Queues with hyper-poisson arrivals and bulk exponential service
In this paper the time-dependent solution of a queueing system is discussed under the conditions (i) the units arrive according to Hyper-Poisson distribution withl branches (ii) the queue-discipline is ‘first come first served’ (iii) the Service-time distribution is exponential with maximum capacity ofM units being served at one instant. Some results have been obtained when the waiting space is finite; in particular the probability for service to be idle has been obtained. Also for infinite queueing-space case, the expressions for the state probabilities and the mean queuelength under steady state conditions have been found.
KeywordsUnit Circle State Probability Service Facility Service Pattern Generate Function Technique
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