As the speed and the dynamic range of computer networks evolve, the issue of efficient traffic management becomes increasingly important. This work describes an approach to traffic management using explicit rate information provided to the source by the network. We present an asynchronous distributed algorithm for optimal rate calculation across the network, where optimality is understood in the maxmin sense. The algorithm quickly converges to the optimal rates and is shown to be well-behaved in transience. 1 Introduction 1.1 Background In the past decade several mechanisms for congestion control have been developed and implemented. DECbit [34] and Slow Start [20] are perhaps the best known. Both of these schemes were developed for connectionless networks with window flow control, in which the routers had no knowledge of the individual flows and their demands, the routes changed frequently and the header space was scarce. With the rapid increase of the ratio of propagation delay to...

As the speed and complexity of computer networks evolve, sharing network resources becomes increasingly important. Thus, the issue of how to allocate the available bandwidth among the multitude of users needs to be addressed. Such allocation needs to be in some sense efficient and fair to different users. In this work the so-called maxmin fairness is chosen as the optimality criterion. A new distributed and asynchronous algorithm is suggested. The algorithm is shown to converge to the optimal rate allocation in a network with general topology under dynamic changes in the set of network users, individual user load and occasional route changes. An upper bound on convergence time is given. The algorithm is shown to be well-behaved in transience. Unlike previous work, the algorithm takes bandwidth consumed by feedback traffic into account. Further, an extension of the algorithm is suggested to address the problem of policing misbehaved users.

Several issues in the design and analysis of rate based flow control algorithms are addressed in this paper. We suggest a new approach for rate based flow control algorithms which may be considered more "optimistic" than traditional approaches. Three variations of the approach are presented and their rate of convergence to an optimal max-min fairness solution is analyzed. Finally, we suggest and analyze approximate rate based flow control algorithms. We show that under certain conditions the approximate algorithms may converge faster. However, in rare configurations we show that the resulting rates may be substantially different than the rates of the max-min vector (this difference is not necessarily bad). A byproduct of this research is an example showing that the max-min vector is fairly unstable, namely that a change of ffi is the rate of some session may change the allocation of another session by \Omega\Gamma ffi \Delta 2 n 2 ).

This paper gives a new definition of general weighted (GW) fairness and shows how this can achieve various fairness definitions, such as those mentioned in the ATM Forum TM 4.0 specifications. The GW fairness can be achieved by calculating the ExcessFairshare (weighted fairshare of the left over bandwidth) for each VC. We show how a switch algorithm can be modified to support the GW fairness by using the ExcessFairshare term. We use ERICA+ as an example switch algorithm and show how it can be modified to achieve the GW fairness. For simulations, the weight parameters of the GW fairness are chosen to map a typical pricing policy. Simulation results are presented to demonstrate that, the modified switch algorithm achieves GW fairness. An analytical proof for convergence of the modified ERICA+ algorithm is given in the appendix.

Key Words ATM networks, traffic management, congestion control, rate-based schemes, maxmin fair allocation

The maxmin fair bandwidth allocation has been proposed as a flow/congestion control mechanism for managing the best-effort data traffic in connection-oriented networks. It achieves the fairness by assigning an equal share of bandwidth to each flow passing a link whenever possible; it improves the system throughput by fully utilizing the link capacity whenever possible. This type of fairness- and throughput-aware bandwidth allocation and corresponding routing schemes are important in multimedia connection-oriented networks for a class of services, such as ABR in ATM networks, which will carry heterogeneous types of best-effort traffic from non-real-time multimedia to ASCII text flows. We present two contributions in this paper. The first contribution is to define a new set of fairness-throughput relational operators on the set of feasible bandwidth allocations and to show that the maxmin fair allocation maximizes the fairness-throughput performance measured by the new operators. The se...

We develop a new class of asynchronous distributed algorithms for the explicit rate control of elastic sessions in an integrated packet network. Sessions can request for minimum guaranteed rate allocations (e.g., MCRs in the ATM context), and, under this constraint, we seek to allocate the max-min fair rates to the sessions. We capture the integrated network context by permitting the link bandwidths available to elastic sessions to be stochastically time varying. The available capacity of each link is viewed as some statistic of this stochastic process (e.g., a fraction of the mean, or a large deviations Equivalent Service Capacity (ESC)). For fixed available capacity at each link, we show that the vector of max-min fair rates can be computed from the root of a certain vector equation. A distributed asynchronous stochastic approximation technique is then used to develop a provably convergent distributed algorithm for obtaining the root of the equation, even when the link flows and the ...

Abstract—The ad hoc deployment of a sensor network causes unpredictable patterns of connectivity and varied node density, resulting in uneven bandwidth provisioning on the forwarding paths. When congestion happens, some sensors may have to reduce their data rates. It is an interesting but difficult problem to determine which sensors must reduce rates and how much they should reduce. This paper attempts to answer a fundamental question about congestion resolution: What are the maximum rates at which the individual sensors can produce data without causing congestion in the network and unfairness among the peers? We define the maxmin optimal rate assignment problem in a sensor network, where all possible forwarding paths are considered. We provide an iterative linear programming solution, which finds the maxmin optimal rate assignment and a forwarding schedule that implements the assignment in a low-rate sensor network. We prove that there is one and only one such assignment for a given configuration of the sensor network. We also study the variants of the maxmin fairness problem in sensor networks. Index Terms—Multipath maxmin fairness, wireless sensor networks, data collection applications, iterative linear programming. 1

isson Modeling. In IEEE/ACM Trans. on Networking, 3(3):226-244, June 1995. [PST 94] S. Plotkin, D. Shmoys and E. Tardos. Fast Approximation Algorithms for Fractional Packing and Covering Problems. Technical Report ORIE-999 of the School of Operations Research and Industrial Engineering, Cornell Univer, 1995. A preliminary version of this work appeared in Proc. of 25th ACM Symp. on Theory of Computing, 1993. [PY 93] C. Papadimitriou and M. Yannakakis. Linear Programming without the Matrix. In Proc. of 25th ACM Symposium on Theory of Computing, pp. 121-129, 1993. [Riz 97] L. Rizzo. On the Feasibility of Software FEC. Technical Report, Universita di Pisa, Italy, January 1997. [ST 85] D. Sleator and R. Tarjan. Amortized Efficiency of List Update and Paging Rules. In Communications of the ACM, 28(2):202-208, 1985. 106 [Kes 91] S. Keshav. A Control-Theoretic Approach to Flow Control. In Proc. ACM SIGCOMM '91

The future high-speed networks will need to support diverse traffic and provide services to flows with Quality of Service (QoS) requirements as well as to best effort flows. In this paper we analyze the coexistence of the QoS and best effort flows from the routing and scheduling point of view. We concentrate in our routing and scheduling analysis on the network bandwidth resource. We present two sets of source routing algorithms: (1) the bandwidth-constrained routing with imprecise state information for QoS flows, and (2) the maxmin fair routing for best effort flows. The routing analysis includes an extensive description of various algorithms in their domains and their complexity discussion. Furthermore, we discuss two level hierarchical scheduling which is tailored towards the needs raised by the coexistence of QoS and best effort flows. We show that this scheduling design accomplishes two design goals (1) guaranteeing QoS for QoS flows and (2) ensuring fairness for best effort flows...