Stability and instability of a two-station queueing network

Annals of Applied Probability

Volumn 14, Issue 1, 2004, Pages 326-377

  Dai, J G ^a   Hasenbein, John J ^b,c   Vande Vate, John H ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c The University of Texas at Austin   (United States)

Author keywords

Fluid model; Large deviations estimate; Multiclass queueing network; Push start; Reentrant line; Stability; Virtual station

Indexed keywords

EID: 26844489409     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/aoap/1075828055     Document Type: Article

References (32)

1. BERTSIMAS, D., GAMARNIK, D. and TSITSIKLIS, J. N. (1996). Stability conditions for multiclass fluid queueing networks. IEEE Trans. Automat. Control 41 1618-1631. [Correction (1997) 42 128.]
2. BRAMSON, M. (1994). Instability of FIFO queueing networks. Ann. Appl. Probab. 4 414-431.
3. BRAMSON, M. (1996). Convergence to equilibria for fluid models of FIFO queueing networks. Queueing Systems Theory Appl. 22 5-45.
4. BRAMSON, M. (1998). Stability of two families of queueing networks and a discussion of fluid limits. Queueing Systems Theory Appl. 28 7-31.
5. BRAMSON, M. (1999). A stable queueing network with unstable fluid model. Ann. Appl. Probab. 9 818-853.
6. CHEN, H. (1995). Fluid approximations and stability of multiclass queueing networks I: Work-conserving disciplines. Ann. Appl. Probab. 5 637-665.
7. CHEN, H. and ZHANG, H. (1997). Stability of multiclass queueing networks under FIFO service discipline. Math. Oper. Res. 22 691-725.
8. DAI, J. G. (1995). On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. 5 49-77.
9. DAI, J. G. (1995). Stability of open multiclass queueing networks via fluid models. Stochastic Networks (F. Kelly and R. Williams, eds.) 71-90. Springer, New York.
10. DAI, J. G. (1996). A fluid-limit model criterion for instability of multiclass queueing networks. Ann. Appl. Probab. 6 751-757.
11. DAI, J. G. and MEYN, S. P. (1995). Stability and convergence of moments for multiclass queueing networks via fluid limit models. IEEE Trans. Automat. Control 40 1889-1904.
12. DAI, J. G. and VANDE VATE, J. (1996). Global stability of two-station queueing networks. In Proceedings of Workshop on Stochastic Networks: Stability and Rare Events (K. S. P. Glasserman and D. Yao, eds.) 1-26. Springer, New York.
13. DAI, J. G. and VANDE VATE, J. (2000). The stability of two-station multitype fluid networks. Oper. Res. 48 721-744.
14. DUMAS, V. (1997). A multiclass network with non-linear, non-convex, non-monotonic stability conditions. Queueing Systems Theory Appl. 25 1-43.
15. EL-TAHA, M. and STIDHAM, S. (1999). Sample-Path Analysis of Queueing Systems. Kluwer, New York.
16. FOSS, S. G. and KOVALEVSKII, A. (1999). A stability criterion via fluid limits and its application to a polling system. Queueing Systems Theory Appl. 32 131-168.
17. HARRISON, J. M. and NGUYEN, V. (1990). The QNET method for two-moment analysis of open queueing networks. Queueing Systems Theory Appl. 6 1-32.
18. HARRISON, J. M. and NGUYEN, V. (1995). Some badly behaved closed queueing networks. Stochastic Networks (F. Kelly and R. Williams, eds.) 117-124. Springer, New York.
19. HASENBEIN, J. J. (1997). Necessary conditions for global stability of multiclass queueing networks. Oper. Res. Lett. 21 87-94.
20. HASENBEIN, J. J. (2001). Stability of fluid networks with proportional routing. Queueing Systems Theory Appl. 38 319-349.
21. KARLIN, S. and TAYLOR, H. M. (1975). A First Course in Stochastic Processes, 2nd ed. Academic Press, New York.
22. KUMAR, P. R. (1993). Re-entrant lines. Queueing Systems Theory Appl. 13 87-110.
23. KUMAR, S. and KUMAR, P. R. (1996). Fluctuation smoothing policies are stable for stochastic reentrant lines. Discrete Event Dynamical Systems 6 361-370.
24. LU, S. H. and KUMAR, P. R. (1991). Distributed scheduling based on due dates and buffer priorities. IEEE Trans. Automat. Control 36 1406-1416.
25. MEYN, S. P. (1995). Transience of multiclass queueing networks via fluid limit models. Ann. Appl. Probab. 5 946-957.
26. MEYN, S. P. and TWEEDIE, R. L. (1993). Markov Chains and Stochastic Stability. Springer, New York.
27. PULHASKII, A. and RYBKO, A. (2000). Non-ergodicity of queueing networks when their fluid model is unstable. Problems Inform. Transmission 36 26-46.
28. RYBKO, A. N. and STOLYAR, A. L. (1992). Ergodicity of stochastic processes describing the operation of open queueing networks. Problems Inform. Transmission 28 199-220.
29. SCHWARTZ, A. and WEISS, A. (1995). Large Deviations for Performance Analysis. Chapman and Hall, New York.
30. STOLYAR, A. (1995). On the stability of multiclass queueing networks: A relaxed sufficient condition via limiting fluid processes. Markov Process. Related Fields 1 491-512.
31. STOLYAR, A. L. and RAMAKRISHNAN, K. K. (1999). The stability of a flow merge point with non-interleaving cut-through scheduling disciplines. In Proceedings of INFOCOM'99.
32. WILLIAMS, R. J. (1998). Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse. Queueing Systems Theory Appl. 30 27-88.