Hop-by-hop congestion control over a wireless multi-hop network

This paper focuses on congestion control over multi-hop, wireless networks. In a wireless network, an important constraint that arises is that due to the MAC (media access control) layer. Many wireless MACs use a time-division strategy for channel access, where, at any point in space, the physical channel can be accessed by a single user at each instant of time. We develop a fair hop-by-hop congestion control algorithm with the MAC constraint being imposed in the form of a channel access time constraint, using an optimization based framework. In the absence of delay, we show that this algorithm is globally stable using a Lyapunov function based approach. Next, in the presence of delay, we show that the hop-by-hop control algorithm has the property of spatial spreading. In other words, focused loads at a particular spatial location in the network get "smoothed" over space. We derive bounds on the "peak load" at a node, both with hop-by-hop control, as well as with end-to-end control, show that significant gains are achieved with the hop-by-hop scheme, and validate the analytical results with simulation.