A class of throughput optimal routing policies

This paper considers the problem of routing packets across a multi-hop wireless network while ensuring throughput optimality. One of the main challenges in the design of throughput optimal routing policies is identifying an appropriate Lyapunov function with negative expected drift. The only known throughput optimal routing policies in the literature, most notably backpressure routing, are constructed using simple node-based quadratic or exponential Lyapunov functions of the queue backlogs and as such exhibit poor delay performance under many network topologies and traffic conditions. By constructing a class of continuous, differentiable, and piece-wise quadratic Lyapunov functions, this paper provides a large class of throughput optimal routing policies. The nature of the proposed Lyapunov functions is such that, under a “sufficiently unbalanced” backlog state, the traffic must be routed away from nodes with significantly large backlogs (consistent with backpressure) in order to ensure a negative expected drift. In contrast, under all other backlog states, any non-idling policy can ensure a negative expected drift in the proposed Lyapunov function, providing tremendous flexibility in controlling routing decisions for most of the state-space.