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Abstract : |
Unlike the leaky-bucket scheme which regulates the input rate, the lters we study in this paper reduce the variability of interarrival times (subject to a maximum delay constraint for each customer). These lters are called \smoothing " lters for point processes. By considering the output processes of various queueing systems, we show that (i) an inniteserver queue acts as a smoothing lter for a doubly stochastic Poisson process and (ii) a single-server queue with deterministic service times acts as a smoothing lter for a stationary and ergodic point process. Based on (ii), we provide a smoothing algorithm that satises a maximum delay constraint. The algorithm is shown to be robust and consistent. We then consider two examples where these lters can be applied to increase throughput: one is the single-server loss system with exponential service times, the other is the leaky-bucket scheme with token buer size 1. Numerical examples and simulations are also given for comparing the trade-o between delay and throughput. Our approach is based on the variability ordering and a cut criterion for the majorization ordering. The criterion appears to be new and to be of independent interest. 0, |
