This paper focuses on congestion control over multihop, 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. This paper develops 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, it shows that this algorithm is globally stable using a Lyapunov function based approach.
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