An MX/G/1 queueing system with disasters and repairs under a multiple adapted vacation policy

Document Type

Article

Publication Date

4-1-2015

Abstract

We consider a queueing system with batch Poisson arrivals subject to disasters which occur independently according to a Poisson process but affect the system only when the server is busy, in which case the system is cleared of all customers. Following a disaster that affects the system, the server initiates a repair period during which arriving customers accumulate without receiving service. The server operates under a Multiple Adapted Vacation policy. The stationary regime of this process is analyzed using the supplementary variables method. We obtain the probability generating function of the number of customers in the system, the fraction of customers who complete service, and the Laplace transform of the system time of a typical customer in stationarity. The stability condition for the system and the Laplace transform of the time between two consecutive disasters affecting the system is obtained by analyzing an embedded Markov renewal process. The statistical characteristics of the batches that complete service without being affected by disasters and those of the partially served batches are also derived.

Identifier

84928107764 (Scopus)

Publication Title

Naval Research Logistics

External Full Text Location

https://doi.org/10.1002/nav.21621

e-ISSN

15206750

ISSN

0894069X

First Page

171

Last Page

189

Issue

3

Volume

62

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