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

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.Comment: 31 pages (one column), 8 figures, (revision submitted to IEEE Transactions on Information Theory

Fairness in overloaded parallel queues

Maximizing throughput for heterogeneous parallel server queues has received quite a bit of attention from the research community and the stability region for such systems is well understood. However, many real-world systems have periods where they are temporarily overloaded. Under such scenarios, the unstable queues often starve limited resources. This work examines what happens during periods of temporary overload. Specifically, we look at how to fairly distribute stress. We explore the dynamics of the queue workloads under the MaxWeight scheduling policy during long periods of stress and discuss how to tune this policy in order to achieve a target fairness ratio across these workloads

Throughput Optimal Scheduling Policies in Networks of Constrained Queues

(In press