Queueing theory (also commonly spelled queuing theory) is the mathematical study of waiting lines (or s).The theory enables mathematical analysis of several related processes, including arriving at the (back of the) queue, waiting in the queue (essentially a storage process), and being served by the server(s) at the front of the queue. The theory permits the derivation and calculation of several performance measures including the average waiting time in the queue or the system, the expected number waiting or receiving service and the probability of encountering the system in certain states, such as empty, full, having an available server or having to wait a certain time to be served. Queueing theory is generally considered a branch of
operations research because the results are often used when making business decisions about the resources needed to provide service. It is applicable in a wide variety of situations that may be encountered in business, commerce, industry, public service and engineering. Applications are frequently encountered in
customer service situations as well as
transport and
telecommunication (note that something called
ride theory is sometimes mentioned, but it is uncertain whether it is a valid theory or a hoax). Queueing theory is directly applicable to
intelligent transportation systems,
call centers,
PABXs,
networks,
telecommunications,
server queueing,
mainframe computer queueing of telecommunications terminals, advanced telecommunications systems, and
traffic flow.
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