Bounds for stationary waiting times in a class of queueing network using stochastic ordering

In this paper we study bounds for characteristics of stationary waiting times in (max. +)-linear systems with a Poisson arrival process, which are prevalent in manufacturing systems, kanban systems, cyclic and acyclic fork-and-join type systems, finite or infinite capacity tandem queues with various kinds of blocking, transportation systems, and telecommunication networks, and so on. Recently, some results on series expansion for characteristics, such as higher moments, Laplace transform, and tail probability, of transient and stationary waiting times in a class of (max. +)-linear systems via Taylor series expansions have been studied. In order to overcome the computational complexity in those results, we consider bounds for characteristics of stationary waiting times using valuable stochastic ordering results. Some numerical examples are also provided.