Duality and linear programs for stability and performance analysis of queuing networks and scheduling policies

IEEE Transactions on Automatic Control

Volumn 41, Issue 1, 1996, Pages 4-17

  Kumar, P R ^a,b   Meyn, Sean P ^a,b  

^a IEEE

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; FAILURE ANALYSIS; LINEAR PROGRAMMING; MATHEMATICAL MODELS; MATRIX ALGEBRA; PERFORMANCE; PERTURBATION TECHNIQUES; SYSTEM STABILITY; SYSTEMS ANALYSIS;

COPOSITIVE MATRIX; DRIFT LINEAR PROGRAM; FINITE TIME LINEAR PROGRAM; LINEAR PROGRAMS; PERFORMANCE ANALYSIS; PERFORMANCE LINEAR PROGRAM; SCHEDULING POLICIES;

COMPUTER NETWORKS;

EID: 0029732538     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.481604     Document Type: Article

References (33)

1. D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, NJ: Prentice-Hall, 1987.
2. J. A. Buzacott and J. G. Shanthikumar, Stochastic Models of Manufacturing Systems. Englewood Cliffs, NJ: Prentice-Hall, 1993.
3. S. B. Gershwin, Manufacturing Systems Engineering. Englewood Cliffs, NJ: Prentice-Hall, 1993.
4. S. Lavenberg, Ed., Computer Performance Modeling Handbook. New York: Academic, 1983.
5. S. H. Lu and P. R. Kumar, "Distributed scheduling based on due dates and buffer priorities," IEEE Trans. Automat. Contr., vol. 36, pp. 1406-1416, Dec. 1991.
6. F. Baskett, K. M. Chandy, R. R. Muntz, and F. G. Palacios, "Open, closed and mixed networks of queues with different classes of customers," J. Assoc. Comput. Mach., vol. 22, pp. 248-260, Apr. 1975.
7. F. P. Kelly, Reversibility and Stochastic Networks. New York: Wiley, 1979.
8. P. R. Kumar, "Re-entrant lines," Queueing Systems: Theory Appl.: Special Issue Queueing Networks, vol. 13, pp. 87-110. May 1993.
9. D. Bertsimas, I. C. Paschalidis, and J. N. Tsitsiklis, "Optimization of multiclass queueing networks: Polyhedral and nonlinear characterizations of achievable performance," Ann. Appl. Probability, vol. 4, pp. 43-75, 1994.
10. S. Kumar and P. R. Kumar, "Performance bounds for queueing networks and scheduling policies," IEEE Trans. Automat. Contr., vol. 39, pp. 1600-1611, Aug. 1994.
11. P. R. Kumar and S. P. Meyn, "Stability of queueing networks and scheduling policies," IEEE Trans. Automat. Contr., vol. 40, pp. 251-260, Feb. 1995.
12. A. N. Rybko and A. L. Stolyar, "On the ergodicity of stochastic processes describing open queueing networks," Problemy Peredachi Informatsii, vol. 28, pp. 2-26, 1991.
13. J. G. Dai, "On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models," Ann. Appl. Probability, vol. 5, pp. 49-77, 1995.
14. H. Chen, "Fluid approximations and stability of multiclass queueing networks I: Work conserving disciplines," Tech. Rep., Univ. of British Columbia, 1993.
15. J. M. Harrison, "Brownian models of heterogeneous customer populations," in Stochastic Differential Systems, Stochastic Control Theory and Applications, IMA Volumes in Mathematics and its Applications, W. Fleming and P. L. Lions, Eds. New York: Springer-Verlag, 1988, pp. 147-186, ch. 10.
16. J. G. Dai and Y. Wang, "Nonexistence of Brownian models for certain multiclass queueing networks," Queueing Syst.: Theory Appl.: Special Issue Queueing Networks, vol. 13, pp. 41-46, May 1993.
17. S. Lippman, "Applying a new device in the optimization of exponential queueing systems," Operations Res., vol. 23, pp. 687-710, 1975.
18. D. Blackwell, "Positive dynamic programming," in Proc. 5th Berkeley Symp. Math., Statistics Probability, 1965, pp. 415-18.
19. S. M. Ross, Applied Probability Models with Optimization Applications. San Francisco, CA: Holden-Day, 1970.
20. H. Kushner, Approximation and Weak Convergence Methods for Random Processes With Application to Stochastic Systems Theory. Cambridge, MA: MIT Press, 1984.
21. G. Fayolle, "On random walks arising in queueing systems: Ergodicity and transience via quadratic forms as Lyapounov functions - Part I," Queueing Syst., vol. 5, pp. 167-184, 1989.
22. G. Fayolle, V. A. Malyshev, M. V. Mensikov, and A. F. Sidorenko, "Lyapunov functions for Jackson networks," Rapports de Recherche no. 1380, INRIA, Rocquencourt, France, 1991.
23. D. D. Botvich and A. A. Zamyatin, "Ergodicity of conservative communication networks," Rapports de Recherche no. 1772, INRIA, Rocquencourt, France, 1992.
24. K. G. Murty, Linear Programming. New York: Wiley, 1983.
25. S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, Control and Communication in Engineering. London: Springer-Verlag, 1993.
26. F. G. Foster, "On Markoff chains with an enumerable infinity of states," in Proc. Cambridge Phil. Soc., vol. 47, pp. 587-591, 1952.
27. G. Fayolle and R. Iasnogorodski, "Criteria for the nonergodicity of stochastic processes: Application to the exponential back-off protocol," J. Appl. Probability, vol. 24, pp. 347-354, 1987.
28. J. L. Doob, Stochastic Processes. New York: Wiley, 1953.
29. R. W. Cottle, G. J. Habetler, and C. E. Lemke, "On classes of copositive matrices," Linear Algebra Appl., vol. 3, pp. 295-310, 1970.
30. L. Andersson, G. Chang, and T. Elfving, "Criteria for copositive matrices and nonnegative Bezier patches," Tech. Rep. LiTH-MAT-R-93-27, Linkoping Univ. and Univ. of Science and Technology, China, Aug. 1993.
31. K. G. Murty and S. N. Kabadi, "Some NP-complete problems in quadratic and nonlinear programming," Math. Programming, vol. 39, pp. 117-129, 1987.
32. V. A. Malyshev, "Networks and dynamical systems," Advances Appl. Probability, vol. 25, pp. 140-175, 1993.
33. P. Billingsley, Weak Convergence of Measures: Applications in Probability. Philadelphia, PA: SIAM, 1971.