Monotonicity and stochastic bounds for simultaneous service multiserver systems

Abstract

A multiserver model with simultaneous service (cluster model) is considered. The monotonicity properties of the workload process and the queue-size process in this model are established. In addition, two-sided bounds of the workload process are proved. Moreover, the tightness of the difference of the components of workload process is proved. A key ingredient of the analysis is a modification of the well-known Kiefer-Wolfowitz recursion. The obtained results generalize the results known for classical multiserver system. These results are formulated as stochastic inequalities between the basic queueing processes in the cluster models with ordered predefined governing distributions. The results can be useful for stability analysis.