Stochastic convexity for multidimensional processes

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 that differ only in their parametric processes are compared. The known stochastic convexity results for one-dimensional stochastic processes, which were developed by M. Shaked and J. G. Shanthikumar (1988), are extended to multidimensional processes. These results are then used to obtain comparison results for various queuing systems that are subject to different processes, which may be the arrival processes, service processes, etc. Based on these comparison results, it is shown how the performances of queuing systems can be affected by the variability of parametric processes.