Asymptotic Performance Limits for Fair Routing and Rate Allocation

| We consider the performance evaluation of routing and rate allocation (RRA) algorithms in multi-class rate-based networks, in particular, networks supporting the IntServ architecture. An RRA algorithm will result in a vector of carried traacs, with each element corresponding to a class. While maximising the aggregate weighted carried traac is a natural objective, it can lead to unfair operation with very small carried traac for some classes. Keeping the fairness issue in mind, we seek an RRA policy that maximizes the minimum carried traac. In this paper, we derive an upper bound on the minimum carried traac of any routing and rate allocation algorithm. We show that a Channel Reservation RRA algorithm achieves the bound asymptotically, i.e., when the ooered traac and link capacities scale up in proportion. To illustrate the utility of the upper bound, we simulate the performance of a heuristic RRA algorithm, namely the Complete Sharing RRA and compare its performance with the upper bound.