An End-to-End Approach to the Resequencing Problem
Journal of the ACM (JACM)
Exchangeable items in repair systems: delay times
Operations Research
Some Ergodic Results on Stochastic Iterative Discrete Events Systems
Discrete Event Dynamic Systems
Transient and stationary waiting times in (max,+)-linear systems with Poisson input
Queueing Systems: Theory and Applications
A max-algebra approach to modeling and simulation of tandem queueing systems
Mathematical and Computer Modelling: An International Journal
Block diagram-based modeling of manufacturing systems using max-plus algebra
ACC'09 Proceedings of the 2009 conference on American Control Conference
Memory Loss Property for Products of Random Matrices in the Max-Plus Algebra
Mathematics of Operations Research
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The (max,+)-algebra has been successfully applied to many areas of queueing theory, like stability analysis and ergodic theory. These results are mainly based on two ingredients: (1) a (max,+)-linear model of the time dynamic of the system under consideration, and (2) the time-invariance of the structure of the (max,+)-model. Unfortunately, (max,+)-linearity is a purely algebraic concept and it is by no means immediate if a queueing network admits a (max,+)-linear representation satisfying (1) and (2). In this paper we derive the condition a queueing network must meet if it is to have a (max,+)-linear representation. In particular, we study (max,+)-linear systems with time-invariant transition structures. For this class of systems, we find a surprisingly simple necessary and sufficient condition for (max,+)-linearity, based on the flow of customers through the network.