B-Neck: a distributed and quiescent max-min fair algorithm

Abstract

The problem of fairly distributing a network capacity among a set of sessions has been widely studied. In this problem, each session connects via a single path a source and a destination, and its objective is to maximize its as- signed transmission rate (i.e., its throughput). Since the links of the network have limited bandwidth, some form of criterion has to be defined to fairly distribute them among the sessions. A popular criterion is max-min fairness that, in short, guarantees that each session i gets a rate λi such that no session s can increase λs without causing another session s′ to end up with a rate λs′< λs. Many max-min fair algorithms have been proposed, both centralized and distributed. However, to our knowledge, all proposed distributed algorithms require control packets being continuously transmitted to recompute the max-min fair rates when needed.

In this paper we propose B-Neck, a max-min fair distributed algorithm that is also quiescent. This means that, in absence of changes (i.e., session arrivals or departures), once the max-min rates have been computed B-Neck stops generating network traffic. As far as we know, B-Neck is the first max-min fair distributed algorithm that does not require a continuous injection of control traffic to compute the rates. When changes occur, affected sessions are asynchronously informed of their new rate (i.e., sessions do not need to poll the network for changes). The correctness of B-Neck is formally proved, and extensive simulations are conducted. In them it is shown that B-Neck converges relatively fast and behaves nicely in presence of sessions arriving and departing.