Analysis of batch arrival cyclic service multiqueue systems with limited service discipline

In this paper, the batch arrival cyclic service multiqueue system is studied. For a compound Poisson arrival cyclic service multiqueue sytem, useful equalities are derived with respect to the weighted sum of the mean waiting times for E-limited and G-limited service disciplines. Using these equalities, the upper bound of the mean waiting time at each queue is derived for symmetric system. Further, for general batch arrival cyclic service multiqueue system, an approximate formula with respect to the weighted sum of the mean waiting times is derived. For symmetric system, this approximate formula reduces to the approximate formula of the mean waiting time for exhaustive, gated, E-limited and G-limited service disciplines. In numerical results, these characteristic quantities are evaluated by comparing those to simulation results and other approximate results.