Queueing analysis of state dependent MX/Ga,b/1 queue with balking, multiple vacations of alternate type and setup times

Abstract

A single server queueing system with state dependent Poisson bulk arrival, general bulk service and multiple vacations of alternate type and setup times is studied./The operator provides service in batches according to a general bulk service rule such that the service starts only when a minimum number of units, say a is present in the queue and the maximum service capacity of the batch is b. For the analysis purpose, we introduce a supplementary variable technique and then Laplace transforms and generating functions are used to obtain steady state formulae. The system size distribution and expected length of idle and busy periods are derived. Finally, we establish a condition under which the optimal stationary operating policy is achieved under a linear cost structure. A numerical illustration is provided to examine the effect of parameters on various performance indices.