An Optimal Medium Access Control with Partial Observations for Sensor Networks
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An Optimal Medium Access Control with Partial Observations for Sensor Networks ˘ Razvan Cristescu Center for the Mathematics of Information, California Institute of Technology, Caltech 13693, Pasadena, CA 91125, USA Email: [email protected]
Sergio D. Servetto School of Electrical and Computer Engineering, College of Engineering, Cornell University, 224 Philips Hall, Ithaca, NY 14853, USA Email: [email protected] Received 10 December 2004; Revised 13 April 2005 We consider medium access control (MAC) in multihop sensor networks, where only partial information about the shared medium is available to the transmitter. We model our setting as a queuing problem in which the service rate of a queue is a function of a partially observed Markov chain representing the available bandwidth, and in which the arrivals are controlled based on the partial observations so as to keep the system in a desirable mildly unstable regime. The optimal controller for this problem satisfies a separation property: we first compute a probability measure on the state space of the chain, namely the information state, then use this measure as the new state on which the control decisions are based. We give a formal description of the system considered and of its dynamics, we formalize and solve an optimal control problem, and we show numerical simulations to illustrate with concrete examples properties of the optimal control law. We show how the ergodic behavior of our queuing model is characterized by an invariant measure over all possible information states, and we construct that measure. Our results can be specifically applied for designing efficient and stable algorithms for medium access control in multiple-accessed systems, in particular for sensor networks. Keywords and phrases: MAC, feedback control, controlled Markov chains, Markov decision processes, dynamic programming, stochastic stability.
1.
INTRODUCTION
1.1. Multiple access in dynamic networks Communication in large networks has to be done over an inherently challenging multiple-access channel. An important constraint is associated with the nodes that relay transmission from the source to the destination (relay nodes, or routers). Namely, the relay nodes have an associated maximum bandwidth, determined for instance by the limited size of their buffers and the finite rate of processing. Thus, the nodes using the relay need usually to contend for the access. A typical example of such a system is a sensor network, where deployed nodes measure some property of the environment like temperature or seismic data. Data from these nodes is transmitted over the network, using other nodes as relays, to one or more base stations, for storage or control purposes. The additional constraints in such networks result This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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