Transcription of Queuing Formulas - Missouri S&T
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Queuing Formulas - Missouri S&T
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. c: number of servers. Pn: probability that there arencustomers in the system. L: Mean number of customers in the system. Lq: mean number of customers in the queue.
3.2 Some additional useful facts If the random variable X is uniformly distributed with parameters (a;b), where a is the minimum value and b the maximum value, then the mean of X is (a+b)=2 and the variance is (b 2a) 12. For the exponential distribution if the mean if 1= , the variance is 1= 2. When a variable is deterministic, e.g., inter-arrival time is fixed, its variance is zero
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