Editorial introduction
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Editorial introduction
Received: 18 August 2012 / Published online: 7 September 2012 © Springer Science+Business Media, LLC 2012
This is the second volume of the special issue “Recent Trends in the Mathematics of Wireless Communication Networks: Algorithms, Models, and Methods,” bringing together a collection of papers describing various recent advances in the mathematical treatment and stochastic analysis of wireless communication systems. The paper by Banerjee, Gopalan, Reddy, Shakkottai, and Ying studies the problem of distributed scheduling in wireless networks, where each node makes individual scheduling decisions based on heterogeneously delayed network state information (NSI). This leads to inconsistency in the views of the network across nodes, which coupled with interference, renders it hard to schedule for high throughputs. The paper characterizes the network throughput region for this setup, and devises optimal scheduling policies to achieve the same. The proposed scheduling policies have a threshold-based structure and, moreover, require the nodes to use only the “smallest critical subset” of the available delayed NSI to make decisions. In addition, Markov chain mixing techniques are used to assess the impact of delayed NSI on the throughput region. This not only highlights the value of extra NSI for scheduling, but also quantifies the loss in throughput incurred by lower complexity scheduling policies which use homogeneously delayed NSI. The paper by Banerjee, Gupta, and Shakkottai addresses the design of network algorithms for function computation in sensor networks. The paper specifically seeks dynamic joint aggregation, routing, and scheduling algorithms that have analytically provable performance benefits due to in-network computation as compared to data forwarding. The authors define a class of “fully-multiplexible” functions, which includes several functions such as parity, MAX, and kth order statistics, and for which the maximum achievable refresh rate of the network can be exactly characterized in terms of an underlying graph primitive, the min-mincut. In wireline networks, they show that the maximum refresh rate is achievable by a simple algorithm that is dynamic, distributed, and only dependent on local information. In the case of wireless
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networks, a MaxWeight-like algorithm with dynamic flow splitting is provided and proved to be throughput-optimal. The paper by Celik and Modiano considers the use of controlled mobility in wireless networks where messages arrive randomly in time and space. Mobile receivers (collectors) are responsible for gathering these messages via wireless transmission by dynamically adjusting their position in the network. The central objective is to use a combination of wireless transmission and controlled mobility in order to improve the throughput and delay performance. The authors first analyze a system with a single collector, and establish a necessary and sufficient stability condition. They also present lower bounds for the
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