A General Class of Throughput Optimal Routing Policies in Multi-hop Wireless Networks

TL;DR

This paper introduces a broad class of throughput optimal routing policies for multi-hop wireless networks using novel Lyapunov functions, improving traffic control and network performance.

Contribution

It proposes a new class of Lyapunov functions for designing throughput optimal routing policies, including a congestion-diversity based opportunistic routing method.

Findings

The new policies are proven to be throughput optimal.

The class includes and generalizes existing backpressure routing.

Opportunistic routing with congestion diversity is throughput optimal.

Abstract

This paper considers the problem of throughput optimal routing/scheduling in a multi-hop constrained queueing network with random connectivity whose special case includes opportunistic multi-hop wireless networks and input-queued switch fabrics. The main challenge in the design of throughput optimal routing policies is closely related to identifying appropriate and universal Lyapunov functions with negative expected drift. The few well-known throughput optimal policies in the literature are constructed using simple quadratic or exponential Lyapunov functions of the queue backlogs and as such they seek to balance the queue backlogs across network independent of the topology. By considering a class of continuous, differentiable, and piece-wise quadratic Lyapunov functions, this paper provides a large class of throughput optimal routing policies. The proposed class of Lyapunov functions allow for the routing policy to control the traffic along short paths for a large portion of state-space while ensuring a negative expected drift. This structure enables the design of a large class of routing policies. In particular, and in addition to recovering the throughput optimality of the well known backpressure routing policy, an opportunistic routing policy with congestion diversity is proved to be throughput optimal.