A Quorum Queueing System with a Random Setup Time under N-policy and with Bernoulli Vacation Schedule

We aim in this paper at designing an optimal management policy for a bulk service queueing system with random set-up time under Bernoulli vacation schedule and N-policy. We first study the discrete time parameter and continuous time parameter stochastic processes and derive all the quantities required to build a linear cost structure. Then an algorithm is suggested to determine the optimal management policy. An illustrative example is presented to show how to implement this policy and a sensitivity analysis is conducted to determine the effect of the system parameters.