Queueing theory

Queueing theory is the mathematical study of waiting lines, or queues.[1] A queueing model is constructed so that queue lengths and waiting time can be predicted.[1] 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 a service.

Queue networks are systems in which single queues are connected by a routing network. In this image, servers are represented by circles, queues by a series of rectangles and the routing network by arrows. In the study of queue networks one typically tries to obtain the equilibrium distribution of the network, although in many applications the study of the transient state is fundamental.

Queueing theory has its origins in research by Agner Krarup Erlang when he created models to describe the system of Copenhagen Telephone Exchange company, a Danish company.[1] The ideas have since seen applications including telecommunication, traffic engineering, computing[2] and, particularly in industrial engineering, in the design of factories, shops, offices and hospitals, as well as in project management.[3][4]


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