Stability of multiclass queueing networks under FIFO service discipline

Mathematics of Operations Research

Volumn 22, Issue 3, 1997, Pages 691-725

  Chen, Hong ^a,b   Zhang, Hanqin ^c  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^c INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

A fluid network; A multiclass queueing network; Fluid approximations; Stability

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; PROBABILITY; QUEUEING THEORY; RANDOM PROCESSES; SYSTEM STABILITY;

FIRST IN FIRST OUT (FIFO) SERVICE DISCIPLINE; FLUID APPROXIMATION THEOREM;

OPERATIONS RESEARCH;

EID: 0031207921     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.22.3.691     Document Type: Article

References (30)

1. Berman, A., R. J. Plemmons (1979). Nonnegative Matrices in the Mathematical Science, Academic Press, New York.
2. Botvich, D. D., A. A. Zamyatin, Ergodicity of conservative communication networks, Rapport de recherche 1772, INTRA, October 1992.
3. Bramson, M. (1994a). Instability of FIFO queueing networks. Ann. Appl. Probab. 4 414-431.
4. _ (1994b). Instability of FIFO queueing networks with quick service times. Ann. Appl. Probab. 4 693-718.
5. _ (1994c). Convergence to equilibria for fluid models of FIFO queueing networks, preprint.
6. Chen, H. (1995). Fluid approximations and stability of multiclass queueing networks: Work-conserving disciplines. Ann. Appl. Probab. 5 637-655.
7. _, and A. Mandelbaum (1991). Discrete flow networks: Bottleneck Analysis and Fluid Approximations. Math. Oper. Res. 16 408-446.
8. Dai, J. G. (1995a). On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Probab. 5 49-77.
9. _ (1995b). Stability of open multiclass queueing networks via fluid models. Stochastic Networks, F. Kelly and R. Williams, eds., Volume 71 of the IMA Volumes in Mathematics and Its Applications, 71-90, Springer-Verlag, New York.
10. _, T. G. Kurtz (1995). A multiclass station with Markovian feedback in heavy traffic. Math. Oper. Res. 22 721-742.
11. _, V. Nguyen (1994). On the convergence of multiclass queueing networks in heavy traffic. Ann. Appl. Probab. 4 26-42.
12. _, Y. Wang (1993). Nonexistence of Brownian models of certain multiclass queueing networks. Queueing Systems : Theory and Appl. 13 41-46.
13. _, G. Weiss (1996). Stability and instability of fluid models for reentrant lines. Math. Oper. Res. 21 115-134.
14. Down, D., S. Meyn (1994). Piecewise linear test functions for stability of queueing networks. Proceedings of the 33rd Conference on Decision and Control 2069-2074.
15. Foss, S., Rybko, A. (1995). Stability of multiclass Jackson-type networks, preprint.
16. Harrison, J. M. (1985). Brownian Motion and Stochastic Flow Systems, Wiley, New York.
17. _ (1995). Balanced fluid models of multiclass queueing networks: a heavy traffic conjecture. Stochastic Networks, F. Kelly and R. Williams, eds., Volume 71 of the IMA Volumes in Mathematics and Its Applications, 1-20, Springer-Verlag, New York.
18. _, V. Nguyen (1993). Brownian models of multiclass queueing networks: current status and open problems. Queueing Systems: Theory and Appl. 13 5-40.
19. Johnson, D. P. (1983). Diffusion Approximations for Optimal Filtering of Jump Processes and for Queueing Networks, Ph.D. Dissertation, University of Wisconsin.
20. Kumar, P. R., S. P. Meyn (1995). Stability of queueing networks and scheduling policies. IEEE Trans. Automat. Control 40 251-260.
21. _, T. I. Seidman (1990). Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems. IEEE Trans. Automat. Control 35 289-298.
22. Lu, S. H., P. R. Kumar (1991). Distributed scheduling based on due dates and buffer priorities. IEEE Trans. Automat. Control 36 1406-1416.
23. Meyn, S. P., R. L. Tweedie (1993). Markov Chains and Stochastic Stability, Springer-Verlag, London.
24. Royden, H. L. (1988). Real Analysis, Macmillan, New York.
25. Rybko, A. N., A. L. Stolyar (1992). Ergodicity of stochastic processes describing the operations of open queueing networks. Problemy Peredachi Informatsii 28 2-26.
26. Seidman, T. I. (1993). 'First come first serve' can be unstable. IEEE Trans. Automat. Control 39 2166-2171.
27. Stolyar, A. L. (1996). On the stability of multiclass queueing networks: a relaxed sufficient condition via limiting fluid processes. Markov Processes and Related Fields (to appear).
28. Whitt, W. (1980). Some useful functions for functional limit theorems. Math. Oper. Res. 5 67-85.
29. _ (1993). Large fluctuations in a deterministic multiclass network of queues. Management Sci. 39, 81020-1028.
30. Winograd, G. I., P. R. Kumar (1995). The FCFS service discipline: stable network topologies, bounds on traffic burstiness and delay, and control by regulators. Math. Comput. Modelling: Special Issue on Recent Advances in Discrete Event Systems (to appear).