Document Type

Article

Publication Date

2013

Publication Title

Mathematica Applicanda

Abstract

In this paper we study a multi-server queueing model in which the customer arrive according to a Markovian arrival process. The customers may require, with a certain probability, an optional secondary service upon completion of a primary service. The secondary services are offered (in batches of varying size) when any of the following conditions holds good: (a) upon completion of a service a free server finds no primary customer waiting in the queue and there is at least one secondary customer (including possibly the primary customer becoming a secondary customer) waiting for service; (b) upon completion of a primary service, the customer requires a secondary service and at that time the number of customers needing a secondary service hits a pre-determined threshold value; (c) a server returning from a vacation finds no primary customer but at least one secondary customer waiting. The servers take vacation when there are no customers (either primary or secondary) waiting to receive service. The model is studied as a QBD-process using matrix-analytic methods and some illustrative examples arediscussed.

Volume

41

Issue

2

First Page

145

Last Page

169

DOI

10.14708/ma.v41i2.389

ISSN

1730-2668 (print), 2299-4009 (electronic)

Rights

© 2013 Polskie Towarzystwo Matematyczne and simultaneously licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.

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