Heavy-traffic-optimal scheduling with regular service guarantees in wireless networks.

We consider the design of throughput-optimal scheduling policies in multi-hop wireless networks that also possess good mean delay performance and provide regular service for all links -- critical metrics for real-time applications. To that end, we study a parametric class of maximum-weight type scheduling policies with parameter α ≥ 0, called Regular Service Guarantee (RSG) Algorithm, where each link weight consists of its own queue-length and a counter that tracks the time since the last service. This policy has been shown to be throughput-optimal and to provide more regular service as the parameter α increases, however at the cost of increasing mean delay. This motivates us to investigate whether satisfactory service regularity and low mean-delay can be simultaneously achieved by the RSG Algorithm by carefully selecting its parameter α. To that end, we perform a novel Lyapunov-drift based analysis of the steady-state behavior of the stochastic network. Our analysis reveals that the RSG Algorithm can minimize the total mean queue-length to establish mean delay optimality under heavily-loaded conditions as long as α scales no faster than the order of 1/5√∈, where ∈ measures the closeness of the network load to the boundary of the capacity region. To the best of our knowledge, this is the first work that provides regular service to all links while also achieving heavy-traffic optimality in mean queue-lengths.