STABILITY CONDITION OF A PRIORITY QUEUEING SYSTEM

Volume: 1 Number: 2 December 1, 2013
Amina Angelika Bouchentouf , Hananesakhi
EN

STABILITY CONDITION OF A PRIORITY QUEUEING SYSTEM

Abstract

The present paper is devoted to the study of a priority multiclasssystem stability, where we establish a sufficient condition for the stability of aqueueing network composed of N-units, N ≥ 3 and N2classes (N classes ateach unit); that is the stability under all work conserving disciplines with thepriority discipline

Keywords

Stability, fluid models, multiclass queueing networks, global stability,piecewise linear Lyapunov functions, linear Lyapunov functions

References

  1. Bertsimas, D., Gamarnik, D., and Tsitsiklis, J. N., Stability conditions for multiclass fluid queueing networks, IEEE Trans. Automat. Control., 41 (1996), no. 11, 1618-1631.
  2. Botvich, D. D., and Zamyatin, A. A., Ergodicity of conservative communication networks, Rapport de recherche, 1772, INRIA, (1992).
  3. Chen, H., Fluid approximations and stability of multiclass queueing networks I: Work- conserving disciplines, Annals of Applied Probability, 5 (1995), 637-665.
  4. Dai, J. G., On possitive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models, Mathematics and its applications, 71 (1995), 71-90.
  5. Dai, J. G., Hasenbein, J. J., and Vande Vate, J., Stability of a three-station fluid network, Queueing Systems, 33 (1999), 293-325.
  6. Dai, J. G., and Vande Vate, J., Global stability of two-station queueing networks, Lecture Notes in Statistics. Columbia University, New York, Springer-Verlag, 117 (1996), 1-26.
  7. Dai, J. G., and Vande Vate, J., The stability of two-station fluid networks, Operations Re- search, 48 (2000), 721-744.
  8. Dai, J. G., and Weiss, G., Stability and instability of fluid models for re-entrant lines, Math- ematics of operations Research, 21 (1996), 115-134.
  9. Down, D. and Meyn, S.P., Piecewise linear test functions for stability and instability of queueing networks, Queueing Systems, 27 (1997), 205-226.
  10. Rybko, A. N., and Stolyar, A. L., On the ergodicity of random processes that describe the
Vancouver
1.Amina Angelika Bouchentouf, Hananesakhi . STABILITY CONDITION OF A PRIORITY QUEUEING SYSTEM. Math. Sci. Appl. E-Notes [Internet]. 2013 Dec. 1;1(2):165-72. Available from: https://izlik.org/JA32WF85JG