Performance analysis of queueing networks via robust optimization

Operations Research

Volumn 59, Issue 2, 2011, Pages 455-466

  Bertsimas, Dimitris ^a   Gamarnik, David ^a   Anatoliy Rikun, Alexander ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Applications; Linear applications; Optimization; Probability; Programming; Queues; Tandem

Indexed keywords

CORRECTION FACTORS; HEAVY TRAFFICS; LAW OF THE ITERATED LOGARITHM; LINEAR APPLICATIONS; LINEAR CONSTRAINTS; MULTI-CLASS; PERFORMANCE ANALYSIS; PERFORMANCE BOUNDS; PERFORMANCE MEASURE; PROBABILITY LAW; PRODUCT-FORM; PROGRAMMING; QUEUEING MODEL; QUEUES; ROBUST OPTIMIZATION; SERVICE TIME; SOJOURN TIME; STEADY STATE PERFORMANCE; TANDEM; TRAFFIC INTENSITY; UPPER AND LOWER BOUNDS; UPPER BOUND;

ALGEBRA; OPTIMIZATION; PROBABILITY DISTRIBUTIONS; QUEUEING NETWORKS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

QUEUEING THEORY;

EID: 79957485610     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1100.0879     Document Type: Article

References (38)

1. Andrews, M., B. Awerbuch, A. Fernandez, T. Leighton, Z. Liu, J. Kleinberg. 2001. Universal-stability results and performance bounds for greedy contention-resolution protocols. J. ACM 48(1) 39-69.
2. Ben-Tal, A., A. Nemirovski. 1998. Robust convex optimization. Math. Oper. Res. 23(4) 769-805. (Pubitemid 128508557)
3. Ben-Tal, A., A. Nemirovski. 1999. Robust solutions of uncertain linear programs. Oper. Res. Lett. 25(1) 1-13.
4. Bertsimas, D., J. Niño-Mora. 1999. Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part II, the multi-station case. Math. Oper. Res. 24(2) 331-361.
5. Bertsimas, D., M. Sim. 2003. Robust discrete optimization and network flows. Math. Programming Ser. B 98(1-3) 49-71.
6. Bertsimas, D., M. Sim. 2004. The price of robustness. Oper. Res. 52(1) 35-53. (Pubitemid 40000812)
7. Bertsimas, D., D. Gamarnik, J. Tsitsiklis. 1996. Stability conditions for multiclass fluid queueing networks. IEEE Trans. Automat. Control 41 1618-1631. (Pubitemid 126769005)
8. Bertsimas, D., D. Gamarnik, J. Tsitsiklis. 2001. Performance of multiclass Markovian queueing networks via piecewise linear Lyapunov functions. Ann. Appl. Prob. 11(4) 1384-1428. (Pubitemid 33571766)
9. Bertsimas, D., I. Paschalidis, J. Tsitsiklis. 1994. Optimization of multiclass queueing networks: Polyhedral and nonlinear characterization of achievable performance. Ann. Appl. Probab. 4(1) 43-75.
10. Borodin, A., J. Kleinberg, P. Raghavan, M. Sudan, D. Williamson. 2001. Adversarial queueing theory. J. ACM 48 13-38.
11. Chen, H., D. Yao. 2001. Fundamentals of Queueing Networks: Performance, Asymptotics and Optimization. Springer-Verlag, New York.
12. Chung, K. L. 2001. A Course in Probability Theory, 3rd ed. Academic Press, San Diego.
13. Cruz, R. 1991a. A calculus for network delay, part I: Network elements in isolation. IEEE Trans. Inform. Theory 37(1) 114-131.
14. Cruz, R. 1991b. A calculus for network delay, part II: Network analysis. IEEE Trans. Inform. Theory 37(1) 132-141.
15. Dai, J. G. 1995. On the positive Harris recurrence for multiclass queueing networks: A unified approach via fluid models. Ann. Appl. Probab. 5(1) 49-77.
16. Dai, J. G., T. G. Kurtz. 1995. A multiclass station with Markovian feedback in heavy traffic. Math. Oper. Res. 20(3) 721-742.
17. Dai, J. G., S. P. Meyn. 1995. Stability and convergence of moments for multiclass queueing networks via fluid limit models. IEEE Trans. Automatic Control 40 1889-1904.
18. Gallager, G., A. Parekh. 1993. A generalized processor sharing approach to flow control in integrated services networks: The single node case. IEEE/ACM Trans. Networking 1(3) 344-357.
19. Gallager, G., A. Parekh. 1994. A generalized processor sharing approach to flow control in integrated services networks: The multiple node case. IEEE/ACM Trans. Networking 2(2) 137-150.
20. Gamarnik, D. 2000. Using fluid models to prove stability of adversarial queueing networks. IEEE Trans. Automatic Control 45(4) 741-746.
21. Gamarnik, D. 2003. Stability of adaptive and nonadaptive packet routing policies in adversarial queueing networks. SIAM J. Comput. 32(2) 371-385.
22. Gamarnik, D., A. Zeevi. 2006. Validity of heavy traffic steady-state approximations in open queueing networks. Ann. Appl. Probab. 16(1) 56-90. (Pubitemid 43535927)
23. Ganesh, A., N. O'Connell, D. Wischik. 2004. Big Queues. Lecture Notes in Mathematics, Vol. 1838. Springer-Verlag, Berlin
24. Goel, A. Stability of networks and protocols in the adversarial queueing model for packet routing. Proc. 10th ACM-SIAM Sympos. Discrete Algorithms. Society for Industrial and Applied Mathematics, Philadelphia.
25. Harrison, J. M. 1990. Brownian Motion and Stochastic Flow Systems. Krieger Publishing Company, Malabar, FL.
26. Harrison, J. M. 2000. Stochastic networks and activity analysis. Ann. Appl. Probab. 10 75-103.
27. Jin, H., J. Ou, P. R. Kumar. 1997. The throughput of irreducible closed Markovian queueing networks: Functional bounds, asymptotic loss, efficiency, and the Harrison-Wein conjectures. Math. Oper. Res. 22(4) 886-920. (Pubitemid 127653366)
28. Kleinrock, L. 1975. Queueing Systems. John Wiley & Sons, New York. Kumar, S., P. R. Kumar.
29. 1994. Performance bounds for queueing networks and scheduling policies. IEEE Trans. Automatic Control 39(8) 1600-1611.
30. Latouche, G., V. Ramaswami. 1987. Introduction to Matrix Analytic Methods in Stochastic Modeling. Society for Industrial and Applied Mathematics, Philadelphia.
31. Meyn, S. P., R. L. Tweedie. 1993. Markov Chains and Stochastic Stability. Springer-Verlag, London.
32. Morrison, J., P. R. Kumar. 1999. New linear program performance bounds for queueing networks. J. Optim. Theory Appl. 100(3) 575-597.
33. Reiman, M. I. 1984. Open queueing networks in heavy traffic. Math. Oper. Res. 9(3) 441-458.
34. Shwartz, A., A. Weiss. 1995. Large Deviations for Performance Analysis. Chapman and Hall, London.
35. Sigman, K. 1990. The stability of open queueing networks. Stochastic Processes Their Appl. 35(1) 11-25.
36. Soyster, A. L. 1973. Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21(5) 1154-1157.
37. Turner, J. 1986. New directions in communications, or which way to the information age? IEEE Commun. Mag. 24 8-15. (Pubitemid 17483935)
38. Whitt, W. 2002. Stochastic-Process Limits. Springer, London.