Optimization and design of network routing using refined asymptotic approximations

Abstract

The problems of route optimization, and the sizing of virtual paths and explicit routes in wide-area multi-service broadband networks are considered. The problems are formulated at the call-level in the framework of multi-rate, circuit-switched, loss networks, with effective bandwidth encapsulating cell and packet-level behavior. Broadband networks are characterized by links with very large capacities in circuits, and are expected to support many services each having a characteristic bandwidth or rate. Various asymptotic results based on Uniform Asymptotic Approximations (UAA) have previously been obtained to reduce the complexity of the numerical calculations. This paper offers refinements (RUAA) to UAA to the loss probabilities for a single link, as well as their sensitivities to the offered traffic. Network loss probabilities are obtained by solving fixed-point equations. Another system of equations determines the implied costs for services and links, which are used to guide the network optimization. Refined asymptotic approximations to the network's loss probabilities as well as to the implied costs are proposed based on the RUAA. The refinements are crucial for the accurate evaluations of the implied costs. The complexity of these calculations remains bounded as the link capacities and traffic intensities become increasingly large, and the complexity for the implied costs is independent of the number of services. A network design tool TALISMAN has been extended to implement the refined approximations. Numerical examples illustrate the accuracy of the RUAA.