The Stability of Two-Station Multitype Fluid Networks

References

• Ahuja R. K., Magnanti T. L., Orlin J. B.Network Flows: Theory, Algorithms, and Applications (1993) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
• Bertsimas D., Gamarnik D., Tsitsiklis J. N. Stability conditions for multiclass fluid queueing networks. IEEE Trans. Automatic Control (1996) 41:1618–1631(Correction: 1997. 42 128.)Crossref, Google Scholar
• Botvich D. D., Zamyatin A. A. Ergodicity of conservative communication networks. (1992) . Rapport de recherche 1772, INRIAGoogle Scholar
• Bramson M. Instability of FIFO queueing networks. Ann. Appl. Probab. (1994a) 4:414–431Crossref, Google Scholar
• Bramson M. Instability of FIFO queueing networks with quick service times. Ann. Appl. Probab. (1994b) 4:693–718Crossref, Google Scholar
• Bramson M. Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks. Queueing Systems: Theory Appl. (1997) 23:1–26Crossref, Google Scholar
• Bramson M. Stability of two families of queueing networks and a discussion of fluid limits. Queueing Systems: Theory Appl. (1998) 28:7–31Crossref, Google Scholar
• Bramson M. A stable queueing network with unstable fluid network. Ann. Appl. Probab. (1999) 9:818–853Crossref, Google Scholar
• Chen H. Fluid approximations and stability of multiclass queueing networks I: Work-conserving disciplines. Ann. Appl. Probab. (1995) 5:637–665Crossref, Google Scholar
• Chen H., Zhang H. Stability of multiclass queueing networks under FIFO service discipline. Math. Oper. Res. (1997) 22:691–725Link, Google Scholar
• Chen H., Zhang H. Stability of multiclass queueing networks under priority service disciplines. Oper. Res. (1998) . ForthcomingGoogle Scholar
• Dai J. G., Kelly F., Williams R. J. Stability of open multiclass queueing networks via fluid models. Stochastic Networks (1995) (Springer, New York) 71–90The IMA Volumes in Mathematics and its ApplicationsCrossref, Google Scholar
• Dai J. G. A fluid-limit model criterion for instability of multiclass queueing networks. Ann. Appl. Probab. (1996) 6:751–757Crossref, Google Scholar
• Dai J. G., Hasenbein J., Vande Vate J. H. Stability of a three-station fluid network. Queueing Systems: Theory Appl. (1999) 33:293–325Crossref, Google Scholar
• Dai J. G., Meyn S. P. Stability and convergence of moments for multiclass queueing networks via fluid limit models. IEEE Trans. Automatic Control (1995) 40:1889–1904Crossref, Google Scholar
• Dai J. G., Vande Vate J. Virtual stations and the capacity of two-station queueing networks. (1996) . Under revision for Oper. Res.Google Scholar
• Dai J. G., Weiss G. Stability and instability of fluid models for re-entrant lines. Math. Oper. Res. (1996) 21:115–134Link, Google Scholar
• Down D., Meyn S. Piecewise linear test functions for stability of queueing networks. Proc. 33rd Conference on Decision and Control (1994) 2069–2074Crossref, Google Scholar
• Dumas V. Essential faces and stability conditions of multiclass networks with priorities. (1996) . Rapport de recherche 3030, INRIAGoogle Scholar
• Dumas V. A multiclass network with non-linear, non-convex, non-monotonic stability conditions. Queueing Systems: Theory Appl. (1997) 25:1–43Crossref, Google Scholar
• El-Taha M., Stidham S. Sample-path stability conditions for multiserver input–output processes. J. Appl. Math. Stochastic Anal. (1994) 7:437–456Crossref, Google Scholar
• Foss S., Rybko A. Stability of multiclass Jackson-type networks. (1995) . PreprintGoogle Scholar
• Harrison J. M., Nguyen V., Kelly F. P., Williams R. J. Some badly behaved closed queueing networks. Stochastic Networks (1995) (Springer, New York) 117–12471 of The IMA volumes in Mathematics and its ApplicationsCrossref, Google Scholar
• Hasenbein J. Capacity and Scheduling of Multiclass Queueing Networks. (1998) . Ph.D. Thesis, School of Industrial and Systems Engineering, Georgia Institute of TechnologyGoogle Scholar
• Hasenbein J. Necessary conditions for global stability of multiclass queueing networks. Oper. Res. Lett. (1997) 21:87–94Crossref, Google Scholar
• Humes C. A regulator stabilization technique: Kumar-Seidman revisited. IEEE Trans. Automatic Control (1994) 39:191–196Crossref, Google Scholar
• Kumar P. R., Meyn S. Duality and linear programs for stability and performance analysis of queueing networks and scheduling policies. IEEE Trans. Automatic Control (1996) 41:4–17Crossref, Google Scholar
• Kumar P. R., Meyn S. Stability of queueing networks and scheduling policies. IEEE Trans. Automatic Control (1995) 40:251–260Crossref, Google Scholar
• Kumar P. R., Seidman T. I. Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems. IEEE Trans. Automatic Control (1990) AC-35:289–298Crossref, Google Scholar
• Lu S. H., Kumar P. R. Distributed scheduling based on due dates and buffer priorities. IEEE Trans. Automatic Control (1991) 36:1406–1416Crossref, Google Scholar
• Meyn S. P. Transience of multiclass queueing networks via fluid limit models. Ann. Appl. Probab. (1995) 5:946–957Crossref, Google Scholar
• Morrison J. R., Kumar P. R. On the guaranteed throughput and efficiency of closed re-entrant lines. Queueing Systems: Theory Appl. (1998) 28:33–54Crossref, Google Scholar
• Rybko A. N., Stolyar A. L. Ergodicity of stochastic processes describing the operation of open queueing networks. Problems Inform. Transmission (1992) 28:199–220Google Scholar
• Seidman T. I. “First come, first served” can be unstable!. IEEE Trans. Automatic Control (1994) 39:2166–2171Crossref, Google Scholar
• Stolyar A. On the stability of multiclass queueing networks. Proceeding of the 2nd International Conference on Telecommunication Systems-Modeling and Analysis (1994) Nashville, TN:23–35Google Scholar
• Winograd G. L., Kumar P. R. The FCFS service discipline: Stable network topologies, bounds on traffic burstiness and delay, and control by regulators. Math. Comput. Modeling (1996) 23:115–129Crossref, Google Scholar