Journal of Applied Probability

Idle and busy periods in stable M/M/k queues

D. J. Daley and L. D. Servi

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This paper finds the first and second moments of the number of arrivals in a stable M/M/k queue during an idle period, i.e. in a period when at least one server is idle. These and similar results are used along with renewal theory asymptotics to find the first and second moments of the proportion of arrivals occurring while there are at least ξ customers waiting for service. The asymptotics of the second moment for large ξ are established.

Article information

J. Appl. Probab. Volume 35, Number 4 (1998), 950-962.

First available in Project Euclid: 19 September 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 60K25: Queueing theory [See also 68M20, 90B22]

Many-server queue busy period idle period


Daley, D. J.; Servi, L. D. Idle and busy periods in stable M / M / k queues. J. Appl. Probab. 35 (1998), no. 4, 950--962. doi:10.1239/jap/1032438390.

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