Bounds based on lumpable matrices for partially ordered state space
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Improving Time Parallel Simulation for Monotone Systems
DS-RT '09 Proceedings of the 2009 13th IEEE/ACM International Symposium on Distributed Simulation and Real Time Applications
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We analyze the effect of a few fiber delay loops on the number of deflections in an all optical packet switch. The switch is based on the ROMEO architecture developed by Alcatel. We use deflection routing because of the lack of optical memory. Some fiber delay loops allow the packets to be locally deflected instead of being sent on the network for much longer delays. As the model is numerically difficult, we apply stochastic bounds. First, we consider a partial ordering on the state space and we prove that the problem is monotone. Then we present a new method which strongly relies on this property. Note that this method is quite general as partial order monotone multicomponent systems are quite frequent in performance evaluation. The upper bounds are computed using robust numerical algorithms on a smaller state space. We also show how we can compute lower bounds to check the accuracy of the method.