Open queueing systems in light traffic
Mathematics of Operations Research
Joint distributions in Poissonian tandem queues
Queueing Systems: Theory and Applications
Light-traffic analysis for queues with spatially distributed arrivals
Mathematics of Operations Research
Transient and stationary waiting times in (max,+)-linear systems with Poisson input
Queueing Systems: Theory and Applications
Laplace Transform and Moments of Waiting Times in Poisson Driven (max,+) Linear Systems
Queueing Systems: Theory and Applications
Synchronized queues with deterministic arrivals
Operations Research Letters
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We give a Taylor series expansion for the joint Laplace transform of stationary 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 good approximations (especially under the assumption of light traffic). Combining this new result with the earlier expansion formula for the mean stationary waiting times, we also provide a Taylor series expansion for the covariance of stationary waiting times in such systems.It is well known that (max,+)-linear systems can be used to represent stochastic Petri nets belonging to the class of event graphs. This class contains various instances of queueing networks like acyclic or cyclic fork-and-join 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, assembly systems and so forth. The applicability of this expansion technique is discussed for several systems of this type.