Stochastic convexity for multidimensional processes and its applications

A multidimensional stochastic process is considered which is a function of a parametric process. The parametric process may be multidimensional as well. Two such processes are compared that differ only in their parametric processes. Known stochastic convexity results for one-dimensional stochastic processes are extended to multidimensional processes. These results are used to obtain comparison results for various queuing systems that are subject to different parametric processes, which may be the arrival processes, service processes, etc. Based on these comparison results it is shown how the performances of queueing systems can be affected by the variability of parametric processes