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We investigate the performance of routing and rate allocation (RRA) algorithms in rate-based multi-class networks, in particular, a network of routers that support the IntServ guaranteed services. We measure the performance of an RRA algorithm in terms of its weighted carried traffic. We derive an upper bound on the weighted carried traffic of any RRA algorithm. The bound can be computed by linear programming. Moreover we show that a fixed RRA algorithm achieves the bound asymptotically. Therefore the bound can be used as an absolute benchmark for the performance of various RRA algorithms. We illustrate this by comparing the simulated performance of a simple shortest-path RRA (SP-RRA) algorithm with the bound.