Heterogeneous Congestion Control: Efficiency, Fairness and Design

When heterogeneous congestion control protocols that react to different pricing signals (e.g. packet loss, queueing delay, ECN marking etc.) share the same network, the current theory based on utility maximization fails to predict the network behavior. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be non-unique, inefficient and unfair. This paper has two objectives. First, we demonstrate the intricate behaviors of a heterogeneous network through simulations and present a rigorous framework to help understand its equilibrium efficiency and fairness properties. By identifying an optimization problem associated with every equilibrium, we show that every equilibrium is Pareto efficient and provide an upper bound on efficiency loss due to pricing heterogeneity. On fairness, we show that intra-protocol fairness is still decided by a utility maximization problem while inter-protocol fairness is the part over which we don¿t have control. However it is shown that we can achieve any desirable inter-protocol fairness by properly choosing protocol parameters. Second, we propose a simple slow timescale source-based algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns and prove its feasibility. The scheme needs only local information

Selfish traffic allocation for server farms

We study the price of selfish routing in noncooperative networks like the Internet. In particular, we investigate the price of selfish routing using the price of anarchy (a.k.a. the coordination ratio) and other (e.g., bicriteria) measures in the recently introduced game theoretic parallel links network model of Koutsoupias and Papadimitriou. We generalize this model toward general, monotone families of cost functions and cost functions from queueing theory. A summary of our main results for general, monotone cost functions is as follows: 1. We give an exact characterization of all cost functions having a bounded/unbounded price of anarchy. For example, the price of anarchy for cost functions describing the expected delay in queueing systems is unbounded. 2. We show that an unbounded price of anarchy implies an extremely high performance degradation under bicriteria measures. In fact, the price of selfish routing can be as high as a bandwidth degradation by a factor that is linear in the network size. 3. We separate the game theoretic (integral) allocation model from the (fractional) flow model by demonstrating that even a very small or negligible amount of integrality can lead to a dramatic performance degradation. 4. We unify recent results on selfish routing under different objectives by showing that an unbounded price of anarchy under the min-max objective implies an unbounded price of anarchy under the average cost objective and vice versa. Our special focus lies on cost functions describing the behavior of Web servers that can open only a limited number of Transmission Control Protocol (TCP) connections. In particular, we compare the performance of queueing systems that serve all incoming requests with servers that reject requests in case of overload. Our analysis indicates that all queueing systems without rejection cannot give any reasonable guarantee on the expected delay of requests under selfish routing even when the injected load is far away from the capacity of the system. In contrast, Web server farms that are allowed to reject requests can guarantee a high quality of service for every individual request stream even under relatively high injection rates

Monotonicity and error bounds for networks of Erlang loss queues

Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably are (i) classical circuit switch telephone networks (loss networks) and (ii) present-day wireless mobile networks. Performance measures of interest such as loss probabilities or throughputs can be obtained from the steady state distribution. However, while this steady state distribution has a closed product form expression in the first case (loss networks), it does not have one in the second case due to blocked (and lost) handovers. Product form approximations are therefore suggested. These approximations are obtained by a combined modification of both the state space (by a hypercubic expansion) and the transition rates (by extra redial rates). It will be shown that these product form approximations lead to (1) upper bounds for loss probabilities and \ud (2) analytic error bounds for the accuracy of the approximation for various performance measures.\ud The proofs of these results rely upon both monotonicity results and an analytic error bound method as based on Markov reward theory. This combination and its technicalities are of interest by themselves. The technical conditions are worked out and verified for two specific applications:\ud (1)• pure loss networks as under (2)• GSM networks with fixed channel allocation as under.\ud The results are of practical interest for computational simplifications and, particularly, to guarantee that blocking probabilities do not exceed a given threshold such as for network dimensioning

A Survey on Delay-Aware Resource Control for Wireless Systems --- Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning

In this tutorial paper, a comprehensive survey is given on several major systematic approaches in dealing with delay-aware control problems, namely the equivalent rate constraint approach, the Lyapunov stability drift approach and the approximate Markov Decision Process (MDP) approach using stochastic learning. These approaches essentially embrace most of the existing literature regarding delay-aware resource control in wireless systems. They have their relative pros and cons in terms of performance, complexity and implementation issues. For each of the approaches, the problem setup, the general solution and the design methodology are discussed. Applications of these approaches to delay-aware resource allocation are illustrated with examples in single-hop wireless networks. Furthermore, recent results regarding delay-aware multi-hop routing designs in general multi-hop networks are elaborated. Finally, the delay performance of the various approaches are compared through simulations using an example of the uplink OFDMA systems.Comment: 58 pages, 8 figures; IEEE Transactions on Information Theory, 201

Equilibrium of Heterogeneous Congestion Control: Optimality and Stability

When heterogeneous congestion control protocols that react to different pricing signals share the same network, the current theory based on utility maximization fails to predict the network behavior. The pricing signals can be different types of signals such as packet loss, queueing delay, etc, or different values of the same type of signal such as different ECN marking values based on the same actual link congestion level. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be non-unique, suboptimal and unstable. In Tang et al. (“Equilibrium of heterogeneous congestion control: Existence and uniqueness,” IEEE/ACM Trans. Netw., vol. 15, no. 4, pp. 824–837, Aug. 2007), existence and uniqueness of equilibrium of heterogeneous protocols are investigated. This paper extends the study with two objectives: analyzing the optimality and stability of such networks and designing control schemes to improve those properties. First, we demonstrate the intricate behavior of a heterogeneous network through simulations and present a framework to help understand its equilibrium properties. Second, we propose a simple source-based algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns by only updating a linear parameter in the sources’ algorithms on a slow timescale. It steers a network to the unique optimal equilibrium. The scheme can be deployed incrementally as the existing protocol needs no change and only new protocols need to adopt the slow timescale adaptation

Cross-layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks

This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition” for time-varying channel models

Monotonicity and error bounds for networks of Erlang loss queues

Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably\ud (i) classical circuit switch telephone networks (loss networks) and\ud (ii) present-day wireless mobile networks.\ud \ud Performance measures of interest such as loss probabilities or throughputs can be obtained from the steady state distribution. However, while this steady state distribution has a closed product form expression in the first case (loss networks), it has not in the second case due to blocked (and lost) handovers. Product form approximations are therefore suggested. These approximations are obtained by a combined modification of both the state space (by a hyper cubic expansion) and the transition rates (by extra redial rates). It will be shown that these product form approximations lead to\ud \ud - secure upper bounds for loss probabilities and\ud - analytic error bounds for the accuracy of the approximation for various performance measures.\ud \ud The proofs of these results rely upon both monotonicity results and an analytic error bound method as based on Markov reward theory. This combination and its technicalities are of interest by themselves. The technical conditions are worked out and verified for two specific applications:\ud \ud - pure loss networks as under (i)\ud - GSM-networks with fixed channel allocation as under (ii).\ud \ud The results are of practical interest for computational simplifications and, particularly, to guarantee blocking probabilities not to exceed a given threshold such as for network dimensioning.\u