Bio-inspired algorithms for decentralized round-robin and proportional fair scheduling

In recent years, several models introduced in mathematical biology and natural science have been used as the foundation of networking algorithms. These bio-inspired algorithms often solve complex problems by means of simple and local interactions of individuals. In this work, we consider the development of decentralized scheduling in a small network of self-organizing devices that are modeled as pulse-coupled oscillators (PCOs). By appropriately designing the dynamics of the PCO, the network of devices can converge to a desynchronous state where the nodes naturally separate their transmissions in time. Specifically, by following Peskin´s PCO model with inhibitory coupling, we first show that round-robin scheduling can be achieved with weak convergence, where the nodes´ transmissions are separated by a constant duration, but the differences of their local clocks continue to shift over time. Then, by having each node accept coupling only from the pulses emitted by a subset of neighboring nodes, we show that it is possible to achieve strict desynchronization, where the difference between local clocks remain fixed over time. More interestingly, by having each node maintain two local clocks, we show that it is possible to further achieve proportional fair scheduling, where the time alloted to each node is proportional to their demands. The convergence of these algorithms is studied both analytically and numerically.