The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Performance analysis of an ingress switch in a JumpStart optical burst switching network
Performance Evaluation
A Generic Mean Field Convergence Result for Systems of Interacting Objects
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
A unified model for synchronous and asynchronous FDL buffers allowing closed-form solution
Performance Evaluation
Mean field limit of non-smooth systems and differential inclusions
ACM SIGMETRICS Performance Evaluation Review
Hybrid Limits of Continuous Time Markov Chains
QEST '11 Proceedings of the 2011 Eighth International Conference on Quantitative Evaluation of SysTems
IEEE Journal on Selected Areas in Communications - Part Supplement
Fluid limit for the machine repairman model with phase-type distributions
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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We consider an asynchronous all optical packet switch (OPS) where each link consists of N wavelength channels and a pool of C ≤ N full range tunable wavelength converters. Under the assumption of Poisson arrivals with rate λ (per wavelength channel) and exponential packet lengths, we determine a simple closed-form expression for the limit of the loss probabilities Ploss(N) as N tends to infinity (while the load and conversion ratio σ=C/N remains fixed). More specifically, for σ ≤ λ2 the loss probability tends to (λ2-σ)/λ(1+λ), while for σ λ2 the loss tends to zero. We also prove an insensitivity result when the exponential packet lengths are replaced by certain classes of phase-type distributions. A key feature of the dynamical system (i.e., set of ODEs) that describes the limit behavior of this OPS switch, is that its right-hand side is discontinuous. To prove the convergence, we therefore had to generalize some existing result to the setting of piece-wise smooth dynamical systems.