A many-server fluid limit for the Gt GI st + GI queueing model experiencing periods of overloading

Operations Research Letters

Volumn 40, Issue 5, 2012, Pages 307-312

  Liu, Yunan ^a,b   Whitt, Ward ^a,b  

^a North Carolina State University   (United States)

^b Department of Earth and Environmental Sciences   (United States)

Author keywords

Deterministic fluid model; Functional weak law of large numbers; Many server heavy traffic limit; Non Markovian queues; Nonstationary queues; Queues with time varying arrivals

Indexed keywords

FLUID MODELS; HEAVY TRAFFIC LIMIT; LAW OF LARGE NUMBERS; NON-MARKOVIAN; NONSTATIONARY; TIME VARYING;

QUEUEING THEORY;

QUEUEING NETWORKS;

EID: 84864454946     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.orl.2012.05.010     Document Type: Article

References (21)

1. P. Billingsley Convergence of Probability Measures second ed. 1999 Wiley New York
2. S.N. Ethier, and T.G. Kurtz Markov Processes: Characterization and Convergence 1986 Wiley New York
3. W. Feller An Introduction to Probability Theory and its Applications 1971 John Wiley and Sons New York
4. L.V. Green, P.J. Kolesar, and W. Whitt Coping with time-varying demand when setting staffing requirements for a service system Prod. Oper. Manag. 16 2007 13 39
5. W. Kang, and K. Ramanan Fluid limits of many-server queues with reneging Ann. Appl. Prob. 20 2010 2204 2260
6. H. Kaspi, and K. Ramanan Law of large numbers limits for many-server queues Ann. Appl. Prob. 21 2011 33 114
7. H. Kaspi, K. Ramanan, SPDE limits of many-server queues. arxiv:1010.0330v1, October 2, 2010.
8. E.V. Krichagina, and A.A. Puhalskii A heavy-traffic analysis of a closed queueing system with a GI ∞ service center Queueing Syst. 25 1997 235 280 (Pubitemid 127534246)
9. st + GI many-server fluid queue, Queueing Systems. http://dx.doi.org/10.1007/s11134-012-9291-0 (forthcoming).
10. Y. Liu, W. Whitt, Many-server heavy-traffic limit for queues with time-varying parameters, Columbia University, NY, 2011. http://www.columbia.edu/ ∼ww2040/allpapers.html (submitted for publication).
11. Y. Liu, and W. Whitt A network of time-varying many-server fluid queues with customer abandonment Oper. Res. 59 2011 835 846
12. A. Mandelbaum, W.A. Massey, and M.I. Reiman Strong approximations for Markovian service networks Queueing Syst. 30 1998 149 201 (Pubitemid 128370856)
13. G. Pang, R. Talreja, and W. Whitt Martingale proofs of many-server heavy-traffic limits for Markovian queues Probab. Surv. 4 2007 193 267
14. G. Pang, and W. Whitt Two-parameter heavy-traffic limits for infinite-server queues Queueing Syst. 65 2010 325 364
15. A.A. Puhalskii, and J. Reed On many-server queues in heavy traffic Ann. Appl. Prob. 20 2010 129 195
16. J. Reed The G GI N queue in the Halfin-Whitt regime Ann. Appl. Prob. 19 2009 2211 2269
17. A.V. Skorohod Limit theorems for stochastic processes Theor. Probab. Appl. 1 1956 261 290
18. R. Talreja, and W. Whitt Heavy-traffic limits for waiting times in many-server queues with abandonment Ann. Appl. Prob. 19 2009 2137 2175
19. W. Whitt Fluid models for multiserver queues with abandonments Oper. Res. 54 2006 37 54
20. W. Whitt Stochastic-Process Limits 2002 Springer New York
21. J. Zhang, Fluid models of many-server queues with abandonment, Queueing Syst., http://dx.doi.org/10.1007/s11134-012-9307-9 (forthcoming).