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Tutorial for Use of Basic Queueing Formulas

Queuing Formulas Contents1 Notation22 Basic Queueing Formulas23 Single-Server Formulas .. Some additional useful facts .. Examples .. 44 Multiple-Server Queues5 Notes prepared by A. Gosavi, Department of Engineering Management and Systems Engineering, Mis-souri S & Notation : mean rate of arrival. It is equal to 1=E[Inter-arrival-Time] whereE[:] denotes theexpectation operator. : mean service rate. It is equal to 1=E[Service-Time]. = = for single server queues: utilization of the server; also the probability that theserver is busy or the probability that someone is being served.

in this tutorial are technically called two-moment approximations, we really only need the mean and the variance, and the calculation of the second moment is not needed. 3 Basic Queueing Formulas Little’s rule provides the following results: L= W;L q= W q; the rst of the above applies to the system and the second to the queue, which is a part of

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