Mean-Field Analysis Of A Scaling Mac Radio Protocol
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION(2021)
Abstract
We examine the transient behavior of a positioning system with a large number of tags trying to connect to the infrastructure with an exponential backoff policy in case of unsuccessful connection. Using a classic mean-field approach, we derive a system of differential equations whose solution approximates the original process. Analysis of the solution shows that both the solution and the original system exhibits an unusual log-periodic behavior in the mean-field limit, along with other interesting patterns of behavior. We also perform numerical optimization for the backoff policy.
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Key words
Population model, density dependent behavior, asymptotic limit, log-periodicity, positioning, ultra wideband, MAC, random access channel, exponential backoff
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