An overarching issue in resource management of wireless networks is assessing their capacity: How much communication can be achieved in a network, utilizing all the tools available: power control, scheduling, routing, channel assignment and rate adjustment? We propose the first framework for approximation algorithms in the physical model of wireless interference that addresses these questions in full. The approximations obtained are at most doubly logarithmic in the link length and rate diversity. Where previous bounds are known, this gives an exponential improvement (or better). A key contribution is showing that the complex interference relationship of the physical model can be simplified, at a small cost, into a novel type of amenable conflict graphs. We also show that the approximation obtained is provably the best possible for any conflict graph formulation.
We consider a communication network and study the problem of designing a high-throughput and low-delay scheduling policy that only requires a polynomial amount of computation at each time step. The well-known maximum weight scheduling policy, proposed by Tassiulas and Ephremides (1992), has favorable performance in terms of throughput and delay but, for general networks, it can be computationally very expensive. A related randomized policy proposed by Tassiulas (1998) provides maximal throughput with only a small amount of computation per step, but seems to induce exponentially large average delay. These considerations raise some natural questions. Is it possible to design a policy with low complexity, high throughput, and low delay for a general network? Does Tassiulas' randomized policy result in low average delay? In this paper, we answer both of these questions negatively. We consider a wireless network operating under two alternative interference models: (a) a combinatorial model involving independent set constraints and (b) the standard SINR (signal to interference noise ratio) model. We show that unless NP ⊆ BPP (or P = NP for the case of determistic arrivals and deterministic policies), and even if the required throughput is a very small fraction of the network's capacity, there does not exist a low-delay policy whose computation per time step scales polynomially with the number of queues. In particular, the average delay of Tassiulas' randomized algorithm must grow super-polynomially. To establish our results, we employ a clever graph transformation introduced by Lund and Yannakakis (1994). In multihop wireless networks, designing distributed scheduling algorithms to achieve the maximal throughput is a challenging problem because of the complex interference constraints among different links. Traditional maximal-weight scheduling (MWS), although throughput-optimal, is difficult to implement in distributed networks. On the other hand, a distributed greedy protocol similar to IEEE 802.11 does not guarantee the maximal throughput. In this paper, we introduce an adaptive carrier sense multiple access (CSMA) scheduling algorithm that can achieve the maximal throughput distributively. Some of the major advantages of the algorithm are that it applies to a very general interference model and that it is simple, distributed, and asynchronous. Furthermore, the algorithm is combined with congestion control to achieve the optimal utility and fairness of competing flows. Simulations verify the effectiveness of the algorithm. Also, the adaptive CSMA scheduling is a modular MAC-layer algorithm that can be combined with various protocols in the transport layer and network layer. Finally, the paper explores some implementation issues in the setting of 802.11 networks. The stability of a queueing network with interdependent servers is considered. The dependency among the servers is described by the definition of their subsets that can be activated simultaneously. Multihop radio networks provide a motivation for the consideration of this system. The problem of scheduling the server activation under the constraints imposed by the dependency among servers is studied. The performance criterion of a scheduling policy is its throughput that is characterized by its stability region, that is, the set of vectors of arrival and service rates for which the system is stable. A policy is obtained which is optimal in the sense that its stability region is a superset of the stability region of every other scheduling policy, and this stability region is characterized. The behavior of the network is studied for arrival rates that lie outside the stability region. Implications of the results in certain types of concurrent database and parallel processing systems are discussed. > We study the joint problem of allocating data rates and finding a stabilizing scheduling policy in a multihop wireless network. We propose a dual optimization based approach through which the rate control problem and the scheduling problem can be decomposed. We demonstrate via both analytical and numerical results that the proposed mechanism can fully utilize the capacity of the network, maintain fairness, and improve the quality of service to the users. Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. It has been recently used to design distributed carrier-sense multiple-access (CSMA) scheduling algorithms for multihop wireless networks. In this paper, we derive bounds on the mixing time of a generalization of Glauber dynamics where multiple links update their states in parallel and the fugacity of each link can be different. The results are used to prove that the average queue length (and hence, the delay) under the parallel-Glauber-dynamics-based CSMA grows polynomially in the number of links for wireless networks with bounded-degree interference graphs when the arrival rate lies in a fraction of the capacity region. Other versions of adaptive CSMA can be analyzed similarly. We also show that in specific network topologies, the low-delay capacity region can be further improved.