Consider a wireless network where each communication link has a minimum bandwidth quality-of-service requirement. Certain pairs of wireless links interfere with each other due to being in the same vicinity, and this interference is modeled by a conflict graph. Given the conflict graph and link bandwidth requirements, the objective is to determine, using only localized information, whether the demands of all the links can be satisfied. At one extreme, each node knows the demands of only its neighbors; at the other extreme, there exists an optimal, centralized scheduler that has global information. The present work interpolates between these two extremes by quantifying the tradeoff between the degree of decentralization and the performance of the distributed algorithm. This open problem is resolved for the primary interference model, and the following general result is obtained: if each node knows the demands of all links in a ball of radius @math centered at the node, then there is a distributed algorithm whose performance is away from that of an optimal, centralized algorithm by a factor of at most @math . The tradeoff between performance and complexity of the distributed algorithm is also analyzed. It is shown that for line networks under the protocol interference model, the row constraints are a factor of at most @math away from optimal. Both bounds are best possible.
The design of distributed admission control mechanisms and distributed scheduling mechanisms are well-known open problems and are an active area of research; see @cite_27 and references therein. Some distributed algorithms for admission control are the row constraints @cite_2 @cite_23 , the scaled clique constraints @cite_2 , and the degree and mixed conditions @cite_23 ; the worst-case performance of these sufficient conditions was analyzed in @cite_6 .
@cite_27 @cite_6 @cite_23 @cite_2
2139386764 2148414233 2056643664 2950999367
This paper builds upon the scalable admission control schemes for CDMA networks developed in F. (2003, December 2004). These schemes are based on an exact representation of the geometry of both the downlink and the uplink channels and ensure that the associated power allocation problems have solutions under constraints on the maximal power of each station user. These schemes are decentralized in that they can be implemented in such a way that each base station only has to consider the load brought by its own users to decide on admission. By load we mean here some function of the configuration of the users and of their bit rates that is described in the paper. When implemented in each base station, such schemes ensure the global feasibility of the power allocation even in a very large (infinite number of cells) network. The estimation of the capacity of large CDMA networks controlled by such schemes was made in these references. In certain cases, for example for a Poisson pattern of mobiles in an hexagonal network of base stations, this approach gives explicit formulas for the infeasibility probability, defined as the fraction of cells where the population of users cannot be entirely admitted by the base station. In the present paper we show that the notion of infeasibility probability is closely related to the notion of blocking probability, defined as the fraction of users that are rejected by the admission control policy in the long run, a notion of central practical importance within this setting. The relation between these two notions is not bound to our particular admission control schemes, but is of more general nature, and in a simplified scenario it can be identified with the well-known Erlang loss formula. We prove this relation using a general spatial birth-and-death process, where customer locations are represented by a spatial point process that evolves over time as users arrive or depart. This allows our model to include the exact representation of the geometry of inter-cell and intra-cell interferences, which play an essential role in the load indicators used in these cellular network admission control schemes. An admission control algorithm must coordinate between flows to provide guarantees about how the medium is shared. In wired networks, nodes can monitor the medium to see how much bandwidth is being used. However, in ad hoc networks, communication from one node may consume the bandwidth of neighboring nodes. Therefore, the bandwidth consumption of flows and the available resources to a node are not local concepts, but related to the neighboring nodes in carrier-sensing range. Current solutions do not address how to perform admission control in such an environment so that the admitted flows in the network do not exceed network capacity. In this paper, we present a scalable and efficient admission control framework - contention-aware admission control protocol (CACP) - to support QoS in ad hoc networks. We present several options for the design of CACP and compare the performance of these options using both mathematical analysis and simulation results. We also demonstrate the effectiveness of CACP compared to existing approaches through extensive simulations. We consider the problem of designing distributed mechanisms for joint congestion control and resource allocation in spatial-reuse TDMA wireless networks. The design problem is posed as a utility maximization subject to link rate constraints that involve both power allocation and transmission scheduling over multiple time-slots. Starting from the performance limits of a centralized optimization based on global network information,we proceed systematically in the development of distributed and transparent protocols. In the process,we introduce a novel decomposition method for convex optimization,establish its convergence for the utility maximization problem and demonstrate how it suggests a distributed solution based on flow control optimization and incremental updates of the transmission schedule.We develop a two-step procedure for finding the schedule updates and suggest two schemes for distributed channel reservation and power control under realistic interference models. Although the final protocols are suboptimal,we isolate and quantify the performance losses incurred by each simplification and demonstrate strong performance in examples. This paper presents a distributed O(1)-approximation algorithm, with expected- @math running time, in the @math model for the metric facility location problem on a size- @math clique network. Though metric facility location has been considered by a number of researchers in low-diameter settings, this is the first sub-logarithmic-round algorithm for the problem that yields an O(1)-approximation in the setting of non-uniform facility opening costs. In order to obtain this result, our paper makes three main technical contributions. First, we show a new lower bound for metric facility location, extending the lower bound of B a (ICALP 2005) that applies only to the special case of uniform facility opening costs. Next, we demonstrate a reduction of the distributed metric facility location problem to the problem of computing an O(1)-ruling set of an appropriate spanning subgraph. Finally, we present a sub-logarithmic-round (in expectation) algorithm for computing a 2-ruling set in a spanning subgraph of a clique. Our algorithm accomplishes this by using a combination of randomized and deterministic sparsification.