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Optimal Transmission Policies for Noisy Channels

Division of Mathematics and Computer Science, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
IBM T.J. Watson Research Center, 30 Saw Mill River Road, Hawthorne, New York 10532
Department of Operations and Management Information Systems, Santa Clara University, Santa Clara, California 95053
koole{at}cs.vu.nl
zhenl{at}us.ibm.com
rrighter{at}scu.edu

We consider transmission policies for multiple users sharing a single wireless link to a base station. The noise, and hence the probability of correct transmission of a packet, depends on the state of the user receiving the packet. The state for each user is independent of the states of the other users and changes according to a two-state (good/bad) Markov chain. The state of a user is observed only when it transmits. We give conditions under which the optimal policy is the myopic policy, in which a packet is transmitted to the user that is most likely to be in the better of the two states. We do this by showing that the optimal value function is marginally linear in each of the users' probabilities of being in the good state. Our model also may be applied to flexible manufacturing systems with unreliable tools and networked computer systems.

Subject classifications: Communications: transmission policies for noisy channels; Dynamic programming/optimal control: models, scheduling with partial information.
History: Received February 1999; revision received February 2000; revision received June 2000; accepted August 2000.