Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-25T09:25:11.341Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic Distributed Scheduling in Random Access Networks

Part of: Special processes Computer system organization Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Alexander L. Stolyar
Alexander L. Stolyar*
Affiliation:
Bell Laboratories
*
∗Postal address: Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ 07974, USA. Email address: stolyar@research.bell-labs.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider a model of random access (slotted-aloha-type) communication networks of general topology. Assuming that network links receive exogenous arrivals of packets for transmission, we seek dynamic distributed random access strategies whose goal is to keep all network queues stable. We prove that two dynamic strategies, which we collectively call queue length based random access (QRA), ensure stability as long as the rates of exogenous arrival flows are within the network saturation rate region. The first strategy, QRA-I, can be viewed as a random-access-model counterpart of the max-weight scheduling rule, while the second strategy, QRA-II, is a counterpart of the exponential (EXP) rule. The two strategies induce different dynamics of the queues in the fluid scaling limit, which can be exploited for the quality-of-service control in applications.

Keywords

Random multiple accessqueueing networkstabilitymedium access controlslotted aloha

MSC classification

Secondary: 90B15: Network models, stochastic 60K25: Queueing theory 68M12: Network protocols
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 297 - 313
Copyright
Copyright © Applied Probability Trust 2008 

References

[1] Anantharam, V. (1991). The stability region of the finite-user slotted Aloha protocol. IEEE Trans. Inf. Theory 37, 535–540.CrossRefGoogle Scholar
[2] Andrews, M. et al. (2004). Scheduling in a queueing system with asynchronously varying service rates. Prob. Eng. Inf. Sci. 18, 191–217.CrossRefGoogle Scholar
[3] Bonald, T. and Massoulie, L. (2001). Impact of fairness on Internet performance. In Proc. ACM SIGMETRICS, ACM, New York, pp. 82–91.CrossRefGoogle Scholar
[4] Chen, H. (1995). Fluid approximations and stability of multiclass queueing networks: work-conserving disciplines. Ann. Appl. Prob. 5, 637–665.Google Scholar
[5] Dai, J. G. (1995). On the positive Harris recurrence for open multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Prob. 5, 49–77.CrossRefGoogle Scholar
[6] Dai, J. G. and Lin, W. (2005). Maximum pressure policies in stochastic processing networks. Operat. Res. 53, 197–218.CrossRefGoogle Scholar
[7] Dai, J. G. and Meyn, S. P. (1995). Stability and convergence of moments for open multiclass queueing networks via fluid limit models. IEEE Trans. Automatic Control 40, 1889–1904.CrossRefGoogle Scholar
[8] De Veciana, G., Lee, T. J., and Konstantopoulos, T. (2001). Stability and performance analysis of networks supporting elastic services. IEEE/ACM Trans. Networking 9, 2–14.CrossRefGoogle Scholar
[9] Eryilmaz, A., Srikant, R. and Perkins, J. (2005). Stable scheduling policies for fading wireless channels. IEEE/ACM Trans. Networking 13, 411–424.Google Scholar
[10] Gupta, P. and Stolyar, A. L. (2005). Throughput region of random access networks of general topology. Submitted.Google Scholar
[11] Gupta, P. and Stolyar, A. L. (2006). Optimal throughput allocation in general random-access networks. In Proc. 40th Annual Conf. Inf. Sci. Systems (Princeton, NJ, March 2006), IEEE, pp. 1254–1259.Google Scholar
[12] Kar, K., Sarkar, S. and Tassiulas, L. (2004). Achieving proportionally fair rates using local information in Aloha networks. IEEE Trans. Automatic. Control 49, 1858–1862.Google Scholar
[13] Malyshev, V. A. and Menshikov, M. V. (1979). Ergodicity, continuity, and analyticity of countable Markov chains. Trans. Moscow Math. Soc. 39, 3–48.Google Scholar
[14] Massey, J. and Mathys, P. (1985). The collision channel without feedback. IEEE Trans. Inf. Theory 31, 192–204.CrossRefGoogle Scholar
[15] Rybko, A. N. and Stolyar, A. L. (1992). Ergodicity of stochastic processes describing the operation of open queueing networks. Problems Inf. Transmission 28, 199–220.Google Scholar
[16] Shakkottai, S. and Stolyar, A. L. (2002). Scheduling for multiple flows sharing a time-varying channel: the exponential rule. In Analytic Methods in Applied Probability (Amer. Math. Soc. Transl. Ser. 2 207), American Mathematical Society, Providence, RI, pp. 185–201.Google Scholar
[17] Shakkottai, S., Srikant, R. and Stolyar, A. L. (2004). Pathwise optimality of the exponential scheduling rule for wireless channels. Adv. Appl. Prob. 36, 1021–1045.CrossRefGoogle Scholar
[18] Stolyar, A. L. (1995). On the stability of multiclass queueing networks: a relaxed sufficient condition via limiting fluid processes. Markov Process. Relat. Fields 1, 491–512.Google Scholar
[19] Stolyar, A. L. (2004). Max-weight scheduling in a generalized switch: state space collapse and workload minimization in heavy traffic. Ann. Appl. Prob. 14, 1–53.CrossRefGoogle Scholar
[20] Tassiulas, L. and Ephremides, A. (1992). Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Trans. Automatic Control 37, 1936–1936.Google Scholar
[21] Wang, X. and Kar, K. (2004). Distributed algorithms for max-min fair rate allocation in Aloha networks. In Proc. 42nd Annual Allerton Conf. (Urbana-Champaign, October 2004).Google Scholar
[22] Ye, H. Q. (2003). Stability of data networks under an optimization-based bandwidth allocation. IEEE Trans. Automatic Control 48, 1238–1242.Google Scholar