Expansions for joint Laplace transform of stationary waiting times in (max, plus )-linear systems with Poisson input

We give a Taylor series expansion for the joint Laplace transform of statio nary waiting times in open (max, +)-linear stochastic systems with Poisson input. Probabilistic expressions are derived for coefficients of all orders . Even though the computation of these coefficients can be hard for certain systems, it is sufficient to compute only a few coefficients to obtain goo d approximations (especially under the assumption of light traffic). Combin ing this new result with the earlier expansion formula for the mean station ary waiting times, we also provide a Taylor series expansion for the covari ance of stationary waiting times in such systems. It is well known that (max, +)-linear systems can be used to represent stoc hastic Petri nets belonging to the class of event graphs. This class contai ns various instances of queueing networks like acyclic or cyclic fork-and-j oin queueing networks, finite or infinite capacity tandem queueing networks with various types of blocking, synchronized queueing networks and so on. It also contains some basic manufacturing models such as kanban networks, a ssembly systems and so forth. The applicability of this expansion technique is discussed for several systems of this type.