Approximation algorithms for throughput maximization in wireless networks with delay constraints

In this chapter, we explore techniques for capacity estimation and throughput maximization in multi-hop wireless networks. The specific problem we investigate is the following: how can we characterize the set of all feasible end-to-end connection throughput rate vectors which can be supported by the network (i.e., what is the network capacity), and how can we design cross-layer algorithms at the scheduling, routing, and transport layers which are guaranteed to operate the network close to its capacity? We approach this problem from three distinct perspectives which have greatly influenced research in this field: (1) throughput scaling in random geometric graphs whose nodes are distributed uniformly in space, (2) geometric packing and linear programming-based techniques for arbitrary networks, and (3) the dynamic back-pressure scheme based on queueing theoretic principles for achieving network stability. A recurring theme throughout this chapter is the role of geometric insights into the design and analysis of provably good algorithms for multi-hop wireless networks. We also include a brief survey of related developments in the field of cross-layer algorithms for multi-hop wireless networks.

Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary- or secondary-interference constraints have been developed. Due to their distributed operation, these algorithms can achieve only a guaranteed fraction of the maximum possible throughput. It was also recently shown that if a set of conditions (known as Local Pooling) is satisfied, simple distributed scheduling algorithms achieve 100% throughput. However, previous work regarding Local Pooling focused mostly on obtaining abstract conditions and on networks with single-hop interference or single-hop traffic. In this paper, we identify several graph classes that satisfy the Local Pooling conditions, thereby enabling the use of such graphs in network design algorithms. Then, we study the multihop implications of Local Pooling. We show that in many cases, as the interference degree increases, the Local Pooling conditions are more likely to hold. Consequently, although increased interference reduces the maximum achievable throughput of the network, it tends to enable distributed algorithms to achieve 100% of this throughput. Regarding multihop traffic, we show that if the network satisfies only the single-hop Local Pooling conditions, distributed joint routing and scheduling algorithms are not guaranteed to achieve maximum throughput. Therefore, we present new conditions for Multihop Local Pooling, under which distributed algorithms achieve 100% throughout. Finally, we identify network topologies in which the conditions hold and discuss the algorithmic implications of the results.

We develop a distributed throughput-optimal power allocation algorithm in wireless networks. The study of this problem has been limited due to the nonconvexity of the underlying optimization problems that prohibits an efficient solution even in a centralized setting. By generalizing the randomization framework originally proposed for input queued switches to SINR rate-based interference model, we characterize the throughput-optimality conditions that enable efficient and distributed implementation. Using gossiping algorithm, we develop a distributed power allocation algorithm that satisfies the optimality conditions, thereby achieving (nearly) 100 percent throughput. We illustrate the performance of our power allocation solution through numerical simulation.

This paper addresses the Quality of Service (QoS) degradation problem of wireless relay node failures in multihop Worldwide interoperable Microwave Access (WiMAX) and Long Term Evolution (LTE) networks. In general, node protection in a communication network increases the reliability of the traffic flow from source to destination. For wireless networks, implementing the traditional 1+1 protection scheme increases the capital cost, as resources cannot be fully utilized. On the other hand, the design and implementation of the 1:N protection scheme in wireless networks for greater value of N (> 2) is very difficult, due to wireless network coverage and the physical layer design. To overcome the above drawbacks, a technique based on network coding is proposed for node protection in multihop wireless networks. In multihop wireless networks, few research efforts are concentrated on node protection schemes using network coding. Moreover, to best of our knowledge, no reports have been published on measuring the QoS performance for node protection in 4G wireless networks using network coding. In this paper, we first describe the node protection scheme using XOR network coding for multihop 4G wireless networks. Then, we measure the QoS performance, such as packet delivery ratio (PDR), latency and jitter, for different scenarios. The scenarios include a failure of a single relay node and failures of two relay nodes with and without our protection scheme and user's mobility. The simulation results show that the QoS performance with protection against a single relay node failure and failures of two relay nodes are very close to that of no failure scenario, while the network reliability increases due to the protection mechanism. Also, we report a decoding problem in multihop wireless networks using XOR network coding.

Wireless multi-hop local area networks use in general scheduling schemes that assume the network capacity to be known. Indeed in most of the throughput-optimal algorithms the sources are assumed to send at a rate within the capacity region. However, measurements made on real deployments show that the network capacity is usually difficult to characterize and also time-varying. It is therefore important to understand how the network behaves when the sources attempt to transmit at a rate above capacity. Toward this goal, we show 3-phase regime in the effect of the input rate λ on the end-to-end throughput μ of a multi-hop network. First, when λ is smaller than a threshold λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , μ is an increasing function of λ. Second, when λ is larger than another threshold λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> > λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , μ is independent of λ. Third, when λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> <; λ <; λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , μ decreases with λ. To understand this phenomenon, we capture the relation between the end-to-end throughput and the queue stability with a mathematical model that allows us to explain and derive the exact values of the transition points λi. We then validate experimentally our simulation results with measurements on a testbed composed of five wireless routers.

In this paper, we characterize the performance limits of an important class of scheduling schemes, called greedy maximal matching (GMM), for multi-hop wireless networks. For simplicity, we focus on the well-established node-exclusive interference model, although many of the stated results can be readily extended to more general interference models. The study of the performance of GMM is intriguing because although a lower bound on its performance is well known, empirical observations suggest that this bound is quite loose, and that the performance of GMM is often close to optimal. In fact, recent results have shown that GMM achieves optimal performance under certain conditions. In this paper, we provide new analytic results that characterize the performance of GMM through the topological properties of the underlying graphs. To that end, we generalize a recently developed topological notion called the local pooling condition to a far weaker condition called the sigma-local pooling. We then define the local-pooling factor on a graph, as the supremum of all sigma such that the graph satisfies sigma-local pooling. We show that for a given graph, the efficiency ratio of GMM (i.e., the worst-case ratio of the throughput of GMM to that of the optimal) is equal to its local-pooling factor. Further, we provide results on how to estimate the local-pooling factor for arbitrary graphs and show that the efficiency ratio of GMM is no smaller than d*/(2d*-1) in a network topology of maximum node-degree d*. We also identify a specific network topology for which the efficiency ratio of GMM is strictly less than 1.

In this study we investigate the interaction between TCP and MAC layer in a wireless multi-hop network. This type of network has traditionally found applications in the military (automated battlefield), law enforcement (search and rescue) and disaster recovery (flood, earthquake), where there is no fixed wired infrastructure. Wireless "ad-hoc" multi-hop networks have previously been proposed for nomadic computing applications. Key requirements in all the above applications are reliable data transfer and congestion control, features that are generally supported by TCP. Unfortunately, TCP performs on wireless in a much less predictable way than on wired protocols. Using simulation, we provide new insight into two critical problems of TCP over wireless multi-hop. The first is the conflict between data packets and ACKs, which causes TCP performance to degrade for window sizes greater than 1 packet. The second is the interaction between MAC and TCP layer backoff timers which causes severe unfairness and capture conditions. In the paper, we identify these problems in several representative simulation runs on various topologies and traffic patterns and indicate possible remedies to improve TCP efficiency over a wireless multi-hop network.

This paper studies joint scheduling and network coding in wireless multicast networks with independent sources. Designing a network coding solution for wireless networks involves scheduling interference-free transmissions and optimizing a performance measure for the predetermined scheduling sets, followed by constructing network codes for the specific solution. In such a design process, the results of prior steps need to provide enough information to the subsequent steps. In this paper, we formulate a linear optimization problem whose results can be used to design a coding solution. We build our work on previous works and present statistics that show the importance of incorporating unequal timeshares in designing network codes. In particular, our statistics show a throughput improvement of about 35% in maximum flow problems and energy savings between 13% and 30%, depending on the network size, in minimum energy problems. We also present the requirements of code construction algorithms for wireless networks that capture the broadcast property of these networks and can design proper codes when timeshares are unequal. In particular, the adaptation of a centralized network coding scheme for wireless networks is discussed. Overall, the work reported here provides a three-step solution to derive network codes that optimize a performance criterion of interest while also solving the scheduling problem in multihop wireless networks.

Due to the increasing number of wireless devices, the issue of energy efficiency that requires high data rate with reliability has spawned tremendous research interests in recent years. In wireless networks, major problem that needs to be addressed is that multihop transmission, though requiring lower transmit power, incurs more circuit energy consumption than that of single-hop transmission and leads to more bit errors. Thus we are motivated to study the energy efficiency of multihop wireless networks with unreliable links, where such a problem is even more serious. Specifically, with a flat Rayleigh fading channel, our network model jointly considers the transmit energy and circuit energy, and characterizes the unreliability caused by the wireless nature with the assumption of probabilistic links. Based on that, we formulate our problems of energy consumption normalized by the source-destination (S-D) path loss, and derive the optimal set of signal-to-noise ratios in each hop to minimize the normalized energy consumption. In addition, our theoretical results exhibit a clear relation between the normalized energy consumption and the delay constraint, and meanwhile disclose the crucial impact that the circuit energy has on the monotonicity of the normalized energy consumption. More specifically, we find that the normalized total energy consumption with the delay constraint decreases as the number of hops increases when the number of hops is small, and increases as the number of hops increases when it is large. Extensive simulations confirm the theoretical results. Our findings shed light on the design, implementation, and operation of real-world energy-efficient multihop wireless networks.

The increasing use of multi-hop wireless networks and the growing demand of bandwidth-intensive multimedia applications are the driving force to explore innovative techniques that can enhance the capacity of multi-hop wireless networks. The commonly used omni-directional antennas limit the spatial reusability of the wireless channel and hence reduce the available capacity of wireless networks. On the contrary, bandforming antennas, that enable directional transmissions and receptions, can overcome the aforementioned limitation. With the recent advances in signed processing and antenna technologies, smart beamforming antennas have become feasible in compact sizes and suitable prices and hence pertinent to multi-hop wireless networks. However, lack of appropriate control over the antenna beamforming may deteriorate the overall performance even below the level achieved by omni-directional antennas. Moreover, beamforming antennas introduce unprecedented challenges including deafness and directional hidden terminal problems. Hence, it is important to design efficient mechanisms for both Medium Access Control (MAC) and routing to deal with these challenges that hinder the full exploitation of spatial reusability offered by smart beamforming antennas. In this dissertation, we develop an analytical framework for modeling directional contention-based MAC protocols, which is, up to our knowledge, the first model to include deafness in the analysis. We show that deafness can severely limit the network capacity. Based on the insights gained from our analysis of the limitations of the existing solutions, we propose a novel opportunistic directional MAC protocol for multi-hop wireless networks with beamforming antennas. The proposed MAC protocol employs a new backoff mechanism that aims at minimizing the unnecessary idle waiting time, which is a key factor in leveraging the spatial reuse. Through extensive simulations, we demonstrate that the proposed MAC protocol enhances the performance in terms of throughput, delay, packet delivery ratio and fairness. We have also addressed the question about the theoretical capacity gain achieved by beamforming antennas. We derive a generic interference model that can accommodate any antenna radiation pattern and show that the capacity gain is significant even when realistic antenna radiation patterns are used. Since smart beamforming antennas can significantly spare the network resources, they can be utilized to provide Quality of Service (QoS) guarantees. We study the bandwidth-guaranteed routing problem in contention-based multi-hop wireless networks with beamforming antennas. We first present an analysis for the wireless links interdependencies in a contention-based environment in the presence of beamforming, which helps in our formulation of the QoS routing problem as a mixed-integer non-linear optimization problem. We then propose a routing and admission control algorithm for its solution. Our simulation results demonstrate the accuracy of our analysis and the ability of our proposed algorithm to find bandwidth-guaranteed routes. In summary, the analysis and design approaches, adopted in this dissertation, enhance the throughput of multi-hop wireless networks by grasping the transmission opportunities offered by smart beamforming antennas while dealing with the beamforming-related challenges at the MAC and network layers, which otherwise limit the spatial reusability of the wireless channel.

Interference neutralization (IN) is an interference management technique that allows simultaneous transmission of multiple links by nullifying their mutual interference in the air via cooperation among the transmitters. Although IN has been studied from information theoretic perspective, its potential for a general multi-hop wireless network has not been explored. The goal of this paper is to understand IN in a multi-hop wireless network from networking perspective. We first establish an IN reference model. Based on this reference model, we develop a set of feasibility constraints for a subset of links to be active simultaneously. By identifying each eligible neutralization node (called neut), we study IN in a general multi-hop network and develop a set of necessary constraints to characterize neut selection, IN, and scheduling. These constraints allow us to study the performance of multi-hop networks without the need of getting involved into onerous signal design issues at the physical layer. Finally, we apply our IN model and constraints to study a throughput maximization problem and show that the use of IN can generally increase network throughput. In particular, throughput gain is most significant when the node density increases.

MaxWeight algorithm, a.k.a., back-pressure algorithm, has received much attention as a viable solution for dynamic link scheduling in multi-hop wireless networks. The basic principle of the MaxWeight algorithm is to select a set of interference-free links with the maximum overall link weights in the network, where the link weight is determined by the queue difference between the transmitter and the receiver. While the throughput-optimality of the MaxWeight algorithm is well understood in the literature, the energy consumption induced by the MaxWeight algorithm is less studied, which is of great interest in energy-constrained wireless networks such as wireless sensor networks. In this paper, we propose an energy-conserving scheduling scheme, a.k.a., minimum energy scheduling (MES) algorithm for multi-hop wireless networks with stochastic traffic arrivals and time-varying channel conditions. We show that our algorithm is energy optimal in the sense that the proposed MES algorithm can achieve an energy consumption which is arbitrarily close to the global minimum solution. Moreover, the energy efficiency of the MES algorithm is achieved without losing the throughput- optimality. In other words, the proposed MES algorithm is still throughput optimal whereas the average consumed energy in the network is significantly reduced, as compared to the traditional MaxWeight algorithm. The theoretical results are substantiated via simulations.

MaxWeight algorithm, a.k.a., back-pressure algorithm [1]-[4], has received much attention as a viable solution for dynamic link scheduling in multi-hop wireless networks. The basic principle of the MaxWeight algorithm is to select a set of interference-free links with the maximum overall link weights in the network, where the link weight is determined by the queue difference between the transmitter and the receiver. While the throughput-optimality of the MaxWeight algorithm is well understood in the literature, the energy consumption induced by the MaxWeight algorithm is less studied, which is of great interest in energy-constrained wireless networks such as wireless sensor networks. In this paper, we propose a minimum energy scheduling (MES) algorithm for multi-hop wireless networks with stochastic traffic arrivals and time-varying channel conditions. We show that our algorithm is energy optimal in the sense that the proposed MES algorithm can achieve an energy consumption which is arbitrarily close to the global minimum solution. Moreover, the energy efficiency of the MES algorithm is achieved without losing the throughput-optimality. In other words, the proposed MES algorithm is still throughput optimal whereas the average consumed energy in the network is significantly reduced, as compared to the traditional MaxWeight algorithm. The theoretical results are substantiated via simulations.

In this paper, we provide and study a general framework that allows the development of distributed mechanisms to achieve full utilization of multi-hop wireless networks. In particular, we describe a generic randomized routing, scheduling and flow control scheme that is applicable to a large class of interference models, and that allows for the development of distributed algorithms which maximize network throughput and utilization. In particular, we focus on a specific interference model, namely the secondary interference model, and develop distributed algorithms with polynomial communication and computation complexity in the network size. This is an important result given that earlier throughput-optimal algorithms developed for such a model relies on the solution to an NP-hard problem. This results in a polynomial complexity cross-layer algorithm that achieves throughput optimality and fair allocation of network resources amongst the users. We further show that our algorithmic approach enables us to efficiently approximate the capacity region of a multi-hop wireless network.

In this paper, we present experimental studies on Multi-channel Multi-radio Multi-hop (M3) wireless networks. The interference of multiple channels and multiple radios is studied. The result may help to understand effect of multi-channel and multi-radio in real system and is useful as reference for network performance optimization. We evaluate the coexistence of real-time traffic and best-effort traffic in multi-hop wireless networks. Our experiments show that coordination among wireless nodes is critical for optimal network performance, especially in the scenarios with quality of service (QoS) requirements. To perform the experiments, an M3 testbed with 32 nodes is built. The testbed is based on Windows operating system and provides convenient programming interface and management tools. The architecture and key modules of the testbed design are described.