Stable memoryless queuing under contention

Pawel Garncarek, Tomasz Jurdziński, Dariusz R. Kowalski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this work we study stability of local memoryless packet scheduling policies in a distributed system of n nodes/queues under contention. The local policies at nodes may only access their current local queues, and have no other feedback from the underlying distributed system. Moreover, their memory is limited to some basic parameters. The packets arrive at queues according to arrival patterns controlled by an adversary restricted only by injection rate ρ and burstiness b, or driven by a stochastic process; the former model analyzes worst-case stability while the latter – average case. We assume that the underlying distributed system is a classic shared channel, in which no two packets could be successfully scheduled (and removed from queues) at the same time. We show that there is a local memoryless scheduling policy which is both adversarially and stochastically stable for injection rates Ω(1/log n). Another algorithm achieves even higher – constant – stable injection rate, but only for a bounded range of burstiness. The first algorithm is utilizing properties of interleaved ultra-selectors, for which we prove stronger properties than known so far, while the second one is based on entirely new concept of selector with thresholds, unlike previously considered binary selectors/codes in the literature. Note that popular Backoff algorithms, some of which achieve stability for constant (stochastic) injection rates [18], use memory to record current state (e.g., the number of unsuccessful transmissions or the result of random sampling in each window) as well as randomization and feedback from the channel; unlike solutions in this work, which are memoryless and do not rely on randomization or channel feedback (thus, could be used independently from the link layer protocols).

Original languageEnglish (US)
Title of host publication33rd International Symposium on Distributed Computing, DISC 2019
EditorsJukka Suomela
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771269
DOIs
Publication statusPublished - Oct 2019
Event33rd International Symposium on Distributed Computing, DISC 2019 - Budapest, Hungary
Duration: Oct 14 2019Oct 18 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume146
ISSN (Print)1868-8969

Conference

Conference33rd International Symposium on Distributed Computing, DISC 2019
CountryHungary
CityBudapest
Period10/14/1910/18/19

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Keywords

  • Adversarial injections
  • Memoryless algorithms
  • Online algorithms
  • Packet scheduling
  • Stability
  • Stochastic injections

ASJC Scopus subject areas

  • Software

Cite this

Garncarek, P., Jurdziński, T., & Kowalski, D. R. (2019). Stable memoryless queuing under contention. In J. Suomela (Ed.), 33rd International Symposium on Distributed Computing, DISC 2019 [17] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 146). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.DISC.2019.17