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A note on the waiting time in M[X]/G/1 queueing systems with a removable server

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Jacqueline Loris-Teghem
Jacqueline Loris-Teghem*
Affiliation:
Université de Mons-Hainaut
*
∗ Postal address: Centre de Recherche Warocqué, Place du Parc, 20-B7000 Mons, Belgium. Email address: [email protected]
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Abstract

For the M[X]/G/1 queueing model with a general exhaustive-service vacation policy, it has been proved that the Laplace-Stieltjes transform (LST) of the steady-state distribution function of the waiting time of a customer arriving while the server is active is the product of the corresponding LST in the bulk arrival model with unremovable server and another LST. The expression given for the latter, however, is valid only under the assumption that the number of groups arriving in an inactive phase is independent of the sizes of the groups. We here give an expression which holds in the general case. For the N-policy case, we also give an expression for the LST of the steady-state distribution function of the waiting time of a customer arriving while the server is inactive.

Keywords

Bulk arrivalsremovable serverwaiting timedecomposition formula

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 287 - 291
Copyright
Copyright © Applied Probability Trust 2004 

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References

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