Two Heterogeneous Service Queue With Second Optional Repair Subject to Reneging During Compulsory Vacation and Breakdown Time

Abstract

This paper deals with a single server batch arrival queue, two stages of heterogeneous service with different (arbitrary) service time distribution subject to random breakdowns followed by a repair and compulsory server vacations with general (arbitrary) vacation periods. After first stage service the server must provide second stage service. However after the completion of each second stage service the server will take compulsory vacation. The system may breakdown at random and it must be send to repair process immediately. If the server could not be repaired with first essential repair, subsequent repairs are needed for the restoration of the server. Both first essential repair and second optional repair times follow exponential distribution. We consider reneging to occur when the server is unavailable during the system breakdown or vacation periods. The steady state solutions have been found by using supplementary variable technique.