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An M X / G /1 queueing system with disasters and repairs under a multiple adapted vacation policy
Author(s) -
Mytalas George C.,
Zazanis Michael A.
Publication year - 2015
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21621
Subject(s) - laplace transform , poisson distribution , poisson process , queueing system , computer science , renewal theory , clearance , service (business) , queueing theory , markov process , process (computing) , markovian arrival process , probability generating function , operations research , compound poisson process , service system , mathematics , statistics , cumulative distribution function , computer network , operating system , probability density function , business , medicine , mathematical analysis , urology , marketing
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. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 171–189, 2015