Exact results for the distribution of the partial busy period for a multi-server queue

Josef Zuk () and David Kirszenblat ()
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Josef Zuk: Defence Science and Technology Group
David Kirszenblat: Defence Science and Technology Group

Queueing Systems: Theory and Applications, 2024, vol. 107, issue 1, No 3, 63-108

Abstract: Abstract Exact explicit results are derived for the distribution of the partial busy period of the M/M/c multi-server queue for a general number of servers. A rudimentary spectral method leads to a representation that is amenable to efficient numerical computation across the entire ergodic region. An alternative algebraic approach yields a representation as a finite sum of Marcum Q-functions depending on the roots of certain polynomials that are explicitly determined for an arbitrary number of servers. Asymptotic forms are derived in the limit of a large number of servers under two scaling regimes, and also for the large-time limit. Connections are made with previous work. The present work is the first to offer tangible exact results for the distribution when the number of servers is greater than two.

Keywords: Partial busy period; Multi-server queues; Markovian queue; Spectral decomposition (search for similar items in EconPapers)
JEL-codes: C44 C63 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-024-09906-1

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