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.
The communication ability of packet networks is characterized by the capacity region, i.e. the set of data rates that can be supported by any scheduling policy. In order to achieve (i.e., polynomially bounded queues) and , the classic result of Tassiulas and Ephremides @cite_4 and followup work in the area (e.g. @cite_1 ) imply that is a core optimization problem that lies at the heart of such questions. This reduction applies to very general settings involving single-hop and multi-hop, as well as fixed and controlled transmission rate networks. Moreover, approximating within any factor implies achieving the corresponding fraction of the capacity region. In general, even approximating the capacity region in polynomial time within a non-trivial bound, while keeping the delays low, is hard under standard complexity-theoretic assumptions @cite_30 . Methods with good performance, such as Carrier Sense Multiple Access (CSMA) @cite_18 necessarily require exponential time in the worst case @cite_20 .
@cite_30 @cite_18 @cite_4 @cite_1 @cite_20
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In this paper, we consider CSMA policies for scheduling packet transmissions in multihop wireless networks with one-hop traffic. The main contribution of the paper is to propose a novel CSMA policy, called Unlocking CSMA (U-CSMA), that enables to obtain both high throughput and low packet delays in large wireless networks. More precisely, we show that for torus interference graph topologies with one-hop traffic, U-CSMA is throughput optimal and achieves order-optimal delay. For one-hop traffic, the delay performance is defined to be order-optimal if the delay stays bounded as the network-size increases. Simulations that we conducted suggest that (a) U-CSMA is throughput-optimal and achieves order-optimal delay for general geometric interference graphs and (b) that U-CSMA can be combined with congestion control algorithms to maximize the network-wide utility and obtain order-optimal delay. To the best of our knowledge, this is the first time that a simple distributed scheduling policy has been proposed that is both throughput utility optimal and achieves order-optimal delay. In this paper, we consider CSMA policies for scheduling of multihop wireless networks with one-hop traffic. The main contribution of this paper is to propose Unlocking CSMA (U-CSMA) policy that enables to obtain high throughput with low (average) packet delay for large wireless networks. In particular, the delay under U-CSMA policy becomes order-optimal. For one-hop traffic, delay is defined to be order-optimal if it is O(1), i.e., it stays bounded, as the network-size increases to infinity. Using mean field theory techniques, we analytically show that for torus (grid-like) interference topologies with one-hop traffic, to achieve a network load of @math , the delay under U-CSMA policy becomes @math as the network-size increases, and hence, delay becomes order optimal. We conduct simulations for general random geometric interference topologies under U-CSMA policy combined with congestion control to maximize a network-wide utility. These simulations confirm that order optimality holds, and that we can use U-CSMA policy jointly with congestion control to operate close to the optimal utility with a low packet delay in arbitrarily large random geometric topologies. To the best of our knowledge, it is for the first time that a simple distributed scheduling policy is proposed that in addition to throughput utility-optimality exhibits delay order-optimality. Recently, the capacity region of a multiple-input multiple-output (MIMO) Gaussian broadcast channel, with Gaussian codebooks and known-interference cancellation through dirty paper coding, was shown to equal the union of the capacity regions of a collection of MIMO multiple-access channels. We use this duality result to evaluate the system capacity achievable in a cellular wireless network with multiple antennas at the base station and multiple antennas at each terminal. Some fundamental properties of the rate region are exhibited and algorithms for determining the optimal weighted rate sum and the optimal covariance matrices for achieving a given rate vector on the boundary of the rate region are presented. These algorithms are then used in a simulation study to determine potential capacity enhancements to a cellular system through known-interference cancellation. We study both the circuit data scenario in which each user requires a constant data rate in every frame and the packet data scenario in which users can be assigned a variable rate in each frame so as to maximize the long-term average throughput. In the case of circuit data, the outage probability as a function of the number of active users served at a given rate is determined through simulations. For the packet data case, long-term average throughputs that can be achieved using the proportionally fair scheduling algorithm are determined. We generalize the zero-forcing beamforming technique to the multiple receive antennas case and use this as the baseline for the packet data throughput evaluation. The objective of the paper is to provide qualitative insight into the global effects of distributed mechanisms, such as carrier sense multiple access (CSMA) and rate control, on the performance and stability of multi-hop wireless networks. Toward this end, we introduce a linear queueing network model where the service capacity of each node is modulated by the transmission state of its neighbor. We derive lower bounds on the steady-state utilization at each queue of such networks and demonstrate the existence of a phase transition phenomenon, whereby infinitesimal traffic increase at a single node in the network can suddenly render the entire network instable. We also present NS simulation results that show how this phenomenon can actually take place in IEEE 802.11 multi-hop wireless networks. Our results have direct bearing on rate control schemes, in that they indicate a minimum admissible threshold rate required to prevent network instability.