Reconstructing arrival processes to discrete queueing systems by inverse load transformation

Abstract

In this article we propose methods to estimate the parameters of arrival processes to G/ D/1 queueing systems only based on observed departures from the system. The derived estimates can be used for performance evaluation and capacity planning in cases where the arrival process is not observable directly. Instead, only the departure process modified at the (last) server needs to be observed. Concerning the arrival process we begin by focusing on the normally distributed number of arrivals per interval and on autoregressive processes. Both classes can be used to model traffic in communication networks on links with a high degree of aggregation. In the case of autoregressive processes we apply the Tobit regression model in order to derive accurate estimates of all parameters of the arrival process. We then continue by generalizing the estimation procedures to correlated arrival processes by using the Buckley–James Estimator. The results are presented for the single G/ D/1 queue but are then generalized to the more realistic scenario of sequences of queues with possibly varying bottleneck capacity. The latter especially permits the modeling of effects due to interfering cross traffic. We show how the derived estimates can be used for performance evaluation or capacity planning based on effective bandwidth theory. Finally, we demonstrate that the estimation procedures can be utilized within wireless networks by means of a detailed simulation model.