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

Abstract

<span>A single server provides service to all arriving customers with service</span><br /><span>time following general distribution. After every service completion the</span><br /><span>server has the option to leave for phase one vacation of random length</span><br /><span>with probability p or continue to stay in the system with probability</span><br /><span>1 􀀀 p. As soon as the completion of phase one vacation, the server</span><br /><span>may take phase two vacation with probability q or to remain in the</span><br /><span>system with probability 1􀀀q, after phase two vacation again the server</span><br /><span>has the option to take phase three vacation with probability r or to</span><br /><span>remain in the system with probability 1 􀀀 r. The vacation times are</span><br /><span>assumed to be general. The server is interrupted at random and the</span><br /><span>duration of attending interruption follows exponential distribution. Also</span><br /><span>we assume, the customer whose service is interrupted goes back to the</span><br /><span>head of the queue where the arrivals are Poisson. The time dependent</span><br /><span>probability generating functions have been obtained in terms of their</span><br /><span>Laplace transforms and the corresponding steady state results have been</span><br /><span>obtained explicitly. Also the mean number of customers in the queue</span><br /><span>and system and the waiting time in the queue and system are also</span><br /><span>derived. Particular cases and numerical results are discussed.</span>