Mx/G/1 Retrial Queue with Two Phase Repair | Original Article

ABSTRACT:

In this study, we provide the analysis of a single unreliable server batch arrival queue with repair in two phases. The arrival rate of jobs at service station varies according to the server's status as server being idle, busy, under setup and under ith (1=1,2) phase repair. We assume that the jobs which find the server busy or broken down and under repair, leave the service station and join the retrial orbit with some probability. 'The service time taken by the server is general distributed. The server always has the tendency to breakdown and the repairman restores the broken down server in hvo phases. The life time of server is exponentially distributed but the repair in each phase is performed according to general distribution. The queuing analysis has been done using supplementary variable technique and generating function method. Various performance indices are derived in explicit form which can be computed easily as results depend only upon the first two moments of inter-failure times, phase repair times and batch size distributions. The cost analysis has been attempted successfully. Some special cases of interest have been deduced by setting appropriate parameter values. To show the effect of parameters upon various performance characteristics of the system such as mean queue length, probability that the server is idle, busy, under set up, and under phase repair, etc., the sensitivity analysis is carried out by taking numerical illustration.