Multiclass queueing systems in heavy traffic: An asymptotic approach based on distributional and conservation laws

Operations Research

Volumn 45, Issue 3, 1997, Pages 470-487

  Bertsimas, Dimitris ^a   Mourtzinou, Georgia ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; MATHEMATICAL MODELS; PROBABILITY; PRODUCTION; RANDOM PROCESSES; SCHEDULING;

CONSERVATION LAWS; DISTRIBUTIONAL LAWS; MULTICLASS QUEUEING SYSTEMS;

QUEUEING THEORY;

EID: 0031147516     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.45.3.470     Document Type: Article

References (30)

1. ABATE, J. AND W. WHITT. 1995. Numerical Inversion of Laplace Transforms of Probability Distributions. J. Comput. 7, 36-43.
2. BERTSIMAS, D. AND G. MOURTZINOU. 1996. A Unified Method to Analyze Overtake Free Queueing Systems. Advances in Applied Probability 28, 588-625.
3. BERTSIMAS, D. AND D. NAKAZATO. 1995. The General Distributional Little's Law and Its Applications. Opns. Res. 43, 298-310.
4. COFFMAN, E. G., A. A. PUHALSKII, AND M. I. REIMAN. 1993. Polling Systems with Zero Switchover Times: A Heavy-traffic Averaging Principle. Working Paper.
5. COOPER, R., S. NIU, AND M. SRINIVASAN. 1995. A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive. Opns. Res. 44, 629-634.
6. Cox, D. R. 1962. Renewal Theory. Chapman and Hall, New York.
7. FEDERGRUEN, A. AND H. GROENEVELT. 1988a. M/G/c Queueing Systems with Multiple Customer Classes: Characterization and Control of Achievable Performance under Nonpreemptive Priority Rules. J. Appl. Prob. 24, 709-724.
8. FEDERGRUEN, A. AND H. GROENEVELT. 1988b. Characterization and Optimization of Achievable Performance in Queueing Systems. Opns. Res. 36, 733-741.
9. FENDICK, K. W., V. R. SAKSENA, AND W. WHITT. 1989. Dependence in Packet Queues. IEEE Trans. Commun. 37, 1173-1183.
10. FUHRMANN, S. W. AND R. B. COOPER. 1985. Stochastic Decompositions in a M/G/1 Queue with Generalized Vacation. Opns. Res. 33, 1117-1129.
11. GELENDE, E. AND I. MITRANI. 1980. Analysis and Synthesis of Computer Systems. Academic Press, London.
12. HAJI, R. AND G. NEWELL. 1971. A Relation Between Stationary Queue and Waiting Time Distributions. J. Appl. Prob. 8, 617-620.
13. HEYMAN, D. AND M. SOBEL. 1982. Stochastic Models in Operations Research. Vol. 1, McGraw-Hill Book Company, New York.
14. HOSONO, T. 1981. Numerical Inversion of Laplace Transform and Some Applications to Wave Optics. Radio Sci. 16, 1015-1019.
15. IGLEHART, D. L. AND W. WHITT. 1970. Multiple Channel Queues in Heavy Traffic: I and II. Advances in Applied Probability, 2, 150-177, 355-364.
16. KEILSON, J. AND L. SERVI. 1988. A Distributional Form of Little's Law. O. R. Lett. 7, 5, 223-227.
17. KEILSON, J. AND L. SERVI. 1990. The Distributional Form of Little's Law and the Fuhrmann-Cooper Decomposition. O. R. Lett. 9, 4, 239-247.
18. KLEINROCK, L. 1975. Queueing Systems. Vol. 1: Theory. Wiley, New York.
19. LEMOINE, A. 1974. On Two Stationary Distributions for the Stable GI/G/1 Queue. J. Appl. Prob. 11, 849-852.
20. MOURTZINOU, G. 1995. An Axiomatic Approach to Queueing Systems. Ph.D. Thesis, Massachusetts Institute of Technology.
21. REIMAN, M. AND B. SIMON. 1990. A Network of Priority Queues in Heavy Traffic: One Bottleneck Station. Queueing Sys. 6, 35-58.
22. SARKAR, D. AND W. I. ZANGWILL. 1989. Expected Waiting Times for Nonsymmetric Cyclic Queueing Systems-Exact results and Applications. Mgmt. Sci. 35, 12, 1463-1474.
23. SHANTIKUMAR, J. G. AND D. D. YAO. 1992. Multiclass Queueing Systems: Polymatroidal Structure and Optimal Scheduling Control. Opns. Res. 40, 293-299.
24. SMITH, W. L. 1954. Asymptotric Renewal Theorems. Proc. Roy. Soc. Edinb. A, 64, 9-48.
25. TAKACS, L. 1962. Introduction to the Theory of Queues. Oxford University Press, New York.
26. TAKAGI, H. 1975. Analysis of Polling Systems. The MIT Press, Massachusetts.
27. WHITT, W. 1971. Weak Convergence Theorems for Priority Queues Preemptive Resume Discipline. J. Appl. Prob. 8, 74-94.
28. WHITT, W. 1982. Approximating a Point Process by s Renewal Process I: Two Basic Methods. Opns. Res. 30, 125-147.
29. WHITT, W. 1983. The Queueing Network Analyzer. The Bell System Technical J. 62, 2779-2815.
30. WHITT, W. 1991. A Review of L = λW and Extensions. Queueing Sys. 9, 235-268.