Mean-field analysis of a scaling MAC radio protocol
Illés Antal Horváth, Kristof Attila Horvath, Péter Kovács, Miklós Telek · Journal of Industrial and Management Optimization · 2019
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.