Fluid limits for processor-sharing queues with impatience

Mathematics of Operations Research

Volumn 33, Issue 2, 2008, Pages 375-402

  Gromoll, H Christian ^a   Robert, Philippe ^b   Zwart, Bert ^c  

^a University of Virginia   (United States)

^b INRIA ROCQUENCOURT   (France)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Delay differential equations; Empirical processes; Fluid limits; Measure valued process; Processor sharing; Queues with impatience

Indexed keywords

FLUIDS; PLASMA FLOW; PLASMAS; STOCHASTIC MODELS;

DELAY-DIFFERENTIAL EQUATIONS; EMPIRICAL PROCESSES; FLUID LIMITS; MEASURE-VALUED PROCESS; PROCESSOR SHARING; QUEUES WITH IMPATIENCE;

QUEUEING THEORY;

EID: 57349172124     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1070.0298     Document Type: Article

References (29)

1. Barrer, D. 1957. Queueing with impatient customers and ordered service. Oper. Res. 5 650-656.
2. Billingsley, P. 1986. Probability and Measure, 2nd ed. John Wiley & Sons, New York.
3. Bonald, T., L. Massoulié. 2001. Impact of fairness on Internet performance. Proc. ACM Sigmetrics, Cambridge, MA, 82-91.
4. Bonald, T., J. Roberts. 2003. Congestion at flow level and the impact of user behaviour. Comput. Networks 42 521-536.
5. Boots, N., H. Tijms. 1999. A multi-server queueuing system with impatient customers. Management Sci. 45 444-448.
6. Bramson, M. 2005. Stability of networks for max-min fair routing. 13th INFORMS Appl. Probab. Conf Ottawa, Canada.
7. Coffman, E., A. Puhalskii, M. Reiman, P. Wright. 1994. Processor shared buffers with reneging. Performance Eval. 19 25-46.
8. de Veciana, G., T. Konstantopoulos, T.-J. Lee. 2001. Stability and performance analysis of networks supporting elastic services. IEEE/ACM Trans. Networking 9(1) 2-14.
9. Doytchinov, B., J. Lehoczky, S. Shreve. 2001. Real-time queues in heavy traffic with earliest-deadline-first queue discipline. Ann. Appl. Probab. 11(2) 332-378.
10. Gans, N., G. Koole, A. Mandelbaum. 2002. Telephone call centers: Tutorial, review, and research prospects. Manufacturing Service Oper. Management 5 79-141.
11. Gromoll, H. C., P. Robert, B. Zwart, R. Bakker. 2006. The impact of reneging in processor sharing queues. Proc. ACM Sigmetrics (June), ACM/IFIP WG 7.3, Saint Malo, France.
12. Gromoll, H. C., Ł. Kruk. 2007. Heavy traffic limit for a processor sharing queue with soft deadlines. Ann. Appl. Probab. 17 1049-1101.
13. Gromoll, H. C., R. J. Williams. 2006. Fluid approximation for an Internet congestion control model with fair bandwidth sharing and general document size distributions. Preprint.
14. Guillemin, F., P. Robert, B. Zwart. 2004. Tail asymptotics for processor-sharing queues. Adv. Appl. Probab. 36 525-543.
15. Hale, J., S. Verduyn Lunel. 1993. An Introduction to Functional Differential Equations. Springer Verlag, New York.
16. Jean-Marie, A., P. Robert. 1994. On the transient behavior of some single server queues. Queueing Systems - Theory Appl. 17 129-136.
17. Kallenberg, O. 1986. Random Measures. Academic Press, New York.
18. Kelly, F. P., R. J. Williams. 2004. Fluid model for a network operating under a fair bandwidth sharing policy. Ann. Appl. Probab. 14 1055-1083.
19. Key, P., L. Massoulié, A. Bain, F. Kelly. 2004. Fair internet traffic integration: Network flow models and analysis. Ann. Telecomm. 59 1338-1352.
20. Kruk, Ł., J. Lehoczky, S. Shreve. 2003. Second order approximation for the customer time in queue distribution under the FIFO service discipline. Ann. Univ. Marie Curie-Skłodowska, Sect. AI Inform 1 37-48.
21. Kruk, Ł., J. Lehoczky, S. Shreve. 2006. Accuracy of state space collapse for earliest-deadline-first queues. Ann. Appl. Probab. 13(2) 516-581.
22. Massoulié, L., J. Roberts. 1999. Bandwidth sharing: Objectives and algorithms. INFOCOM'99. 18th Annual Joint Conf. IEEE Comput. Comm. Societies, New York, 1395-1403.
23. Mo, J., J. Walrand. 2000. Fair end-to-end window-based congestion control. IEEE/ACM Trans. Networking 8(5) 556-567.
24. Puha, A. L., A. L. Stolyar, R. J. Williams. 2006. The fluid limit of an overloaded processor sharing queue. Math. Oper. Res. 31(2) 316-350.
25. Roberts, J., L. Massoulié. 2000. Bandwidth sharing and admission control for elastic traffic. Telecomm. Systems 15 185-201.
26. Stanford, R. E. 1979. Reneging phenomena in single channel queues. Math. Oper. Res. 4 162-178.
27. Stanford, R. E. 1990. On queues with impatience. Adv. Appl. Probab. 22(3) 768-769.
28. van der Vaart, A., J. A. Wellner. 1996. Weak Convergence and Empirical Processes. Springer-Verlag, New York.
29. Ward, A., P. Glynn. 2003. A diffusion approximation for a markovian queue with reneging. Queueing Systems 43 103-128.