MAP/PH/1 Retrial Queue with Abandonment, Flush Out and Search of Customers

This paper considers a single server retrial queueing system with search, abandonment and flush out of customers from the system (system clearance) periodically with exponentially distributed duration. A customer on arrival, enters for service, if the server is found to be idle and enter into an orbit of infinite capacity if the server is busy. Orbital customers receive service either by successful retrials or by an orbital search. At the epoch of completion of a service, sever goes for search with probability p as long as the orbit size is atmost L-1. Search stops the moment there are L or more customers in the orbit. Further orbital customers are assumed to renege with certain probability on an unsuccessful retrial. In addition, clearance of system takes place each time a random duration following exponential distribution, expires. The customers arrive to the system according to Markovian arrival Process, inter-retrial times are exponentially distributed and service time follows phase type distribution. We analyze the resulting GI/M/1 Type queue. Steady-state analysis of the model is performed. Some performance measures are evaluated.

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