes occurs, and where there are popular alternative forms of terminology, this will be made clear.

The three main concepts in queueing theory are customers, queues, and servers (service mechanisms). The meaning of these terms is reasonably self-evident. In general, in a queueing system, customers for the queueing system are generated by an input source. The customers are generated according to a statistical distribution (at least, that is the simplifying assumption made for modelling purposes) and the distribution describes their interarrival times, in other words, the times between arrivals of customers. The customers join a queue. At various times, customers are selected for service by the server (service mechanism). The basis on which the customers are selected is called the queue discipline. The head of the queue is the customer who arrived in the queue first. Another piece of terminology which is sometimes used is the tail of the queue. The meaning of this varies depends upon the context and the source. It normally means either all of the queue except the head or the last item in the queue, in other words the customer who arrived last and is at the back of the queue. Both uses are in common usage, and the terminology front and back of the queue will be used to describe the customers who arrived least recently and most recently (respectively) to avoid ambiguity.

We will now look at each of these pieces of terminology in more detail.

Input Source

The input source is a population of individuals, and as such is called the calling population. The calling population has a size, which is the number of potential customers to the system. The size can either be finite or infinite. As will become apparent, if the calling population is infinite, various simplifying assumptions can be made which make the process of modelling queues much easier. Most queueing models assume that the population is infinite.


Queues can be either infinite or finite. If a queue is finite, it can only hold a limited number of customers. Most queueing models assume an infinite queue, even though this is almost certainly not strictly true in the majority of applications of queueing theory. This assumption is made because it makes the modelling process simpler. Also, if the maximum queue size is significantly larger than the likely number of customers at any one time, then to all intents and purposes it is infinite in size. The amount of time which is a customer waits in the queue for is called the queueing time. The number of customers who arrive from the calling population and join the queue in a given period of time is modelled by a statistical distribution.

Queue Discipline

The queue discipline is the method by which customers are selected from the queue for processing by the service mechanisms (also called servers). The queue discipline is normally first-come-first-served (FCFS), where the customers are processed in the order in which they arrived in the queue, such that the head of the queue is always processed next. Most queueing models assume FCFS as the queue discipline, and only this discipline will be considered in any detail in this project. More information on other queueing disciplines is available in the section on queueing theory variations.

Service Mechanism

The service mechanism is the way that customers receive service once they are selected from the front of a queue. A service mechanism is also called a server (in fact, this is the more common terminology). The amount of time which a customer takes to be serviced by the server is called the service time. A statistical distribution is used to model the service time of a server. Some queueing models assume a single server, some multiple servers. For most general analysis, most queueing models assume that the system has either a single server or allow the number of servers to become a variable. This convention will be explored further in the section on Kendall notation.

Last Updated: 14th June 1999
Written by: Andrew Ferrier