Polynomial Complexity Algorithms for Full Utilization of Multi-Hop Wireless Networks

In this paper, we provide and study a general framework that facilitates the development of distributed mechanisms to achieve full utilization of multihop wireless networks. In particular, we describe a generic randomized routing, scheduling, and flow control scheme that allows for a set of imperfections in the operation of the randomized scheduler to account for potential errors in its operation. These imperfections enable the design of a large class of low-complexity and distributed implementations for different interference models. We study the effect of such imperfections on the stability and fairness characteristics of the system and explicitly characterize the degree of fairness achieved as a function of the level of imperfections. Our results reveal the relative importance of different types of errors on the overall system performance and provide valuable insight to the design of distributed controllers with favorable fairness characteristics. In the second part of the paper, 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 centralized throughput-optimal algorithms developed for such a model relies on the solution to an NP-hard problem at every decision. This results in a polynomial complexity cross-layer algorithm that achieves throughput optimality and fair allocation of network resources among the users. We further show that our algorithmic approach enables us to efficiently approximate the capacity region of a multihop wireless network.

Recently, it has been shown that CSMA algorithms which use queue length-based link weights can achieve throughput optimality in wireless networks. In particular, a key result by Rajagopalan, Shah, and Shin (2009) shows that, if the link weights are chosen to be of the form log log(q) (where q is the queue-length), then throughput optimality is achieved. In this paper, we tighten their result by showing that throughput optimality is preserved even with weight functions of the form log(q)/g(q), where g(q) can be a function that increases arbitrarily slowly. The significance of the result is due to the fact that weight functions of the form log(q)/g(q) seem to achieve the best delay performance in practice.

In communication networks with large delay-bandwidth product, congestion could happen over shorter time scales than those at which end-to-end protocols such as congestion control schemes typically operate. In such cases, the congestion can dissipate rapidly before congestion feedback information returns to the source. Network designers therefore face a challenge. The bursty and cyclic nature of Variable Bit Rate (VBR) traffic creates another issue for transmission in ATM networks. To reach the dual goals of keeping cell loss rate low and network utilization high, we propose an adaptive rate-based flow control scheme for real- time VBR traffic in ATM networks. The goal of the scheme is to minimize the impact of traffic overload in order to limit the cell loss rate to an acceptable range and also increase the network utilization. The proposed flow control scheme is based on predicting the evolution of buffer occupancy over time using a Proportional-plus-Integral-plus-Derivative controller and a linear predictor to adaptively update the optimum data emission rate at the transmitter. The adaptive policy attempts to keep the buffer occupancy for each virtual channel at a steady level and the simulation results show that the proposed scheme works effectively against network congestion. Along with the design of the new flow control scheme, we also develop a hierarchically structured testbed to measure network performance and explore various flow control schemes in ATM networks with diverse classes of incoming traffic.

We study the problem of throughput maximization in multi-hop wireless networks with end-to-end delay constraints for each session. This problem has received much attention starting with the work of Grossglauser and Tse (2002), and it has been shown that there is a significant tradeoff between the end-to-end delays and the total achievable rate. We develop algorithms to compute such tradeoffs with provable performance guarantees for arbitrary instances, with general interference models. Given a target delay-bound Δ(c) for each session c, our algorithm gives a stable flow vector with a total throughput within a factor of O (equation) of the maximum, so that the per-session (end-to-end) delay is O (equation), where Δ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> = max <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> {Δ(c)}; note that these bounds depend only on the delays, and not on the network size, and this is the first such result, to our knowledge.

We consider scheduling in networks with interference constraints and reconfiguration delays, which may be incurred when one service schedule is dropped and a distinct service schedule is adopted. Reconfiguration delays occur in a variety of communication settings, such as satellite, optical, or delay-tolerant networks. In the absence of reconfiguration delays it is well known that the celebrated Max-Weight scheduling algorithm guarantees throughput optimality without requiring any knowledge of arrival rates. As we will show, however, the Max-Weight algorithm may fail to achieve throughput optimality in case of nonzero reconfiguration delays. Motivated by the latter issue, we propose a class of adaptive scheduling algorithms which persist with the current schedule until a certain stopping criterion is reached, before switching to the next schedule. While earlier proposed Variable Frame-Based Max-Weight (VFMW) policies belong to this class, we also present Switching-Curve-Based (SCB) policies that are more adaptive to bursts in arrivals. We develop novel Lyapunov drift techniques to prove that this class of algorithms under certain conditions achieves throughput optimality by dynamically adapting the durations of the interswitching intervals. Numerical results demonstrate that these algorithms significantly outperform the ordinary Max-Weight algorithm, and that SCB policies yield a better delay performance than VFMW policies.

The existence of multiple gateways, as is a common case in wireless mesh networks (WMNs), brings the possibility to improve network performance. However, previous studies, including both heuristic-based works and theory-driven cross-layer design works, cannot guarantee an optimal exploitation of multiple gateways. In this paper, we focus on exploiting multiple gateways optimally to achieve maximum network utility. We first extend the current framework of cross-layer design and formulate a network utility maximization (NUM) problem under WMNs with multiple gateways as a constrained optimization problem. Then, by solving this optimization problem, we propose a novel joint traffic splitting, rate control, routing, and scheduling algorithm called cross-layer control with dynamic gateway selection (CLC_DGS), which splits and distributes network traffic into multiple gateways in an optimal way. We prove that CLC_DGS can achieve maximum network utility. Finally, we run extensive simulations to demonstrate that, compared with the previous methods, CLC_DGS significantly improves the performance of WMNs under various network environments, including gateway heterogeneity, link heterogeneity, and different interference models.

The wireless relay mesh network (WRMN) is designed to provide robust and fault tolerant communications between relay and user nodes in broadband wireless networks. In this paper, we investigate the benefits of decoupled optimization of routing and scheduling in WRMNs using the physical interference model and spatial reuse to maximize overall throughput. We model the routing optimization as a linear program using multicommodity flows (MCF). We refer to this problem as multicommodity flow routing optimization (MCF-ROPT). Using the flow per link determined from MCF-ROPT, we develop an optimization formulation to schedule the link traffic such that interference is minimized and time slots are reused appropriately based on spatial TDMA (STDMA). Furthermore, our scheduling approach incorporates the effect of reuse of multiple carriers on the transmission schedule. We refer to this problem as SM-TSS (STDMA multicarrier traffic sensitive scheduling). The SM-TSS is NP-hard and thus is solved using column generation. We compare our formulations with decoupled optimizations that use the protocol interference model and/or single carrier systems and show that our approach guarantees higher throughput by mitigating interference effectively.

We study the problem of distributed scheduling in multi-hop MIMO networks. We first develop a ``MIMO-pipe" model that provides the upper layers a set of rates and SINR requirements, which capture the rate-reliability tradeoff in MIMO communications. The main thrust of this study is then dedicated to developing CSMA-based MIMO-pipe scheduling under the SINR model. We choose the SINR model over the extensively studied matching or protocol-based interference models because it more naturally captures the impact of interference in wireless networks. The coupling among the links caused by the interference makes the problem of devising distributed scheduling algorithms particularly challenging. To that end, we explore CSMA-based MIMO-pipe scheduling, from two perspectives. First, we consider an idealized continuous time CSMA network. We propose a dual-band approach in which control messages are exchanged instantaneously over a channel separate from the data channel, and show that CSMA-based scheduling can achieve throughput optimality under the SINR model. Next, we consider a discrete time CSMA network. To tackle the challenge due to the coupling caused by interference, we propose a ``conservative" scheduling algorithm in which more stringent SINR constraints are imposed based on the MIMO-pipe model. We show that this suboptimal distributed scheduling can achieve an efficiency ratio bounded from below.

A key open question in IEEE 802.11e networks with enhanced distributed channel access (EDCA) is how to properly tune the backoff parameters to optimize the network throughput performance under a certain differentiation requirement. To tackle this problem, a new analytical model for IEEE 802.11e EDCA networks is proposed in this paper, based on which the maximum network throughput is derived as an explicit function of the holding times of head-of-line (HOL) packets in successful transmission and collision states. The optimal initial backoff window sizes to achieve the maximum network throughput under pre-specified target node-throughput ratios are also obtained, and verified by simulation results.

In wireless ad hoc networks, PHY-layer interference is highly dependent on link scheduling schemes, and in turn heavily affects the performance of link scheduling. However, most existing link scheduling schemes ignore such relationship between the PHY and network layers, and hence fail to achieve the optimal end-to-end throughput due to large co-channel interference. This paper proposed a general framework for optimal TDMA (time division multiple access) link scheduling in multi-hop wireless ad hoc networks with general topology. In contrast to existing work, we maximizes the end-to-end throughput by taking into consideration the explicit relationship between the transmission rate of a link and its PHY-layer SINR (signal to interference and noise ratio). In particular, the authors formulate the scheduling problem into a LP (linear programming) problem based on the rate matrices with each entry being a function of SINR. With this formulation, the cross-layer link scheduling problem can be solved in polynomial time. To further reduce the computational complexity the authors proposed an algorithm to effectively reduce the size of the LP problem. Furthermore, to handle large-scale wireless networks, the authors present a decentralized scheduling algorithm that achieves a suboptimal TDMA scheduling solution with dramatically lower computational complexity comparing to the original LP formulation. Numerical results show that the proposed cross-layer link scheduling schemes outperform the existing schemes that assume a simplistic PHY-layer interference model by 59.45%.

User association and resource allocation for downlink orthogonal frequency division multiplexing (OFDM) should be jointly optimized in small cells networks with limited backhaul in order to maximize the network utility. In general, the joint user association and per-band resource allocation problem is known as an integer NP-hard problem requiring exponential order of computational complexity to find the global optimal point. To obtain a solution with feasible computational complexity, most previous works solve this problem by relaxing the integer problem of the per-band resource allocation to a real-valued problem by assuming that channel gain is averaged out over all the frequency bands and that base stations allocate a real-valued proportion of the bandwidth. We propose two sub-optimal algorithms to solve the original integer problem with polynomial order of computational complexity in pursuit of maximizing the network utility with limited backhaul constraints. The network utility and geometric mean of receiving rates for the two proposed schemes are evaluated via numerical simulations. The computational complexity of the two schemes are also represented, respectively, showing the trade-off between the network utility and complexity.

CSMA algorithms based on Gibbs sampling can achieve throughput optimality if appropriate attempt rates are employed. However, the problem of computing these attempt rates is NP-hard. Inspired by the well-known Kikuchi approximation, we propose a simple distributed algorithm, which obtains closed form estimates for the attempt rates. We also prove that our algorithm is exact for a class of graphs, called the chordal graphs. Numerical results suggest that the proposed algorithm outperforms the existing Bethe approximation based algorithms for spatial networks.

In this paper, we look into the issue of supporting multicast in the well-known three-stage Clos network or /spl nu/(m, n, r) network. We first develop an analytical model for the blocking probability of the /spl nu/(m, n, r) multicast network, and then study the blocking behavior of the network under various routing control strategies through simulations. Our analytical and simulation results show that a /spl nu/(m, n, r) network with a small number of middle switches m, such as m=n+c or dn, where c and d are small constants, is almost nonblocking for multicast connections, although theoretically it requires m/spl ges//spl Theta/ (nlog r/log log r) to achieve nonblocking for multicast connections. We also demonstrate that routing control strategies are effective for reducing the blocking probability of the multicast network. The best routing control strategy can provide a factor of 2 to 3 performance improvement over random routing. The results indicate that a /spl nu/(m, n, r) network with a comparable cost to a permutation network can provide cost-effective support for multicast communication.

Software-Defined Networking (SDN) has emerged as the paradigm of the next-generation networking through separating the data control plane from the data plane. The forwarding routing table at each of its switch nodes is usually implemented by expensive and power-hungry Ternary Content Addressable Memory (TCAM) that only has limited number of entries, and the bandwidth at each of its links is bounded too. Under this new network architecture, providing a quality service to users by admitting user requests to meet their resource demands is challenging, and very little attention has ever been paid in this regard. In this paper, we will study online unicast and multicast request admissions in SDNs with the aim to maximize the network throughput under both critical network resources and user bandwidth demand constraints, for which we first propose a novel model to characterize the usage costs of node and link resources. We then devise efficient online algorithms for unicast and multicast requests. We also analyze the competitive ratios of the proposed online algorithms, which are Ο (log n) and O(K∊ log n) for unicasting and multicasting, respectively, where n is the network size, K is the maximum number of members in a multicast request, and ∊ is a constant with 0 < e ≤ 1. We finally evaluate the proposed algorithms empirically through simulations. The simulation results demonstrate that the proposed algorithms are very promising.

We present a brief account of three problems in wireless networks. First, on the problem of scalability, we show that under a certain model of interference, a network with n nodes can only provide a per-node throughput of order square-root of n bits/sec. However, an experimental investigation with IEEE 802.11 technology yielded the considerably worse power law of n raised to -1.68. We then present a new media access control protocol for ad hoc networks, called SEEDEX. It attempts to make reservations without explicitly doing so for each and every packet. Nodes use random schedule, and can inform each other about their schedules merely by exchanging the seeds of their pseudo random number generators. Last we turn to the problem of power control in ad hoc networks. We present a new protocol called COMPOW, which is designed to find the lowest power level at which the entire network is connected. We provide the theoretical justification for it, and a solution of the architectural issues involved. Using a notion of parallel modularity at the network layer, this protocol provides a joint solution for both the routing and power control problems. It has been implemented in the Linux kernel.