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An application of the reflection principle to the transient analysis of the M/M/1 queue

✍ Scribed by Don Towsley

Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
282 KB
Volume
34
Category
Article
ISSN
0894-069X

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✦ Synopsis

This paper applies the well-known reflection principle for random walks to the analysis of the transient MIMI1 queueing system. A closed-form solution is obtained for the probability that exactly i arrivals and j departures occur over an interval of length t in an MIMI1 queueing system that contains n users at the beginning of the interval. The derivation of this probability is based on the calculation of the number of paths between two points in a two-dimensional xy coordinate system that lie above the x axis and touch the x axis exactly r times. This calculation is readily performed through the application of the reflection principle.

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