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The main queueing models that can be used are the single-server waiting line system and the multiple-server waiting line system, which are discussed further below. These models can be further differentiated depending on whether service times are constant or undefined, the queue length is finite, the calling population is finite, etc. [ 5 ]
In queueing theory, a discipline within the mathematical theory of probability, a BCMP network is a class of queueing network for which a product-form equilibrium distribution exists. It is named after the authors of the paper where the network was first described: Baskett, Chandy, Muntz, and Palacios.
In queueing theory, a discipline within the mathematical theory of probability, Burke's theorem (sometimes the Burke's output theorem [1]) is a theorem (stated and demonstrated by Paul J. Burke while working at Bell Telephone Laboratories) asserting that, for the M/M/1 queue, M/M/c queue or M/M/∞ queue in the steady state with arrivals is a Poisson process with rate parameter λ:
In queueing theory, a discipline within the mathematical theory of probability, the backpressure routing algorithm is a method for directing traffic around a queueing network that achieves maximum network throughput, [1] which is established using concepts of Lyapunov drift. Backpressure routing considers the situation where each job can visit ...
In most queuing systems, service time is the bottleneck that creates the queue. [3] The result applies to any system, and particularly, it applies to systems within systems. [4] For example in a bank branch, the customer line might be one subsystem, and each of the tellers another subsystem, and Little's result could be applied to each one, as ...
In queueing theory, a discipline within the mathematical theory of probability, the flow-equivalent server method (also known as flow-equivalent aggregation technique, [1] Norton's theorem for queueing networks or the Chandy–Herzog–Woo method [2]) is a divide-and-conquer method to solve product form queueing networks inspired by Norton's theorem for electrical circuits. [3]
The formula was derived by Agner Krarup Erlang and is not limited to telephone networks, since it describes a probability in a queuing system (albeit a special case with a number of servers but no queueing space for incoming calls to wait for a free server). Hence, the formula is also used in certain inventory systems with lost sales.
In queueing theory, a discipline within the mathematical theory of probability, the Pollaczek–Khinchine formula states a relationship between the queue length and service time distribution Laplace transforms for an M/G/1 queue (where jobs arrive according to a Poisson process and have general service time distribution). The term is also used ...