The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service

A. Krishnamoorthy, Suresh Babu and Viswanath C. Narayanan

European Journal of Operational Research, 2009, vol. 195, issue 1, 174-185

Abstract: Customers arriving according to a Markovian arrival process are served at a single server facility. Waiting customers generate priority at a constant rate [gamma]; such a customer waits in a waiting space of capacity 1 if this waiting space is not already occupied by a priority generated customer; else it leaves the system. A customer in service will be completely served before the priority generated customer is taken for service (non-preemptive service discipline). Only one priority generated customer can wait at a time and a customer generating into priority at that time will have to leave the system in search of emergency service elsewhere. The service times of ordinary and priority generated customers follow PH-distributions. The matrix analytic method is used to compute the steady state distribution. Performance measures such as the probability of n consecutive services of priority generated customers, the probability of the same for ordinary customers, and the mean waiting time of a tagged customer are found by approximating them by their corresponding values in a truncated system. All these results are supported numerically.

Keywords: Self-generation; of; priorities; Non-preemptive; service; Markovian; arrival; process; PH-distribution; Matrix; analytic; method (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:195:y:2009:i:1:p:174-185

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