Queuing Theory

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Queuing Theory is the mathematical study of waiting lines (or queues). 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.

Queuing 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, healthcare, public service and engineering. Applications are frequently encountered in customer service situations as well as transport and telecommunication. Queuing theory is directly applicable to intelligent transportation systems, call centers, PABXs, networks, telecommunications, server queuing, and mainframe computer queuing of telecommunications terminals, advanced telecommunications systems, and traffic flow. 

Notation for describing the characteristics of a queuing model was first suggested by David G. Kendall in 1953. Kendall’s notation introduced an A/B/C queuing notation that can be found in all standard modern works on queuing theory.

The A/B/C notation designates a queuing system having A as interracial time distribution, B as service time distribution, and C as number of servers. For example, “G/D/1” would indicate a General (may be anything) arrival process, a Deterministic (constant time) service process and a single server. More details on this notation are given in the article about queuing models. 

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