Lingering Issues in Distributed Scheduling

TL;DR

This paper investigates the delay issues in distributed queue-based scheduling algorithms, revealing that aggressive activation rules can cause a lingering effect leading to quadratic delay growth as system load approaches capacity.

Contribution

It provides the first mathematical analysis of the lingering effect in distributed scheduling, quantifies its impact on delay, and compares aggressive versus cautious activation schemes.

Findings

Cautious rules lead to exponential delay growth near capacity.

Aggressive rules induce a lingering effect causing quadratic delay growth.

Simulation results validate the analytical findings.

Abstract

Recent advances have resulted in queue-based algorithms for medium access control which operate in a distributed fashion, and yet achieve the optimal throughput performance of centralized scheduling algorithms. However, fundamental performance bounds reveal that the "cautious" activation rules involved in establishing throughput optimality tend to produce extremely large delays, typically growing exponentially in 1/(1-r), with r the load of the system, in contrast to the usual linear growth. Motivated by that issue, we explore to what extent more "aggressive" schemes can improve the delay performance. Our main finding is that aggressive activation rules induce a lingering effect, where individual nodes retain possession of a shared resource for excessive lengths of time even while a majority of other nodes idle. Using central limit theorem type arguments, we prove that the idleness induced by the lingering effect may cause the delays to grow with 1/(1-r) at a quadratic rate. To the best of our knowledge, these are the first mathematical results illuminating the lingering effect and quantifying the performance impact. In addition extensive simulation experiments are conducted to illustrate and validate the various analytical results.