B-Neck: A Distributed and Quiescent Max-Min Fair Algorithm

Abstract

Abstract-The problem of fairly distributing the capacity of a network 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 goal is to maximize its assigned transmission rate (i.e., its throughput). Since the links of the network have limited bandwidths, some criterion has to be defined to fairly distribute their capacity 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 λ s < λs. Many max-min fair algorithms have been proposed, both centralized and distributed. However, to our knowledge, all proposed distributed algorithms require control data being continuously transmitted to recompute the max-min fair rates when needed (because none of them has mechanisms to detect convergence to the max-min fair rates).In this paper we propose B-Neck, a distributed max-min fair algorithm that is also quiescent. This means that, in absence of changes (i.e., session arrivals or departures), once the maxmin rates have been computed, B-Neck stops generating network traffic. Quiescence is a key design concept of B-Neck, because B-Neck routers are capable of detecting and notifying changes in the convergence conditions of max-min fair rates. As far as we know, B-Neck is the first distributed max-min fair algorithm that does not require a continuous injection of control traffic to compute the rates. 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.

SLBN: A Scalable Max-min Fair Algorithm for Rate-Based Explicit Congestion Control

“…(Informally, bottlenecks are links that limit the sessions' rates.) Recently, a distributed maxmin fair algorithm was proposed, which has the property of stopping all control traffic after computing the rates [20]. All these algorithms require that routers store and process persession state information at each link to compute the rates, what significantly limits their scalability when hundreds of thousands of session flows cross router links.…”

“…This is mainly achieved by moving the per-session state (w.r.t. the above mentioned max-min fair algorithms, and in particular to the one proposed in [20]) from the routers to the session sources and protocol packets.…”