Delay and effective throughput of wireless scheduling in heavy traffic regimes: vacation model for complexity

Distributed scheduling algorithms for wireless ad hoc networks have received substantial attention over the last decade. The complexity levels of these algorithms span a wide spectrum, ranging from no message passing to constant/polynomial time complexity, or even exponential complexity. However, by and large it remains open to quantify the impact of message passing complexity on throughput and delay. In this paper, we study the effective throughput and delay performance in wireless scheduling by explicitly considering complexity through a vacation model, where signaling complexity is treated as "vacations" and data transmissions as "services," with a focus on delay analysis in heavy traffic regimes. We analyze delay performance in two regimes of vacation models, depending on the relative lengths of data transmission and vacation periods. State space collapse properties proved here enable a significant dimensionality reduction in the challenging problem of delay characterization. We then explore engineering implications and quantify intuitions based on the heavy traffic analysis.