2 Search Results for "Garncarek, Pawel"


Document
Stable Memoryless Queuing under Contention

Authors: Paweł Garncarek, Tomasz Jurdziński, and Dariusz R. Kowalski

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)


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 rho 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 Omega(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 [Johan Håstad et al., 1996], 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). {}

Cite as

Paweł Garncarek, Tomasz Jurdziński, and Dariusz R. Kowalski. Stable Memoryless Queuing under Contention. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{garncarek_et_al:LIPIcs.DISC.2019.17,
  author =	{Garncarek, Pawe{\l} and Jurdzi\'{n}ski, Tomasz and Kowalski, Dariusz R.},
  title =	{{Stable Memoryless Queuing under Contention}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.17},
  URN =		{urn:nbn:de:0030-drops-113244},
  doi =		{10.4230/LIPIcs.DISC.2019.17},
  annote =	{Keywords: packet scheduling, online algorithms, adversarial injections, stochastic injections, stability, memoryless algorithms}
}
Document
Local Queuing Under Contention

Authors: Pawel Garncarek, Tomasz Jurdzinski, and Dariusz R. Kowalski

Published in: LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)


Abstract
We study stability of local packet scheduling policies in a distributed system of n nodes. The local policies at nodes may only access their local queues, and have no other feedback from the underlying distributed system. The packets arrive at queues according to arrival patterns controlled by an adversary restricted only by injection rate rho and burstiness b. In this work, we assume that the underlying distributed system is a shared channel, in which in order to get rid of a packet from the queue, a node needs to schedule it for transmission on the channel and no other packet is scheduled for transmission at the same time. We show that there is a local adaptive scheduling policy with relatively small memory, which is universally stable on a shared channel, that is, it has bounded queues for any rho<1 and b >= 0. On the other hand, without memory the maximal stable injection rate is O(1/log n). We show a local memoryless (non-adaptive) scheduling policy based on novel idea of ultra strong selectors which is stable for slightly smaller injection c/log^2 n, for some constant c>0.

Cite as

Pawel Garncarek, Tomasz Jurdzinski, and Dariusz R. Kowalski. Local Queuing Under Contention. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{garncarek_et_al:LIPIcs.DISC.2018.28,
  author =	{Garncarek, Pawel and Jurdzinski, Tomasz and Kowalski, Dariusz R.},
  title =	{{Local Queuing Under Contention}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Schmid, Ulrich and Widder, Josef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.28},
  URN =		{urn:nbn:de:0030-drops-98172},
  doi =		{10.4230/LIPIcs.DISC.2018.28},
  annote =	{Keywords: Distributed algorithms, local queuing, shared channel, multiple-access channel, adversarial packet arrivals, stability, deterministic algorithms}
}
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