Mathematics – Optimization and Control
Scientific paper
2010-01-06
Mathematics
Optimization and Control
22 pages
Scientific paper
We extend stochastic network optimization theory to treat networks with arbitrary sample paths for arrivals, channels, and mobility. The network can experience unexpected link or node failures, traffic bursts, and topology changes, and there are no probabilistic assumptions describing these time varying events. Performance of our scheduling algorithm is compared against an ideal T-slot lookahead policy that can make optimal decisions based on knowledge up to T-slots into the future. We develop a simple non-anticipating algorithm that provides network throughput-utility that is arbitrarily close to (or better than) that of the T-slot lookahead policy, with a tradeoff in the worst case queue backlog kept at any queue. The same policy offers even stronger performance, closely matching that of an ideal infinite lookahead policy, when ergodic assumptions are imposed. Our analysis uses a sample path version of Lyapunov drift and provides a methodology for optimizing time averages in general time-varying optimization problems.
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