Cell Loss Probability Approximations and Their Application to Call Admission Control

This paper studies the cell loss probability approximation of a statistical multiplexer in high speed networks. For this purpose, we consider discretetime nite-bu er queueing models. In particular, we study an approximate formula of the cell loss probability which is computed from the (asymptotic) tail distribution of the queue length in the corresponding in nite-bu er queue. We then apply the results to a queue where the arrival process is a superposition of many independent sources. In such a queue, it is hard to get the asymptotic decay constant in general. For this reason, the asymptotic decay constant has been assumed to be one in most studies. It is known, however, that the asymptotic decay constant can vary by several orders of magnitude. Contrary to the previous works, we consider an approximate formula of the loss probability taking the asymptotic decay constant into account. Thus, our approximation is expected to give more accurate estimation, compared with approximations proposed in the past. Further, we discuss the application of the results to call admission control (CAC) in high speed networks. In numerical examples, we observe that the CAC based on our approximate formula can use network resource e ectively, while guaranteeing quality of service (QoS).