Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

Queueing Systems

Volumn 53, Issue 1-2, 2006, Pages 19-30

  Hampshire, Robert C ^a   Harchol Balter, Mor ^a   Massey, William A ^b  

^a Princeton University   (United States)

^b Carnegie Mellon University ^*  (United States)

Author keywords

Diffusion limits; Fluid limits; Processor sharing; Sojourn times; Time varying queues; Transient behavior; Uniform acceleration; Virtual customers

Indexed keywords

QUEUEING THEORY; SALES;

DIFFUSION LIMITS; FLUID LIMITS; PROCESSOR SHARING; SOJOURN TIME; TIME VARYING; TRANSIENT BEHAVIOR; VIRTUAL CUSTOMERS;

DIFFUSION IN LIQUIDS;

EID: 33646709697     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1007/s11134-006-7584-x     Document Type: Article

References (25)

1. N. Bansal and M. Harchol-Balter, Analysis of SRPT scheduling: Investigating unfairness, in: Proceedings of Association of Computing Machinery Sigmetrics 2001 Conference on Measurement and Modeling of Computer Systems, Cambridge, MA, (2001).
2. T. Bonald and A. Proutière, On performance bounds for the integration of elastic and adaptive streaming flows, in: Proceedings of Association of Computing Machinery Sigmetrics/Performance Joint International Conference on Measurement and Modeling of Computer Systems, (2004) 235-245.
3. H. Chen, O. Kella, and G. Weiss, Fluid approximations for a processor sharing queue, Queueing Systems: Theory and Applications. 27 (1997) 99-125.
4. E.G. Coffman, R.R. Muntz, and H. Trotter, Waiting time distribution for processor-sharing systems, Journal of the Association of Computing Machinery 17 (1970) 123-130.
5. F. Delcoigne, A. Proutière, and G. Règniè, Modeling integration of streaming and data traffic, Performance Evaluation 55 (2004) 185-209.
6. M. Harchol-Balter, B. Schroeder, N. Bansal, and M. Agrawal, Size-based scheduling to improve web performance, Association of Computing Machinery Transactions on Computer Systems 21(2) (2003) 207-233.
7. F. Guillemin and J. Boyer, Analysis of the M/M/1 queue with processor sharing via spectral theory, Queueing Systems 39(4) (2001) 377-397.
8. A. Jean-Marie and P. Robert, On the transient behavior of the processor sharing queue, Queueing Systems 17 (1994) 129-136.
9. M. Yu, Kitaev, The M/G/1 processor-sharing model: Transient behavior, Queueing Systems 14 (1993) 239-273.
10. L. Kleinrock. Queueing Systems, Volume II: Computer Applications (John Wiley & Sons. 1976).
11. J.D.C. Little, A proof of the queueing formula L = λW. Operations Research 9 (1961) 383-387.
12. A. Mandelbaum and W.A. Massey, Strong approximations for time dependent queues, Mathematics of Operations Research 20(1) (1995) 33-64.
13. W.A. Massey, Asymptotic analysis of the time dependent M/M/1 queue, Mathematics of Operations Research 10 (1985) 305-327.
14. H. Masuyama and T. Takine, Sojourn time distribution in a MAP/M/1 processor-sharing queue, Operations Research Letters 31(5) (2003) 406-412.
15. J. Morrison, Response time for a processor-sharing system, SIAM J. Appl. Math. 45(1) (1985) 152-167.
16. R. Nunez-Queija, Processor sharing models for integrated services networks, Ph.D. Thesis Eindhoven University of Technology (2000).
17. T. Ott, The sojourn time distribution in the M/G/1 queue with processor sharing, J. Appl. Prob. 21 (1984) 360-378.
18. J.W. Roberts, Engineering for quality of service, in: K. Park and W. Willinger (eds.), Self-Similar Network Traffic and Performance Evaluation (Wiley. New York, 2000) pp. 401-420.
19. R. Schassberger, A new approach to the M/G/1 processor sharing queue. Adv. Appl. Prob. 16 (1984) 202-213.
20. B. Schroeder and M. Harchol-Balter, Web servers under overload: How scheduling can help, 18th International Teletraffic Congress (Berlin, Germany, 2003).
21. B. Sengupta and D.E. Jagerman, A conditional response time of the M/M/1 processor-sharing queue, AT& T Technical Journal 64 (1985) 409-421.
22. S.F. Yashkov, A derivation of response time distribution for a M/G/1 processor-sharing queue, Problems of Control and Information Theory 12(2) (1983) 133-148.
23. S.F. Yashkov, Processor-sharing queues: Some progress in analysis, Queueing Systems 2 (1987) 1-17.
24. S.F. Yashkov, Mathematical problems in the theory of shared-processor systems, Journal of Soviet Mathematics 58 (1992) 101-147.
25. B. Zwart and O.J. Boxma, Sojourn time asymptotics in the M/G/1 processor sharing queue, Queueing Systems 35 (2000) 141-166.