On the distribution of the number of customers in the symmetric M/G/1 queue |
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Authors: | Denis Denisov Artëm Sapozhnikov |
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Institution: | (1) EURANDOM, Eindhoven, The Netherlands;(2) Department of Mathematics/Boole Centre for Research in Informatics, University College Cork, Cork, Ireland |
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Abstract: | We consider an M/G/1 queue with symmetric service discipline. The class of symmetric service disciplines contains, in particular, the preemptive
last-come-first-served discipline and the processor-sharing discipline. It has been conjectured in Kella et al. 1] that the
marginal distribution of the queue length at any time is identical for all symmetric disciplines if the queue starts empty.
In this paper we show that this conjecture is true if service requirements have an Erlang distribution. We also show by a
counterexample, involving the hyperexponential distribution, that the conjecture is generally not true.
AMS Subject Classifications Primary—60K25; Secondary—90B22 |
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Keywords: | Symmetric queue Time-dependent analysis Insensitivity Processor-sharing queue Last come first served queue |
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