Quantitative system performance: computer system analysis using queueing network models
Quantitative system performance: computer system analysis using queueing network models
Stability condition of a service system with precedence constraints between tasks
Performance Evaluation
Stochastic Automata Network of Modeling Parallel Systems
IEEE Transactions on Software Engineering
Performance of Synchronous Parallel Algorithms with Regular Structures
IEEE Transactions on Parallel and Distributed Systems
A characterisation of (max,+)-linear queueing systems
Queueing Systems: Theory and Applications
From max-plus algebra to nonexpansive mappings: a nonlinear theory for discrete event systems
Theoretical Computer Science
Spectral theorem for convex monotone homogeneous maps, and ergodic control
Nonlinear Analysis: Theory, Methods & Applications
Asymptotic Properties of Monotonic Nonexpansive Mappings
Discrete Event Dynamic Systems
Memory Loss Property for Products of Random Matrices in the Max-Plus Algebra
Mathematics of Operations Research
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This paper deals with the asymptotic behavior of thestochastic dynamics of discrete event systems. In this paperwe focus on a wide class of models arising in several fieldsand particularly in computer science. This class of models maybe characterized by stochastic recurrence equations in real^Kof the form T(n+1) = &phis;_{n+1}{ T}(n))where phi_n is a random operator monotone and1- linear. We establish that the behaviour of theextremas of the process T(n) are linear.The results are an application of the sub-additive ergodic theoremof Kingman. We also give some stability properties of such sequencesand a simple method of estimating the limit points.