Transient state analysis of the queueing system Ek/Ma,b/1/N

The queueing system Ek/M^a,b/1/N with finite waiting space is the modification of the system studied by Kambo and Chaudhry with infinite waiting space. Bulk service is governed by a general rule: service begins only when a units (quorum) are present. If the queue length is a but ≤ b then entire queue is taken up for service; if there are more than b units in queue then the server accepts first b units. This rule was first discussed by Neuts and then by Holman and others. Borthakur studied the busy-period distribution for the system M^x/G^a,b/1 and obtained its Laplace transform. Our interest here is to discuss the distribution of the busy period for the same system with finite waiting space. We obtain the Laplace transform of pdf of the busy period.