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

Annals of Applied Probability - Tập 19 Số 6 - 2009
Josh Reed1
1New York University

Tóm tắt

Từ khóa


Tài liệu tham khảo

[9] Jacod, J. and Shiryaev, A. N. (2003). <i>Limit Theorems for Stochastic Processes</i>, 2nd ed. <i>Grundlehren der Mathematischen Wissenschaften</i> [<i>Fundamental Principles of Mathematical Sciences</i>] <b>288</b>. Springer, Berlin.

[1] Billingsley, P. (1999). <i>Convergence of Probability Measures</i>, 2nd ed. Wiley, New York.

[3] Brémaud, P. (1981). <i>Point Processes and Queues</i>, <i>Martingale Dynamics</i>. Springer, New York.

[4] Evans, L. C. and Gariepy, R. F. (1992). <i>Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics</i>. CRC Press, Boca Raton, FL.

[5] Gamarnik, D. and Momcilovic, P. (2007). Steady-state analysis of a multi-server queue in the Halfin–Whitt regime. Preprint.

[11] Karlin, S. and Taylor, H. M. (1975). <i>A First Course in Stochastic Processes</i>, 2nd ed. Academic Press, New York.

[12] Kaspi, H. and Ramanan, K. (2006). Fluid limits of many-server queue. Preprint.

[15] Liptser, R. S. and Shiryaev, A. (1989). <i>Theory of Martingales</i>. Kluwer, Dordrecht.

[16] Mandelbaum, A. and Momcilovic, P. (2005). Queues with many servers: The virtual waiting-time process in the QED regime. <i>Math. Oper. Res.</i> To appear.

[18] Reed, J. E. The <i>G</i>/<i>GI</i>/<i>N</i> queue in the Halfin–Whitt regime II: Idle time system equations. To appear.

[19] Ross, S. M. (1996). <i>Stochastic Processes</i>, 2nd ed. Wiley, New York.

[20] Whitt, W. (2002). <i>Stochastic-Process Limits</i>. Springer, New York.

[2] Borovkov, A. A. (1967). Limit laws for queueing processes in multichannel systems. <i>Sibirsk. Mat. Ž.</i> <b>8</b> 983–1004.

[6] Halfin, S. and Whitt, W. (1981). Heavy-traffic limits for queues with many exponential servers. <i>Oper. Res.</i> <b>29</b> 567–588.

[7] Harrison, J. M. and Reiman, M. I. (1981). Reflected Brownian motion on an orthant. <i>Ann. Probab.</i> <b>9</b> 302–308.

[8] Harrison, J. M. and Williams, R. J. (1987). Multidimensional reflected Brownian motions having exponential stationary distributions. <i>Ann. Probab.</i> <b>15</b> 115–137.

[10] Jelenković, P., Mandelbaum, A. and Momčilović, P. (2004). Heavy traffic limits for queues with many deterministic servers. <i>Queueing Syst.</i> <b>47</b> 53–69.

[13] Kiefer, J. and Wolfowitz, J. (1955). On the theory of queues with many servers. <i>Trans. Amer. Math. Soc.</i> <b>78</b> 1–18.

[14] Krichagina, E. V. and Puhalskii, A. A. (1997). A heavy-traffic analysis of a closed queueing system with a <i>GI</i>/∞ service center. <i>Queueing Syst.</i> <b>25</b> 235–280.

[17] Puhalskii, A. A. and Reiman, M. I. (2000). The multiclass <i>GI</i>/<i>PH</i>/<i>N</i> queue in the Halfin-Whitt regime. <i>Adv. in Appl. Probab.</i> <b>32</b> 564–595.

[21] Whitt, W. (2005). Heavy-traffic limits for the <i>G</i>/<i>H</i><sub>2</sub><sup>*</sup>/<i>n</i>/<i>m</i> queue. <i>Math. Oper. Res.</i> <b>30</b> 1–27.