Analysis of MAP/PH/1 Model with Working Vacation, Working Breakdown and Two-Phase Repair

In this paper, we investigate the single server queueing model where arrival of units is based on Markovian arrival process and service provided by server is in phase type distribution (MAP/PH/1) with working vacation and working breakdown. The study of working vacation and working breakdown is very important and applicable in real life. The absence of a server during vacation or server breakdown due to any reason may cause service interruption in queueing systems. We consider the repair process in two phases to recover the server from breakdown to working state with improved service rate phase-wise. Arrival process is based on Neuts' versatile point process that follows MAP and service times follow phase type distributions. The arrival rate, the service rate, working vacation rate and working breakdown are mutually independent. Matrix geometric solution method is used to obtain stationary probability vectors. Long run probabilities for all the states are derived in the results. Also with the different combination of arrival and service process the flow of average expected length with several parameters have been presented graphically.