Approximate state probabilities in large shared multirate loss systems with an application to trunk reservation

Abstract

AbstractThe saddle‐point method of integration is used to derive a non‐recursive approximation for the distribution of occupied bandwidth units of the multirate loss system with complete sharing, which achieves complexity O(1) per state. For the multirate finite sources model an asymptotic scaling is assumed in which the capacity and the number of sources are large and as an application the tail probability is approximated in the region 10− 4–10− 10. The limits for the infinite sources model are obtained as well and the approximate distribution is used to initialise a partial recursion, which transforms the state probabilities into an approximate distribution of the same system with trunk reservation. As a result the blockings are obtained with a low numerical complexity, which scales independent of the capacity. Numerical results show the accuracy and efficiency of the approximations. The estimate of the tail probability is shown to be superior if compared to the modified Chernoff bound. Copyright © 2005 AEIT.