A note on a bulk arrivals quorum queuing system with an unreliable server

This paper considers a service system with bulk service and an unreliable server, generalising the work of Tadj and Choudhury [Applied Mathematics Letters, 22 (2009) 1710-1714]. While Tadj and Choudhury assume single arrivals, we allow arrivals to occur in bulk, which increases the analytical challenge. The first objective is to derive the probability generating function of the number of customers in the system at a service completion epoch and at an arbitrary instant of time as well as the performance characteristics of the system. The second objective is to develop an optimal management policy to obtain the optimal value of the parameter which minimises a suitable cost structure. This model is useful in different real-world operational management problems to minimise the organisation costs while keeping a high customer satisfaction level.