Unreliable bulk queueing model with optional services, Bernoulli vacation schedule and balking

This paper deals with MX/G/1 queueing system in which arriving units join a single waiting line. Server provides the first essential service and one of the optional services among m available optional services, to all arriving units. After completion of both phases of services of each unit the server may take optional vacation with probability p. It is assumed that during any phase of service, server may stop working due to random failure and is sent for repair. Further it is assumed that arriving units may balk from the system when server is busy, vacation and under repair with probability -b = 1 – b. Using the probability generating functions we derive the queue size distribution at different time points as well as waiting time distribution. Finally numerical illustration is provided to analyse the sensitivity of different parameters on various performance measures.