A multiple access window protocol: Analysis for large finite populations

Techniques or schemes for sharing a common communication channel among a population of users are called multiple access protocols. Under the assumptions of a large finite user population and a time-slotted channel with limited feedback, the performance and dynamic behavior of a particular protocol, referred to as a Window protocol, are analyzed. From the performance analysis, an optimal finite horizon control for the protocol is determined. From the dynamic behavior analysis, it is found that there exists a potential bistability which can be avoided if the protocol is allowed to adapt dynamically. Finally, by letting the population size grow to infinity, a link is established between the finite and infinite population problems.