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.
A line network is one where all nodes are positioned in a straight line, say on the @math -axis. If each node has a certain radius of coverage and two nodes interfere with each other whenever their coverage areas intersect, then one obtains a conflict graph called an interval graph @cite_9 . Conflict graphs arising in spectrum allocation are also interval graphs @cite_17 . Polynomial-time algorithms are known for finding maximum weight independent sets in interval graphs.
@cite_9 @cite_17
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One of the most compelling technological advances of this decade has been the advent of deploying wireless networks of heterogeneous smart sensor nodes for complex information gathering tasks. A wireless distributed sensor network (DSN) is a self-organizing , ad-hoc network of a large number of cooperative intelligent sensor nodes. Due to the limited power of sensor nodes, energy-efficient DSN are essentially multi-hop networks. The self-organizing capabilities, and the cooperative operation of DSN allow for forming reliable clusters of sensors deployed near, or at, the sites of target phenomena. Reliable monitoring of a phenomenon (or event detection) depends on the collective data provided by the target cluster of sensors, and not on any individual node. The failure of one or more nodes may not cause the operational data sources to be disconnected from the data sinks (command nodes or end user stations). However, it may increase the number of hops a data message has to go through before reaching its destination (and subsequently increase the message delay). In this paper, we focus on two related problems: computing a measure for the reliability of DSN, and computing a measure for the expected & the maximum message delay between data sources (sensors) & data sinks in an operational DSN. Given an estimation of the failure probabilities of the sensors, as well as the intermediate nodes (nodes used to relay messages between data sources, and data sinks), we use a probabilistic graph to model DSN. We define the DSN reliability as the probability that there exists an operating communication path between the sink node, and at least one operational sensor in a target cluster. We show that both problems are #P-hard for arbitrary networks. We then present two algorithms for computing the reliability, and the expected message delay for arbitrary networks. We also consider two special cases where efficient (polynomial time) algorithms are developed. Finally, we present some numerical results that demonstrate some of the applications of our algorithms. Wireless virtualization is a promising approach to foster innovation and prevent the ossification of wireless networks. Within a virtualized wireless network, multiple network slices, or virtual operators (VO), are co- hosted on the same physical infrastructure. A fundamental question in this environment is which multiplexing technique, TDMA, FDMA or SDMA, should be used to slice the network among the VOs. Another related question is how should the stochastic arrival process affect the slicing and QoS criteria. To answer these two questions, we study the problem of QoS-aware joint admission control and network slicing. Due to the NP- hardness of the problem, we approach it using a heuristic algorithm composed of three steps: spectrum allocation, admission control and spatial multiplexing. The proposed algorithm incorporates the effects of QoS and stochastic traffic. We study through simulations the benefits of joint spatial- frequency multiplexing over the static frequency slicing approach. Finally, our simulation results help shed some light on the trade-offs between frequency and spatial multiplexing as well as between QoS and utilization.