Understanding stability of rate control schemes on dynamic communication networks

Questions of rate control on dynamic networks have been open due to lack of rigorous tools in applied Mathematics regarding dynamic networks. Recent developments in theoretical modeling of dynamic networks pave the way for new insights in better understanding of rate control on dynamic networks in general and processes on dynamic networks in particular. Making further progress on our earlier work of modeling framework for a spatio-temporal process, we explore the issue the of stability of such processes using Lyapunov theory. We formulate Lyapunov functions for rate control scheme and provide new insights about long term stability of these processes as they evolve in a very natural setting for packet transfer over communication networks. We present fresh simulation and analytical results to demonstrate the impact of topological changes in communication network and quantify the performance metric in the presence of dynamic transformations. Such scenarios arise natural in swarming, moving vehicles convoys, troop movements, UAV formations and in the community of fast moving receivers and senders during man-made or natural gatherings and disasters.

1. Introduction

Topology changes in the networks are important due to various natural causes, and if there is a change in topology, then the performance of the network is also be affected. Network structure may change due to the failure of links, safety issues when resource heavily loaded, etc.. Hence, there is a need for designing a network which is robust or, at least, has graceful degradation in the presence of topological changes and rate control mechanism is also changed accordingly. A natural extension is to understand the processes and performance regarding space and time modeling rather than just graph theoretical constructs. Therefore, networking community has smartly avoided the impact of the temporal behavior of the networks, and it is hardly found the papers which talk about the spatial temporal processes. This is where new research and new thought process is required. Some philosophical ideas can pave the way for new design paradigm and philosophy altogether.