Wireless Scheduling Design for Optimizing Both Service Regularity and Mean Delay in Heavy-Traffic Regimes

We consider the design of throughput-optimal scheduling policies in multihop 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, 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, namely Time-Since-Last-Service (TSLS). The RSG Algorithm not only is throughput-optimal, but also achieves a tradeoff between the service regularity performance and the mean delay, i.e., the service regularity performance of the RSG Algorithm improves 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 design parameter. 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 the design parameter weighting for the TSLS scales no faster than the order of 1/5√ϵ, where ϵ 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.