This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channel-aware) scheduling for cellular (single-hop) networks, where easily implementable myopic policies are shown to optimize system performance. We then describe key lessons learned and the main obstacles in extending the work to general resource allocation problems for multi-hop wireless networks. Towards this end, we show that a clean-slate optimization based approach to the multi-hop resource allocation problem naturally results in a “loosely coupled” crosslayer solution. That is, the algorithms obtained map to different layers (transport, network, and MAC/PHY) of the protocol stack are coupled through a limited amount of information being passed back and forth. It turns out that the optimal scheduling component at the MAC layer is very complex and thus needs simpler (potentially imperfect) distributed solutions. We demonstrate how to use imperfect scheduling in the crosslayer framework and describe recently developed distributed algorithms along these lines. We conclude by describing a set of open research problems.

wireless mesh network

Abstract — The implementation of distributed network utility maximization (NUM) algorithms hinges heavily on information feedback through message passing among network elements. In practical systems the feedback is often obtained using errorprone measurement mechanisms and suffers from random errors. In this paper, we investigate the impact of noisy feedback on distributed NUM. We first study the distributed NUM algorithms based on the Lagrangian dual method, and focus on the primal-dual (P-D) algorithm, which is a single time-scale algorithm in the sense that the primal and dual parameters are updated simultaneously. Assuming strong duality, we study both cases when the stochastic gradients are unbiased or biased, and develop a general theory on the stochastic stability of the P-D algorithms in the presence of noisy feedback. When the gradient estimators are unbiased,

Abstract—Back-pressure based algorithms based on the algorithm by Tassiulas and Ephremides have recently received much attention for jointly routing and scheduling over multihop wireless networks. However a significant weakness of this approach has been in routing, because the traditional back-pressure algorithm explores and exploits all feasible paths between each source and destination. While this extensive exploration is essential in order to maintain stability when the network is heavily loaded, under light or moderate loads, packets may be sent over unnecessarily long routes and the algorithm could be very inefficient in terms of end-to-end delay and routing convergence times. This paper proposes new routing/scheduling back-pressure algorithms that not only guarantees network stability (throughput optimality), but also adaptively selects a set of optimal routes based on shortest-path information in order to minimize average path-lengths between each source and destination pair. Our results indicate that under the traditional back-pressure algorithm, the end-to-end packet delay first decreases and then increases as a function of the network load (arrival rate). This surprising low-load behavior is explained due to the fact that the traditional back-pressure algorithm exploits all paths (including very long ones) even when the traffic load is light. On the otherhand, the proposed algorithm adaptively selects a set of routes according to the traffic load so that long paths are used only when necessary, thus resulting in much smaller end-to-end packet delays as compared to the traditional back-pressure algorithm. I.

abstract It has been an intensively sought-after goal to achieve high throughput and fairness in wireless scheduling through simple and distributed algorithms. Many recent papers on the topic have relied on various types of message passing among the nodes. The following question remains open: can scheduling without any message passing guarantee throughput-optimality and fairness? Over the last year, it has been suggested in three papers [1]–[3] that random access without message passing may be designed and proved to be optimal in terms of throughput and utility. In this paper, we first extend the algorithm in [2] and provide a rigorous proof of utility-optimality for random access without message passing for Poisson clock model. Then we turn to the more difficult discrete contention and backoff model with collisions, study its optimality properties, and control a tradeoff between long-term efficiency and short-term fairness that emerges in this model. I.

We consider wireless mesh networks, and exploit the inherent broadcast nature of wireless by making use of multipath routing. We present an optimization framework that enables us to derive optimal flow control, routing, scheduling, and rate adaptation schemes, where we use network coding to ease the routing problem. We prove optimality and derive a primal-dual algorithm that lays the basis for a practical protocol. Optimal MAC scheduling is difficult to implement, and we use random scheduling rather than optimal for comparisons. Under random scheduling, our protocol becomes fully decentralised. We use simulation to show on realistic topologies that we can achieve 20-200 % throughput improvement compared to single path routing, and several times compared to a recent related opportunistic protocol (MORE). 1

In this paper, we extend recent results on fair and stable resource allocation in wireless networks to include multicast sessions, in particular multi-rate multicast. The solution for multi-rate multicast is based on scheduling virtual (shadow) “traffic ” that “moves ” in reverse direction from destinations to sources. This shadow scheduling algorithm can also be used to control delays in wireless networks.

Abstract—Network utility maximization (NUM) problem formulations provide an important approach to conduct network resource allocation and to view layering as optimization decomposition. In the existing literature, distributed implementations are typically achieved by means of the so-called dual decomposition technique. However, the span of decomposition possibilities includes many other elements that, thus far, have not been fully exploited, such as the use of the primal decomposition technique, the versatile introduction of auxiliary variables, and the potential of multilevel decompositions. This paper presents a systematic framework to exploit alternative decomposition structures as a way to obtain different distributed algorithms, each with a different tradeoff among convergence speed, message passing amount and asymmetry, and distributed computation architecture. Several specific applications are considered to illustrate the proposed framework, including resource-constrained and direct-control rate allocation, and rate allocation among QoS classes with multipath routing. For each of these applications, the associated generalized NUM formulation is first presented, followed by the development of novel alternative decompositions and numerical experiments on the resulting new distributed algorithms. A systematic enumeration and comparison of alternative vertical decompositions in the future will help complete a mathematical theory of network architectures. Index Terms—Congestion control, distributed algorithm, mathematical programming/optimization, network control by pricing, network utility maximization (NUM), rate control, resource allocation.

Abstract—Many emerging information processing applications require applying various fork and join type operations such as correlation, aggregation, and encoding/decoding to data streams in real-time. Each operation will require one or more simultaneous input data streams and produce one or more output streams, where the processing may shrink or expand the data rates upon completion. Multiple tasks can be co-located on the same server and compete for limited resources. Effective innetwork processing and resource management in a distributed heterogeneous environment is critical to achieving better scalability and provision of quality of service. In this paper, we study the distributed resource allocation problem for a synchronous fork and join processing network, with the goal of achieving the maximum total utility of output streams. Using primal and dual based optimization techniques, we propose several decentralized iterative algorithms to solve the problem, and design protocols that implement these algorithms. These algorithms have different strengths in practical implementation and can be tailored to take full advantage of the computing capabilities of individual servers. We show that our algorithms guarantee optimality and demonstrate through simulation that they can adapt quickly to dynamically changing environments.

In this paper, we provide and study a general framework that facilitates 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 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 throughputoptimal 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 amongst the users. We further show that our algorithmic approach enables us to efficiently approximate the capacity region of a multi-hop wireless network.