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One major challenge in communication networks is the problem of dynamically distributing load in the presence of bursty and hard to predict changes in traffic demands. Current traffic engineering operates on time scales of several hours which is too slow to react to phenomena like flash crowds or BGP reroutes. One possible solution is to use load sensitive routing. Yet, interacting routing decisions at short time scales can lead to oscillations, which has prevented load sensitive routing from being deployed since the early experiences in Arpanet. However, recent theoretical results have devised a game theoretical re-routing policy that provably avoids such oscillation and in addition can be shown to converge quickly. In this paper we present ReplEx, a distributed dynamic traffic engineering algorithm based on this policy. Exploiting the fact that most underlying routing protocols support multiple equal-cost routes to a destination, it dynamically changes the proportion of traffic that is routed along each path. These proportions are carefully adapted utilising information from periodic measurements and, optionally, information exchanged between the routers about the traffic condition along the path. We evaluate the algorithm via simulations employing traffic loads that mimic actual Web traffic, i. e., bursty TCP traffic, and whose characteristics are consistent with self-similarity. The simulations quickly converge and do not exhibit significant oscillations on both artificial as well as real topologies, as can be expected from the theoretical results.