Performance Analysis of a Retrial Queueing System with Optional Service, Unreliable Server, Balking and Feedback

Abstract

This paper considers a Markovian retrial queueing system with an optional service, unreliable server, balking and feedback. An arriving customer can avail of immediate service if the server is free. If the potential customer encounters a busy server, it may either join the orbit or balk the system. The customers may retry their request for service from the orbit after a random amount of time. Each customer gets the First Essential Service (FES). After the completion of FES, the customers may seek the Second Optional Service (SOS) or leave the system. In the event of unforeseen circumstances, the server may encounter a breakdown, at which point an immediate repair process will be initiated. After the service completion, the customer may leave the system or re-join the orbit if not satisfied and demand regular service as feedback. In this investigation, the stationary queue size distributions are framed using a recursive approach. Various system performance measures are derived. The effects induced by the system parameters on the performance metrics are numerically and graphically analysed.