Why locally-fair maximal flows in client-server networks perform well

Maximal flows reach at least a 1/2 approximation of the maximum flow in client-server networks. By adding 1 additional time round to any distributed maximal flow algorithm we show how this 1/2-approximation can be improved on bounded-degree networks. We call these modified maximal flows ‘locally fair’ since there is a measure of fairness prescribed to each client and server in the network. Let N =( U , V , E , b ) represent a client-server network with clients U , servers V , network links E , and node capacities b , where we assume that each capacity is at least one unit. Let d ( u ) denote the b -weighted degree of any node u ∈ U ∪ V , Δ =max { d ( u )| u ∈ U } and δ =min { d ( v )| v ∈ V }. We show that a locally-fair maximal flow f achieves an approximation to the maximum flow of }, and this result is sharp for any given integers δ and Δ . This results are of practical importance since local-fairness loosely models the steady-state behavior of TCP/IP and these types of degree-bounds often occur naturally (or are easy to enforce) in real client-server systems.