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The M/M/c queue with mass exodus and mass arrivals when empty

Part of: Special processes Markov processes

Published online by Cambridge University Press:  30 March 2016

Lina Zhang  and
Junping Li
Lina Zhang*
Affiliation:
Central South University
Junping Li*
Affiliation:
Central South University
*
∗Postal address: School of Mathematics and Statistics, Central South University, Changsha, 410075, Hunan Province, P. R. China.
∗Postal address: School of Mathematics and Statistics, Central South University, Changsha, 410075, Hunan Province, P. R. China.
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Abstract

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In this paper we consider an M/M/c queue modified to allow both mass arrivals when the system is empty and the workload to be removed. Properties of queues which terminate when the server becomes idle are firstly developed. Recurrence properties, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no mass exodus. All of these results are then generalized to allow for the removal of the entire workload. In particular, we obtain the Laplace transformation of the transition probability for the absorptive M/M/c queue.

Keywords

M/M/c queueequilibrium distributionidle timequeue sizerecurrence

MSC classification

Primary: 60J35: Transition functions, generators and resolvents
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 4 , December 2015 , pp. 990 - 1002
Copyright
Copyright © Applied Probability Trust 2015 

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