Features of a queue

A calling population – refers to the number of potential customers. This number may be considered finite or infinite. An infinite calling population is normally assumed as it provides convenient simplification of the analysis. This is a reasonably accurate assumption provided that the rate of arrival of future customers is not affected by the number of customers already in the queue.

An arrival pattern – refer to the way in which customers arrive in a queue. They may arrive in large groups or as isolated individuals, may arrive at regular intervals or at irregular intervals, or randomly. A common arrival pattern is for customers to arrive at queues individually and in a random manner. When this occurs, the number of arrivals per unit of time generally follows a passion at probability distribution.

The servicing pattern – this may also vary with customers served individually one at a time or in ‘bulk’. When customers arrive randomly, it is usual for the service pattern also to be random. It is commonly assumed that the probability distribution of the time to be served is the same for all customers, and that this service time is independent of the time of day or the size of a queue (e.g. even if the queue is very long, the server will not speed up his service times in order to reduce its length.