The G/GI/N queue in the Halfin-Whitt regime

Annals of Applied Probability

Volumn 19, Issue 6, 2009, Pages 2211-2269

  Reed, Josh ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Diffusion approximation; Gaussian process; Martingale; Queueing theory; Weak convergence

Indexed keywords

EID: 73949131467     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/09-AAP609     Document Type: Article

References (21)

1. BILLINGSLEY, P. (1999). Convergence of Probability Measures, 2nd ed. Wiley, New York. MR1700749
2. BOROVKOV, A. A. (1967). Limit laws for queueing processes in multichannel systems. Sibirsk. Mat. Ž. 8 983-1004. MR0222973
3. BRÉMAUD, P. (1981). Point Processes and Queues, Martingale Dynamics. Springer, New York. MR636252
4. EVANS, L. C. and GARIEPY, R. F. (1992). Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL. MR1158660
5. GAMARNIK, D. and MOMCILOVIC, P. (2007). Steady-state analysis of a multi-server queue in the Halfin-Whitt regime. Preprint.
6. HALFIN, S. and WHITT, W. (1981). Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29 567-588. MR629195
7. HARRISON, J. M. and REIMAN, M. I. (1981). Reflected Brownian motion on an orthant. Ann. Probab. 9 302-308. MR606992
8. HARRISON, J. M. and WILLIAMS, R. J. (1987). Multidimensional reflected Brownian motions having exponential stationary distributions. Ann. Probab. 15 115-137. MR877593
9. JACOD, J. and SHIRYAEV, A. N. (2003). Limit Theorems for Stochastic Processes, 2nd ed. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 288. Springer, Berlin. MR1943877
10. JELENKOVIĆ, P., MANDELBAUM, A. and MOMČILOVIĆ, P. (2004). Heavy traffic limits for queues with many deterministic servers. Queueing Syst. 47 53-69. MR2074672
11. KARLIN, S. and TAYLOR, H. M. (1975). A First Course in Stochastic Processes, 2nd ed. Academic Press, New York. MR0356197
12. KASPI, H. and RAMANAN, K. (2006). Fluid limits of many-server queue. Preprint.
13. KIEFER, J. and WOLFOWITZ, J. (1955). On the theory of queues with many servers. Trans. Amer. Math. Soc. 78 1-18. MR0066587
14. KRICHAGINA, E. V. and PUHALSKII, A. A. (1997). A heavy-traffic analysis of a closed queueing system with a GI/∞ service center. Queueing Syst. 25 235-280. MR1458591
15. LIPTSER, R. S. and SHIRYAEV, A. (1989). Theory of Martingales. Kluwer, Dordrecht.
16. MANDELBAUM, A. and MOMCILOVIC, P. (2005). Queues with many servers: The virtual waiting-time process in the QED regime. Math. Oper. Res. To appear.
17. PUHALSKII, A. A. and REIMAN, M. I. (2000). The multiclass GI/PH/N queue in the Halfin-Whitt regime. Adv. in Appl. Probab. 32 564-595. MR1778580
18. REED, J. E. The G/GI/N queue in the Halfin-Whitt regime II: Idle time system equations. To appear.
19. ROSS, S. M. (1996). Stochastic Processes, 2nd ed. Wiley, New York. MR1373653
20. WHITT, W. (2002). Stochastic-Process Limits. Springer, New York. MR1876437
21. */n/m queue. Math. Oper. Res. 30 1-27. MR2125135