Application-level network relays possess many desirable properties, including support for communication between disconnected clients, increasing bandwidth between distant clients, and enabling routing around Internet failures. One problem not considered by existing systems is how to assign client load to relay servers in order to maximize throughput of the relay-system. In this paper, we are interested in the particular case where network conditions change frequently so that the ability of clients to adapt flow is restricted and each round of activity is critical. To this end, we present an algorithm, called Aggressive Increase, A{sub}(AI) which improves its competitive ratio in each time round that the network conditions persists. Given a relay network where a client connects to at most N servers, if network conditions persist for log(N) rounds then the algorithm's throughput becomes constant competitive. Our results improve upon the competitive ratio of previous work (of Awerbuch, Hajiaghayi, Kleinberg, and Leighton [2]). In addition we show that the A{sub}(AI) algorithm performs well in simulation studies as compared with the algorithm of [2] and an adaptation of the multiplicative increase algorithm of [8]. On a variety of input graphs, we show that the A{sub}(AI) algorithm typically reaches close to peak bandwidth levels within only a small constant (< 10) number of rounds.
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