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M/M/1 Two-Phase Gated Queueing System with Unreliable Server and State Dependent Arrivals

Author(s): S. Hanumantha Rao, V. Vasanta Kumar, T. Srinivasa Rao and B. Srinivasa Kumar

In this paper, we analyze an N-policy, two-phase queueing system where the service station is subject to breakdowns while in operation and repair may delayed due to non-availability of the repair facility. Arrivals follow a Poisson process with rates depending upon the system state namely-vacation, startup, operational and breakdown state. The service is in two essential phases; the first one being batch service to all the customers waiting in the queue and the second one is individual to each of them. The server is turned off each time the system empties. As and when the total number of customers in the system reaches the threshold N(N ≥1), the server is turned on and requires preparatory time before starting the batch service. The customers who arrive during batch service are not allowed to join the batch, which is in service, but are bunched together and are served along with the other arrivals during the next visit of the server to the batch queue. Startup times, uninterrupted service times, length of each delay period and repair period follows exponential distribution. Closed form expressions for the mean system size at various states of the server are derived. Effect of the system parameters on the optimal threshold N is studied through numerical examples.

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