Mathematical Models and Algorithms for Network Flow Problems Arising in Wireless Sensor Network Applications

We examine multiple variations on two classical network flow problems, the maximum flow and minimum-cost flow problems. These two problems are well-studied within the optimization community, and many models and algorithms have been presented for their solution. Due to the unique characteristics of the problems we consider, existing approaches cannot be directly applied. The problem variations we examine commonly arise in wireless sensor network (WSN) applications. A WSN consists of a set of sensors and collection sinks that gather and analyze environmental conditions. In addition to providing a taxonomy of relevant literature, we present mathematical programming models and algorithms for solving such problems. First, we consider a variation of the maximum flow problem having node-capacity restrictions. As an alternative to solving a single linear programming (LP) model, we present two alternative solution techniques. The first iteratively solves two smaller auxiliary LP models, and the second is a heuristic approach that avoids solving any LP. We also examine a variation of the maximum flow problem having semicontinuous restrictions that requires the flow, if positive, on any path to be greater than or equal to a minimum threshold. To avoid solving a mixed-integer programming (MIP) model, we present a branch-and-price algorithm that significantly improves the computational time required to solve the problem. Finally, we study two dynamic network flow problems that arise in wireless sensor networks under non-simultaneous flow assumptions. We first consider a dynamic maximum flow problem that requires an arc to transmit a minimum amount of flow each time it begins transmission. We present an MIP for solving this problem along with a heuristic algorithm for its solution. Additionally, we study a dynamic minimum-cost flow problem, in which an additional cost is incurred each time an arc begins transmission. In addition to an MIP, we present an exact algorithm that iteratively solves a relaxed version of the MIP until an optimal solution is found

Optimization driven multi-hop network design and experimentation: the approach of the FP7 project OPNEX

International audienceThe OPNEX project exemplifies system and optimization theory as the foundations for algorithms that provably maximize capacity of wireless networks. The algorithms termed in abstract network models have been converted to protocols and architectures practically applicable to wireless systems. A validation methodology through experimental protocol evaluation in real network testbeds has been proposed and used. OPNEX uses recent advances in system theoretic network control, including the Back-Pressure principle, max-weight scheduling, utility optimization, congestion control, and the primal-dual method for extracting network algorithms. These approaches exhibited vast potential for achieving high capacity and full exploitation of resources in abstract network models and found their way to reality in high performance architectures developed as a result of the research conducted within OPNEX

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

Control of transport dynamics in overlay networks

Transport control is an important factor in the performance of Internet protocols, particularly in the next generation network applications involving computational steering, interactive visualization, instrument control, and transfer of large data sets. The widely deployed Transport Control Protocol is inadequate for these tasks due to its performance drawbacks. The purpose of this dissertation is to conduct a rigorous analytical study on the design and performance of transport protocols, and systematically develop a new class of protocols to overcome the limitations of current methods. Various sources of randomness exist in network performance measurements due to the stochastic nature of network traffic. We propose a new class of transport protocols that explicitly accounts for the randomness based on dynamic stochastic approximation methods. These protocols use congestion window and idle time to dynamically control the source rate to achieve transport objectives. We conduct statistical analyses to determine the main effects of these two control parameters and their interaction effects. The application of stochastic approximation methods enables us to show the analytical stability of the transport protocols and avoid pre-selecting the flow and congestion control parameters. These new protocols are successfully applied to transport control for both goodput stabilization and maximization. The experimental results show the superior performance compared to current methods particularly for Internet applications. To effectively deploy these protocols over the Internet, we develop an overlay network, which resides at the application level to provide data transmission service using User Datagram Protocol. The overlay network, together with the new protocols based on User Datagram Protocol, provides an effective environment for implementing transport control using application-level modules. We also study problems in overlay networks such as path bandwidth estimation and multiple quickest path computation. In wireless networks, most packet losses are caused by physical signal losses and do not necessarily indicate network congestion. Furthermore, the physical link connectivity in ad-hoc networks deployed in unstructured areas is unpredictable. We develop the Connectivity-Through-Time protocols that exploit the node movements to deliver data under dynamic connectivity. We integrate this protocol into overlay networks and present experimental results using network to support a team of mobile robots

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

Performance Optimization and Dynamics Control for Large-scale Data Transfer in Wide-area Networks

Transport control plays an important role in the performance of large-scale scientific and media streaming applications involving transfer of large data sets, media streaming, online computational steering, interactive visualization, and remote instrument control. In general, these applications have two distinctive classes of transport requirements: large-scale scientific applications require high bandwidths to move bulk data across wide-area networks, while media streaming applications require stable bandwidths to ensure smooth media playback. Unfortunately, the widely deployed Transmission Control Protocol is inadequate for such tasks due to its performance limitations. The purpose of this dissertation is to conduct rigorous analytical study of the design and performance of transport solutions, and develop an integrated transport solution in a systematical way to overcome the limitations of current transport methods. One of the primary challenges is to explore and compose a set of feasible route options with multiple constraints. Another challenge essentially arises from the randomness inherent in wide-area networks, particularly the Internet. This randomness must be explicitly accounted for to achieve both goodput maximization and stabilization over the constructed routes by suitably adjusting the source rate in response to both network and host dynamics.The superior and robust performance of the proposed transport solution is extensively evaluated in a simulated environment and further verified through real-life implementations and deployments over both Internet and dedicated connections under disparate network conditions in comparison with existing transport methods

Resource Allocation in Relay Enhanced Broadband Wireless Access Networks

The use of relay nodes to improve the performance of broadband wireless access (BWA) networks has been the subject of intense research activities in recent years. Relay enhanced BWA networks are anticipated to support multimedia traffic (i.e., voice, video, and data traffic). In order to guarantee service to network users, efficient resource distribution is imperative. Wireless multihop networks are characterized by two inherent dynamic characteristics: 1) the existence of wireless interference and 2) mobility of user nodes. Both mobility and interference greatly influence the ability of users to obtain the necessary resources for service. In this dissertation we conduct a comprehensive research study on the topic of resource allocation in the presence of interference and mobility. Specifically, this dissertation investigates the impact interference and mobility have on various aspects of resource allocation, ranging from fairness to spectrum utilization. We study four important resource allocation algorithms for relay enhanced BWA networks. The problems and our research achievements are briefly outlined as follows. First, we propose an interference aware rate adaptive subcarrier and power allocation algorithm using maximum multicommodity flow optimization. We consider the impact of the wireless interference constraints using Signal to Interference Noise Ratio (SINR). We exploit spatial reuse to allocate subcarriers in the network and show that an intelligent reuse of resources can improve throughput while mitigating the impact of interference. We provide a sub-optimal heuristic to solve the rate adaptive resource allocation problem. We demonstrate that aggressive spatial reuse and fine tuned-interference modeling garner advantages in terms of throughput, end-to-end delay and power distribution. Second, we investigate the benefits of decoupled optimization of interference aware routing and scheduling using SINR and spatial reuse to improve the overall achievable throughput. We model the routing optimization problem as a linear program using maximum concurrent flows. We develop an optimization formulation to schedule the link traffic such that interference is mitigated and time slots are reused appropriately based on spatial TDMA (STDMA). The scheduling problem is shown to be NP-hard and is solved using the column generation technique. We compare our formulations to conventional counterparts in the literature and show that our approach guarantees higher throughput by mitigating the effect of interference effectively. Third, we investigate the problem of multipath flow routing and fair bandwidth allocation under interference constraints for multihop wireless networks. We first develop a novel isotonic routing metric, RI3M, considering the influence of interflow and intraflow interference. Second, in order to ensure QoS, an interference-aware max-min fair bandwidth allocation algorithm, LMX:M3F, is proposed where the lexicographically largest bandwidth allocation vector is found among all optimal allocation vectors while considering constraints of interference on the flows. We compare with various interference based routing metrics and interference aware bandwidth allocation algorithms established in the literature to show that RI3M and LMX:M3F succeed in improving network performance in terms of delay, packet loss ratio and bandwidth usage. Lastly, we develop a user mobility prediction model using the Hidden Markov Model(HMM) in which prediction control is transferred to the various fixed relay nodes in the network. Given the HMM prediction model, we develop a routing protocol which uses the location information of the mobile user to determine the interference level on links in its surrounding neighborhood. We use SINR as the routing metric to calculate the interference on a specific link (link cost). We minimize the total cost of routing as a cost function of SINR while guaranteeing that the load on each link does not exceed its capacity. The routing protocol is formulated and solved as a minimum cost flow optimization problem. We compare our SINR based routing algorithm with conventional counterparts in the literature and show that our algorithm reinforces routing paths with high link quality and low latency, therefore improving overall system throughput. The research solutions obtained in this dissertation improve the service reliability and QoS assurance of emerging BWA networks