Single Server Bulk Queue with Service Interruption, Two Phase Repairs and State Dependent Rates

This paper reports a study on a single server queue with bulk arrival and bulk service patterns wherein the incoming traffic depends on the state of the server which may be in operating or breakdown state. The repair of the breakdown server is performed in two phases. The operating duration of server, repair duration of both phases of repairing as well as job's inter-arrival times and service times are exponentially distributed. By using generating function approach, the transient analysis for the queue size distribution has been carried out. For steady state, the stability condition and average queue length for various states have been derived. By taking a numerical illustration, the effect of various parameters on the average queue length has been depicted graphically.

Keywords:

Bulk Queue , Breakdown , Phase Repairs , State Dependent Rates , Generating Functions , Queue Length