Smoothing Point Processes as a Means to Increase Throughput

Unlike the leaky-bucket scheme which regulates the input rate, the filters we study in this paper reduce the variability of interarrival times (subject to a maximum delay constraint for each customer). These filters are called smoothing filters for point processes. By considering the output processes of various queueing systems, we show that an infinite-server queue acts as a smoothing filter for a doubly stochastic Poisson process, and a single-server queue with deterministic service times acts as a smoothing filter for a stationary and ergodic point process. Based on the second point, we provide a smoothing algorithm that satisfies a maximum delay constraint. The algorithm is shown to be robust and consistent. We then consider two examples where these filters 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 buffer size 1. Numerical examples and simulations are also given for comparing the tradeoff 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 of independent interest.