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

Daryl J. Daley · L. D. Servi

29 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

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.

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References

1983The Single Server Queue 1956On the Characteristics of the General Queueing Process, with Applications to Random Walk 1968The serial correlation coefficients of waiting times in a stationary single server queue 1985The busy period of the queueing system M/G/∞1983The Single Server Queue, Revised Edition 1973Some general results for many server queues

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