We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm. In this system sources select transmission rates that maximize their own benefits, utility minus bandwidth cost, and network links adjust bandwidth prices to coordinate the sources' decisions. We allow feedback delays to be different, substantial and time-varying, and links and sources to update at different times and with different frequencies. We provide asynchronous distributed algorithms and prove their convergence in a static environment. We present measurements obtained from a preliminary prototype to illustrate the convergence of the algorithm in a slowly time-varying environment.

We propose a duality model of congestion control and apply it to understand the equilibrium properties of TCP and active queue management schemes. Congestion control is the interaction of source rates with certain congestion measures at network links. The basic idea is to regard source rates as primal variables and congestion measures as dual variables, and congestion control as a distributed primal-dual algorithm carried out over the Internet to maximize aggregate utility subject to capacity constraints. The primal iteration is carried out by TCP algorithms such as Reno or Vegas, and the dual iteration is carried out by queue management such as DropTail, RED or REM. We present these algorithms and their generalizations, derive their utility functions, and study their interaction.

We proposed earlier an optimization approach to reactive flow control where the objective of the control is to maximize the total utility of all sources over their transmission rates. The control mechanism is derived as a gradient projection algorithm to solve the dual problem. In this paper we consider two extensions to the basic algorithm. First, the basic algorithm requires communication from sources of their rates to links in their paths in order to carry out the gradient projection algorithm. We prove that it is possible for the links to estimate the gradient using only local information, thus eliminating the need for explicit communication. Second, the basic algorithm assumes that each source is served by a single path. We generalize the model to the case where there are multiple paths between a source--destination pair. This allows flow control and routing to be jointly optimized. 1 Introduction We have proposed previously an optimization approach to flow control where the cont...

this article, we revisit the topic of the distribution of rates as determined by adherence to the additive increase#multiplicative decrease algorithm. This algorithm #13# was originally believed to exhibit max-min fairness, an allocation favouring smaller rates. This is the allocation reached such that any further increase in the rate of one source results in the decrease of some smaller rate. Results in #5,9# showed that for equal round-trip times TCP appeared to provide proportional fairness, a form of fairness which distributes bandwidth with a bias in favour of #ows using a smaller number of hops

this paper we extend the algorithm to a scaled gradient projection. The diagonal scaling matrix approximates the diagonal terms of the Hessian and can be computed at individual links using the same information required by the unscaled algorithm. We prove the convergence of the scaled algorithm and present simulation results that illustrate its superiority to the unscaled algorithm. Keywords: Flow control, optimization flow control, Newton algorithm 1. Introduction We have proposed previously an optimization approach to flow control where the control mechanism is derived as a gradient projection algorithm to solve the dual of a global optimization problem [18,22]. An important feature is that the problem is decomposed into simple algorithms that are executed at individual links and sources using `local' information. It is well known that Newton method, where the gradient is scaled by the inverse of the second derivative matrix, typically enjoys a m

A duality model of flow control is proposed in Part I of this paper and leads to a basic flow control algorithm. In this sequel we develop a practical implementation of the basic algorithm, Random Exponential Marking (REM). It consists of a link algorithm, that probabilistically marks packets inside the network, and a source algorithm, that adapts source rate to observed marking. REM has three advantages. First the marking probability is exponential in a link congestion measure, so that the end--to--end marking probability observed at a source is exponential in its path congestion measure. Marking allows the source to estimate its path congestion measure and adjusts its rate in a way that aligns individual optimality with social optimality. Second REM achieves high link utilization with very low backlog, and hence negligible loss and queueing delay. Third sources stabilize around a globally optimal equilibrium, thus avoiding the perpetual cycle of sinking into and recovering from congestion. Moreover the equilibrium can be chosen to achieve different fairness criteria. We present extensive simulation results to demonstrate that REM is not only stable and fair, but more importantly, scalable and robust. Finally, the link algorithm itself can also be used for active queue management that interact with existing source algorithms. We compare the performance of Reno, Reno/RED and Reno/REM. I.

Random Early Marking (REM) consists of a link algorithm, that probabilistically marks packets inside the network, and a source algorithm, that adapts source rate to observed marking. The marking probability is exponential in a link congestion measure, so that the end--to--end marking probability is exponential in a path congestion measure. Marking allows a source to estimate its path congestion measure and adjusts its rate in a way that aligns individual optimality with social optimality. Because of the finer measure of congestion provided by REM, sources do not constantly probe the network for spare capacity, but settle around a globally optimal equilibrium, thus avoiding the perpetual cycle of sinking into and recovering from congestion. We first derive REM as a distributed implementation of a gradient projection algorithm to maximize aggregate source utility over source rates. The gradient projection algorithm, whose stability and fairness have been proved even in an asynchronous en...

Flow control, especially in multicast networks, is a problem of significant theoretical and practical...

The dominant paradigm for congestion control in the Internet today is based on the notion of TCP-friendliness.

This paper presents a flow control protocol for multi-sender multi-group multicast and unicast in wide area overlay networks. The protocol is analytically grounded and achieves real world goals, such as simplicity, fairness and minimal resource usage. Flows are regulated based on the "opportunity" costs of network resources used and the benefit provided by the flow. In contrast to existing windowbased flow control schemes, we avoid end-to-end per sender or per group feedback by looking only at the state of the virtual links between participating nodes. This produces control traffic proportional only to the number of overlay network links and independent of the number of groups, senders or receivers. We show the effectiveness of the resulting protocol through simulations and validate the simulations with live Internet experiments.