Delay-Based Network Utility Maximization

Abstract—It is well known that max-weight policies based on a queue backlog index can be used to stabilize stochastic networks, and that similar stability results hold if a delay index is used. Using Lyapunov Optimization, we extend this analysis to design a utility maximizing algorithm that uses explicit delay information from the head-of-line packet at each user. The resulting policy is shown to ensure deterministic worst-case delay guarantees, and to yield a throughput-utility that differs from the optimally fair value by an amount that is inversely proportional to the delay guarantee. Our results hold for a general class of 1-hop networks, including packet switches and multi-user wireless systems with time varying reliability. I

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

Joint rate control and scheduling for providing bounded delay with high efficiency in multihop wireless networks

We consider the problem of supporting traffic with elastic bandwidth requirements and average end-to-end delay constraints in multihop wireless networks, with focus on source rates and link data rates as the key resource allocation decisions. The network utility maximization-based approaches to support delay-sensitive traffic have been predominantly based on either reducing link utilization, or approximation of links as M/D/1 queues, which lead to inefficient link utilization under optimal resource allocation, and mostly to unpredictable transient behavior of packet delays. On the contrary, we present an alternative formulation where the delay constraint is omitted and sources' utility functions are multiplied by a weight factor. The alternative optimization problem is solved by a scheduling algorithm incorporating a duality-based rate control algorithm at its inner layer, where link prices correlate with their average queueing delays. We then present an alternative strategy where the utility weight of each source is adjusted to ensure its desired optimal path prices, and hence the desired average path delays. Since the proposed strategy is based on solving a concave optimization problem for the elastic traffic, it leads to maximal utilization of the network capacity. The proposed approach is then realized by a scheduling algorithm that runs jointly with an integral controller whereby each source independently regulates the queueing delay on its paths at the desired level, using its utility weight factor as the control variable. The proposed algorithms are shown, using theoretical analysis and simulation, to achieve asymptotic regulation of end-to-end delay with good performance

Network Utility Maximization under Maximum Delay Constraints and Throughput Requirements

We consider the problem of maximizing aggregate user utilities over a multi-hop network, subject to link capacity constraints, maximum end-to-end delay constraints, and user throughput requirements. A user's utility is a concave function of the achieved throughput or the experienced maximum delay. The problem is important for supporting real-time multimedia traffic, and is uniquely challenging due to the need of simultaneously considering maximum delay constraints and throughput requirements. We first show that it is NP-complete either (i) to construct a feasible solution strictly meeting all constraints, or (ii) to obtain an optimal solution after we relax maximum delay constraints or throughput requirements up to constant ratios. We then develop a polynomial-time approximation algorithm named PASS. The design of PASS leverages a novel understanding between non-convex maximum-delay-aware problems and their convex average-delay-aware counterparts, which can be of independent interest and suggest a new avenue for solving maximum-delay-aware network optimization problems. Under realistic conditions, PASS achieves constant or problem-dependent approximation ratios, at the cost of violating maximum delay constraints or throughput requirements by up to constant or problem-dependent ratios. PASS is practically useful since the conditions for PASS are satisfied in many popular application scenarios. We empirically evaluate PASS using extensive simulations of supporting video-conferencing traffic across Amazon EC2 datacenters. Compared to existing algorithms and a conceivable baseline, PASS obtains up to $100\%$ improvement of utilities, by meeting the throughput requirements but relaxing the maximum delay constraints that are acceptable for practical video conferencing applications

Delay Minimizing User Association in Cellular Networks via Hierarchically Well-Separated Trees

We study downlink delay minimization within the context of cellular user association policies that map mobile users to base stations. We note the delay minimum user association problem fits within a broader class of network utility maximization and can be posed as a non-convex quadratic program. This non-convexity motivates a split quadratic objective function that captures the original problem's inherent tradeoff: association with a station that provides the highest signal-to-interference-plus-noise ratio (SINR) vs. a station that is least congested. We find the split-term formulation is amenable to linearization by embedding the base stations in a hierarchically well-separated tree (HST), which offers a linear approximation with constant distortion. We provide a numerical comparison of several problem formulations and find that with appropriate optimization parameter selection, the quadratic reformulation produces association policies with sum delays that are close to that of the original network utility maximization. We also comment on the more difficult problem when idle base stations (those without associated users) are deactivated.Comment: 6 pages, 5 figures. Submitted on 2013-10-03 to the 2015 IEEE International Conference on Communications (ICC). Accepted on 2015-01-09 to the 2015 IEEE International Conference on Communications (ICC

Network utility maximization for delay-sensitive applications in unknown communication settings

In the last decades the Internet traffic has greatly evolved. The advent of new Internet services and applications has, in fact, led to a significant growth of the amount of data transmitted, as well as to a transformation of the data type. As a matter of fact, nowadays, the largest amount of traffic share consists of multimedia data, which do not represent classical Internet data. Due to the increasing amount of traffic, the network resources might be scarce, and in such cases it becomes extremely important to optimize network transmission in order to provide a satisfying service to the users. Although methods for maximizing the network utility in scenarios with limited resources have been studied extensively, the evolution of the Internet services poses continuously new challenges that require novel solution methods to meet the transmission requirements. In this thesis we propose novel solutions methods to network utility maximization problems that arise in the context of nowadays network communications. In particular we analyze problems related to delay-sensitive Internet applications and rate allocation in unknown network settings. In the first problem we study how to effectively allocate the transmission rates in a multiparty videoconference system. The main contribution of this chapter is an approximate fast rate rate allocation method that is able to adapt quickly to changes in the videoconference conditions. This fast adaptation cannot be achieved with classical network utility maximization solving methods, as they are usually based on iterative approaches. In this case we leverage the particular structure of the problem to design a novel distributed solving method which proves to be very effective when compared to baseline solutions. The next problem that we address is the design of a congestion control algorithm for delay-sensitive applications. One of the main problems of existing delay-based congestion control algorithms is that they tend to achieve an extremely low throughput when competing against loss-based algorithms. In order to overcome this difficulty we propose a novel adaptive controller based on a bandit problem approach. The adaptive controller tries to infer how the network responds, in terms of rate-delay pair at equilibrium, when changing the delay sensitivity of an underlying delay-based congestion control. Once the network response is inferred, the controller selects the sensitivity that leads to the best trade-off between the transmitting rate and the experienced delay. In the final problem, we analyze the design of an overlay rate allocation systems to be used when: the amount of available network resources is not known, and the user congestion feedback cannot be used as valid signal to reach the optimal rate allocation. Such a scenario appears when an Internet application wants to maximize a certain utility metric, but, at the same time, it must operate using a specific congestion control algorithm that is completely unaware of the application utility. To solve this problem we design a distributed system that coordinates the users in order to perform active learning on the amount of network resource. Adopting such a method reveals to be the key to an effective maximization of the long term application utility for the entire system

Cross-layer optimization in TCP/IP networks

TCP-AQM can be interpreted as distributed primal-dual algorithms to maximize aggregate utility over source rates. We show that an equilibrium of TCP/IP, if exists, maximizes aggregate utility over both source rates and routes, provided congestion prices are used as link costs. An equilibrium exists if and only if this utility maximization problem and its Lagrangian dual have no duality gap. In this case, TCP/IP incurs no penalty in not splitting traffic across multiple paths. Such an equilibrium, however, can be unstable. It can be stabilized by adding a static component to link cost, but at the expense of a reduced utility in equilibrium. If link capacities are optimally provisioned, however, pure static routing, which is necessarily stable, is sufficient to maximize utility. Moreover single-path routing again achieves the same utility as multipath routing at optimality