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.

Virtual Queue-based marking schemes have been recently proposed for AQM (Active Queue Management) in Internet routers. We consider a particular scheme, which we call the Adaptive Virtual Queue (AVQ), and study its following properties: stability in the presence of feedback delays, its ability to maintain small queue lengths and its robustness in the presence of extremely short flows (the so-called web mice). Using a mathematical tool motivated by the earlier work of Hollot et al, we present a simple rule to design the parameters of the AVQ algorithm. We then compare its performance through simulation with several well-known AQM schemes such as RED, REM, PI controller and a non-adaptive virtual queue algorithm. With a view towards implementation, we show that AVQ can be implemented as a simple token bucket using only a few lines of code. 1

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We consider a single link accessed by a single source which responds to congestion signals from the network. The design of controllers for such sources in the presence of feedback delay has received much attention recently. Here we present conditions for the global, asymptotic stability and semi-global exponential stability of congestion controllers which are natural extensions of earlier linearized analysis of such systems. Our result on exponential stability provides the missing link in the proof of how one obtains a single deterministic congestion control equation from a system with many congestion-controlled sources and random disturbances. Using numerical examples, we compare the conditions on the congestion-control parameters obtained using local and global stability analysis.

Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduced in the packet arrival and service processes due to many factors such as arrivals and departures of sources and uncontrollable short flows in the network. To make the simulation tractable, often deterministic fluid model approximations of these algorithms are used. These approximations are in the form of either deterministic delay differential equations, or more generally, deterministic functional differential equations. We justify the use of deterministic models for proportionally-fair congestion controllers under a limiting regime where the number of sources in a network is large. We verify our results through simulations of window-based implementations of proportionally fair controllers and TCP.

Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduced in the packet arrival and service processes due to many factors such as arrivals and departures of sources and uncontrollable short flows in the network. To make the analysis or simulation tractable, often deterministic fluid approximations of these algorithms are used. These approximations are in the form of either deterministic delay differential equations, or more generally, deterministic functional differential equations (FDEs). In this paper, we ignore the complexity introduced by the window-based implementation of such algorithms and focus on the randomness in the network. We justify the use of deterministic models for proportionally-fair congestion controllers under a limiting regime where the number of flows in a network is large.

The problem of congestion control in networks with multicast multirate traffic along with unicast sessions has been addressed in this paper. We present a decentralized algorithm which enables the different rate-adaptive receivers in different multicast sessions to adjust their rates to satisfy some fairness criterion. We propose a one-bit ECN marking strategy to be used at the nodes. The congestion control mechanism does not require any per-flow state information for unicast flows at the nodes. Per receiver state information may be required for each multicast flow. The congestion control mechanism takes into account the diverse user requirements when different receivers within a multicast session have different utility functions, but does not assume the network to have any knowledge about the receiver utility functions and also converges under certain reasonable assumptions.

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...

Mathematical models of congestion control capture the congestion indication mechanism at the router in two different ways: rate-based models, where the queue-length at the router does not explicitly appear in the model, and queue-based models, where the queue length at the router is explicitly a part of the model. Even though most congestion indication mechanisms use the queue length to compute the packet marking or dropping probability to indicate congestion, we argue that, depending upon the choice of the parameters of the AQM scheme, one would obtain a rate-based model or a rate-and-queue-based model as the deterministic limit of a stochastic system with a large number of users.

Fair resource allocation in high-speed networks such as the Internet can be viewed as a constrained optimization program. Kelly and his co-workers have shown that an uncontrained penalty function formulation of this problem can be used to design congestion controllers that are stable. In this paper, we examine the question of providing feedback from the network such that the congestion controllers derived from the penalty function formulation lead to the solution of the original unconstrained problem. This can be viewed as the decentralized design of ECN marking rates at each node in the Internet to ensure global loss-free operation of a fluid model of the network. We then look at the stability of such a scheme using a time-scale decomposition of the system. This results in two seperate systems which are stable individually and we show that under certain assumptions the entire system is semi-globally stable and converges to the equilibrium point exponentially fast. 1