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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Abstract

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

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

Dates
First available: 19 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.jap/1032438390

Digital Object Identifier
doi:10.1239/jap/1032438390

Mathematical Reviews number (MathSciNet)
MR1671245

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

Keywords
Many-server queue busy period idle period

Citation

Daley, D. J.; Servi, L. D. Idle and busy periods in stable M / M / k queues. Journal of Applied Probability 35 (1998), no. 4, 950--962. doi:10.1239/jap/1032438390. http://projecteuclid.org/euclid.jap/1032438390.


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