Stochastic Convexity for Multidimensional Processes and Its Applications

Consider a multidimensional stochastic process, which is a function of a parametric process. The parametric process may be multidimensional as well. In this paper, we compare two such processes that differ only in their parametric processes. We extend known stochastic convexity results for one-dimensional stochastic processes, which are recently obtained by Shaked and Shanthikumar, to multidimensional processes. These results are used to obtain comparison results for various queueing systems that are subject to different parametric processes, which may be the arrival processes, service processes, etc. Based on these comparison results we show how the performances of queueing systems can be affected by the variability of parametric processes. © 1991 IEEE