Deterministic Models for Internet Congestion Control

There has been a lot of recent work on decentralized end-to-end congestion control algorithms for the Internet. These are based on ECN marking with the goal of building a low-loss, low-queueing-delay network. The control algorithms are designed on the premise that each user has a utility function, which the user is trying to maximize, while the network is simultaneously trying to maintain some sort of fairness amongst various users. In the algorithms proposed, the network tries to achieve it’s goal by marking packets during congestion (see [4, 3]). The notion of fairness (from the network’s point of view) which has been used is weighted proportional fairness (see [2]). Through appropriate choice of the weights, other fairness criteria such as minimum potential delay fairness can be realized. If we interpret the utility function of the user as the users’ willingness to pay for bandwidth, and suppose that the price paid by the user is proportional to the number of marks received, then, a weighted proportionally fair scheme leads to same price per unit bandwidth paid by any user for utilizing some resource in the network. The algorithms proposed have a decentralized implementation to achieve the network and user objectives simultaneously. In this paper, we focus on the case where all users have the same utility function of log x , leading to a proportionally fair sharing of the bandwidth.