An efficient stable recursion to compute multiservice blocking probabilities

Quality of service issues are becoming increasingly important in broadband multiservice networks which transport many call classes with widely different bandwidth requirements. The call blocking probability is a major component in the analysis of the QoS. Recursive methods are available to compute the call blocking probabilities — the storage and computation needed to compute the recursion are O( C) and O( KC 2), respectively, where C is proportional to the bandwidth of the link and K the number of call classes. A necessary property of the recursion is that it is not subject to numerical problems such as imprecision and overflow. This is an essential consideration given the large values that K and C assume in modern networks. We present a new recursion to compute the call blocking probabilities. In addition to being numerically stable, the main features of our recursion are its simplicity and its reduced storage and computation requirements which are O( b K ) and O(( K+ b K ) C), respectively, where the class indices are ordered so that calls of class K have the largest bandwidth requirement b K . The computational requirements of our algorithm are significantly lower than those of comparable algorithms, especially when b K ≪ C which will often be the case in modern multiservice networks whose links have large transmission capacities.