Cost analysis of a bulk service retrial queue

Abstract

This paper studies a batch arrival general bulk service retrial queueing model with constant retrial rate. The primary customers arrive in bulk according to Poisson process and they get service under general bulk service rule with minimum of one customer and maximum of ‘b’ customers. If the arriving batch of customers, of size ‘ζ ’, 1≤ζ ≤ b , finds the server free, then all of them get service immediately; while, if the size of the arriving batch is more than ‘b’, then, ‘b’ customers enter the service station and the remaining ζ - b customers join the orbit. However, if an arriving batch of customers finds the server busy, then the entire batch joins the orbit in order to seek service again. The customers in the orbit will try for service one by one with a constant retrial rate ‘v’ when the server is idle. For the proposed model, the probability generating function of the steady-state queue size distribution at an arbitrary time, expected number of customers in the orbit, expected waiting time, expected length of busy period and expected length of busy cycle are obtained. The cost analysis of the queueing system is discussed. The effects of several parameters on the system are analysed numerically.