An $M^{[X]}/G(a,b)/1$ Queueing System with Breakdown and Second Optional Repair, Stand-by Server, Balking, Variant Arrival Rate and Multiple Vacation

Abstract

In this paper, we discussed a Non-Markovian batch arrival general bulk service single server queueing system with server's breakdown and second optional repair, stand-by server, balking, variant arrival rate and multiple vacation. The main server's service time, vacation time, stand-by server's service time are all follows general distributions and breakdown and two types of repair time for main server follows exponential distributions. There is a stand-by server which is employed during the period for which the regular server remains under repair. The probability generating function of queue size at an arbitrary time and some performance measures of the system are derived. Extensive numerical results are also illustrated.