Sufficient conditions for stability of longest-queue-first scheduling: Second-order properties using fluid limits

Advances in Applied Probability

Volumn 38, Issue 2, 2006, Pages 505-521

  Dimakis, Antonis ^a   Walrand, Jean ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Fluid limit; Generalized switch; Local fluid limit; Local pooling; Longest queue first scheduling; MaxWeight scheduling; Second order condition; Stability; Throughput optimality

Indexed keywords

MATHEMATICAL MODELS; OPTIMIZATION; QUEUEING NETWORKS; SCHEDULING; STABILITY;

FLUID LIMIT; GENERALIZED SWITCH; LOCAL POOLING; LONGEST-QUEUE-FIRST SCHEDULING; MAXWEIGHT SCHEDULING; SECOND-ORDER CONDITION; THROUGHPUT OPTIMALITY;

QUEUEING THEORY;

EID: 33745959935     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1151337082     Document Type: Article

References (11)

1. Andrews, M. et al. (2004). Scheduling in a queuing system with asynchronously varying service rates. Prob. Eng. Inf. Sci. 18, 191-217.
2. Dai, J. G. (1995). On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Prob. 5, 49-77.
3. Dai, J. G. and Prabhakar, B. (2000). The throughput of data switches with and without speedup. In Proc. INFOCOM 2000, Vol. 2, IEEE, Piscataway, NJ, pp. 556-564.
4. Durrett, R. (2004). Probability: Theory and Examples, 3rd edn. Duxbury, Belmont, CA.
5. Kumar, S., Giaccone, P. and Leonardi, E. (2002). Rate stability of stable marriage scheduling algorithms in input-queued switches. In Proc. 40th Annual Allerton Conference on Computers, Communication, and Control. University of Illinois, Urbana-Champaign, IL. Available at http://www.stanford.edu/skumar/preprints.htm.
6. Malyshev, V. A. (1993). Networks and dynamical systems. Adv. Appl. Prob. 25, 140-175.
7. McKeown, N. (1995). Scheduling algorithms for input-queued cell switches. Doctoral Thesis, University of California, Berkeley.
8. Shakkottai, S. and Stolyar, A. (2002). Scheduling for multiple flows sharing a time-varying channel: the exponential rule. In Analytic Methods in Applied Probability, ed. Yu. M. Suhov, American Mathematical Society, Providence, RI, pp. 185-202.
9. Stolyar, A. (2004). MaxWeight scheduling in a generalized switch: state space collapse and workload minimization in heavy traffic. Ann. Appl. Prob. 14, 1-53.
10. 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.
11. 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, 1936-1948.