Lingering issues in distributed scheduling

Lingering issues in distributed scheduling

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Article ID: iaor2014808
Volume: 77
Issue: 2
Start Page Number: 243
End Page Number: 273
Publication Date: Jun 2014
Journal: Queueing Systems
Authors: , ,
Keywords: queues: applications
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 ρ ) equ1 , with ρ equ2 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 ρ ) equ3 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.

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