Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
An interpolation approximation for queueing systems with Poisson input
Operations Research
Open queueing systems in light traffic
Mathematics of Operations Research
Queueing Systems: Theory and Applications
Transient and stationary waiting times in (max,+)-linear systems with Poisson input
Queueing Systems: Theory and Applications
RSFDGrC'05 Proceedings of the 10th international conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume Part II
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(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.In their 1997 paper, Baccelli, Hasenfuss and Schmidt provide explicit expressions for the expected value of the waiting time of the nth customer in a given subarea of a (max,+) linear system. Using similar analysis, we present explicit expressions for the moments and the Laplace transform of transient waiting times in Poisson driven (max,+) linear systems. Furthermore, starting with these closed form expressions, we also derive explicit expressions for the moments and the Laplace transform of stationary waiting times in a class of (max,+) linear systems with deterministic service times. Examples pertaining to queueing theory are given to illustrate the results.