A NON-MARKOVIAN BATCH ARRIVAL QUEUE WITH SERVICE INTERRUPTION AND EXTENDED SERVER VACATION

Subject Areas : International Journal of Mathematical Modelling & Computations

G. Ayyappan ¹ , K. Sathiya ²

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Received: 2016-04-15 Accepted : 2016-04-15 Published : 2015-03-21

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Abstract :

A single server provides service to all arriving customers with servicetime following general distribution. After every service completion theserver has the option to leave for phase one vacation of random lengthwith probability p or continue to stay in the system with probability1 􀀀 p. As soon as the completion of phase one vacation, the servermay take phase two vacation with probability q or to remain in thesystem with probability 1􀀀q, after phase two vacation again the serverhas the option to take phase three vacation with probability r or toremain in the system with probability 1 􀀀 r. The vacation times areassumed to be general. The server is interrupted at random and theduration of attending interruption follows exponential distribution. Alsowe assume, the customer whose service is interrupted goes back to thehead of the queue where the arrivals are Poisson. The time dependentprobability generating functions have been obtained in terms of theirLaplace transforms and the corresponding steady state results have beenobtained explicitly. Also the mean number of customers in the queueand system and the waiting time in the queue and system are alsoderived. Particular cases and numerical results are discussed.