On a new formula for the transient state probabilities for M/M/1 queues and computational implications

On a new formula for the transient state probabilities for M/M/1 queues and computational implications

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Article ID: iaor1994342
Country: Israel
Volume: 30
Issue: 1
Start Page Number: 237
End Page Number: 246
Publication Date: Mar 1993
Journal: Journal of Applied Probability
Authors: ,
Abstract:

Past work relating to the computation of time-dependent state probabilities in M/M/1 queueing systems is reviewed, with emphasis on methods that avoid Bessel functions. A new series formula of Sharma is discussed and is connected with traditional Bessel function series is established. An alternative new series is developed which isolates the steady-state component for all values of traffic intensity and which turns out to be computationally superior. A brief comparison of the present formula, Sharma’s formula, and a classical Bessel function formula is given for the computational time of the probability that an initially empty system is empty at time t later.

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