Necessary conditions for global stability of multiclass queueing networks

Operations Research Letters

Volumn 21, Issue 2, 1997, Pages 87-94

  Hasenbein, John J ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

Multiclass queueing networks; Stability; Virtual station

Indexed keywords

EID: 0001870853     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6377(97)00022-9     Document Type: Article

References (20)

1. D. Bertsimas, D. Gamarnik, J.N. Tsitsiklis, Stability conditions for multiclass fluid queueing networks, IEEE Trans. Automat. Control 41 (11) (1996) pp. 1618-1631.
2. D.D. Botvich, A.A. Zamyatin, Ergodicity of conservative communication networks, Rapport de recherche 1772, INRIA, 1992.
3. M. Bramson, Instability of FIFO queueing networks, Ann. Appl. Probab. 4 (1994) 414-431.
4. H. Chen, A. Mandelbaum, Hierarchical modeling of stochastic networks I: fluid models, in: D.D. Yao (Ed.), Probability Models in Manufacturing Systems, Springer, New York, 1994, ch. 2, pp. 47-106.
5. J.G. Dai, On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models, Ann. Appl. Probab. 5 (1995) 49-77.
6. J.G. Dai, A fluid-limit model criterion for instability of multiclass queueing networks; Ann. Appl. Probab. 6 (1996) 751-757.
7. J.G. Dai, J. VandeVate, Virtual stations and the capacity of two-station queueing networks, Oper. Res., under revision.
8. J.G. Dai, G. Weiss, Stability and instability of fluid models for re-entrant lines, Math. Oper. Res. 21 (1996) 115-134.
9. V. Dumas, Approches fluides pour la stabilité et l'instabilité de réseaux de files d'attente stochastiques à plusieurs classes de clients, Ph.D. thesis, L'école Polytechnique, Paris, France, 1996.
10. V. Dumas, Essential faces and stability conditions of multiclass networks with priorities, Rapport de recherche 3030, INRIA, 1996.
11. V. Dumas, A multiclass network with non-linear, non-convex, non-monotonie stability conditions, Queueing Systems: Theory and Applications, 1997, to appear.
12. J.M. Harrison, V. Nguyen, Some badly behaved closed queueing networks, in: F.P. Kelly, R.J. Williams (Eds.), Stochastic Networks, The IMA Volumes in Mathematics and its Applications, vol. 71, Springer, New York, 1995, pp. 117-124.
13. F.P. Kelly, Networks of queues with customers of different types, J. Appl. Probab. 12 (1975) 542-554.
14. P.R. Kumar, Re-entrant lines, Queueing Systems: Theory and Applications 13 (1993) 87-110.
15. P.R. Kumar, T.I. Seidman, Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems, IEEE Trans. Automat. Control AC-35 (1990) 289-298.
16. S. Kumar, P.R. Kumar, Fluctuation smoothing policies are stable for stochastic reentrant lines, Discrete Event Dynamical Systems 6 (1996) 361-370.
17. S.H. Lu, P.R. Kumar, Distributed scheduling based on due dates and buffer priorities, IEEE Trans. Automat. Control 36 (1991) 1406-1416.
18. S.P. Meyn, Transience of multiclass queueing networks via fluid limit models, Ann. Appl. Probab. 5 (1995) 946-957.
19. A.N. Rybko, A.L. Stolyar, Ergodicity of stochastic processes describing the operation of open queueing networks, Problems of Information Transmission 28 (1992) 199-220.
20. T.I. Seidman, 'First come, first served' can be unstable!, IEEE Trans. Automat. Control 39 (1994) 2166-2171.