Fluid limits of many-server queues with reneging

[1] Baccelli, F. and Hebuterne, G. (1981). On queues with impatient customers. In <i>Performance ’</i>81 (E. Gelenbe, ed.) 159–179. North-Holland, Amsterdam.

[5] Dupuis, P. and Ellis, R. S. (1997). <i>A Weak Convergence Approach to the Theory of Large Deviations</i>. Wiley, New York.

[6] Ethier, S. N. and Kurtz, T. G. (1986). <i>Markov Processes</i>: <i>Characterization and Convergence</i>. Wiley, New York.

[10] Jacod, J. and Shiryaev, A. N. (1987). <i>Limit Theorems for Stochastic Processes. Grundlehren der Mathematischen Wissenschaften</i> [<i>Fundamental Principles of Mathematical Sciences</i>] <b>288</b>. Springer, Berlin.

[11] Jacobsen, M. (2006). <i>Point Process Theory and Applications</i>: <i>Markov Point and Piecewise Deterministic Processes</i>. Birkhäuser, Boston, MA.

[12] Kallenberg, O. (1975). <i>Random Measures</i>. Akademie Verlag, Berlin.

[14] Kaspi, H. and Ramanan, K. (2010). Law of large numbers limits for many-server queues. <i>Ann. Appl. Probab.</i> To appear.

[15] Kaspi, H. and Ramanan, K. (2010). SPDE limits for many-server queues. Preprint.

[17] Mandelbaum, A. and Momcilovic, P. (2010). Queues with many servers and impatient customers. Preprint.

[23] Whitt, W. (2002). <i>Stochastic-process Limits</i>: <i>An Introduction to Stochastic-Process Limits and Their Application to Queues</i>. Springer, New York.

[24] Zhang, J. (2010). Fluid models of many-server queues with abandonment. Preprint.

[2] Bassamboo, A., Harrison, J. M. and Zeevi, A. (2005). Dynamic routing and admission control in high-volume service systems: Asymptotic analysis via multi-scale fluid limits. <i>Queueing Syst.</i> <b>51</b> 249–285.

[3] Boxma, O. J. and de Waal, P. R. (1994). Multiserver queues with impatient customers. In <i>Proceedings of ITC</i> <b>14</b> 743–756. Elsevier, Amsterdam.

[4] Brown, L., Gans, N., Mandelbaum, A., Sakov, A., Shen, H., Zeltyn, S. and Zhao, L. (2005). Statistical analysis of a telephone call center: A queueing-science perspective. <i>J. Amer. Statist. Assoc.</i> <b>100</b> 36–50.

[7] Gans, N., Koole, G. and Mandelbaum, A. (2003). Telephone call centers: Tutorial, review and research prospects. <i>Manufacturing Service Oper. Management</i> <b>5</b> 79–141.

[8] Garnett, O., Mandelbaum, A. and Reiman, M. I. (2002). Designing a call center with impatient customers. <i>Manufacturing Service Oper. Management</i> <b>4</b> 208–227.

[9] Harrison, J. M. (2005). A method for staffing large call centers based on stochastic fluid models. <i>Manufacturing Service Oper. Management</i> <b>7</b> 20–36.

[13] Kang, W. N. and Ramanan, K. (2010). Asymptotic approximations for the stationary distributions of many-server queues. Preprint. Available at <a href="http://arxiv.org/abs/1003.3373">http://arxiv.org/abs/1003.3373</a>.

[16] Mandelbaum, A., Massey, W. A. and Reiman, M. I. (1998). Strong approximations for Markovian service networks. <i>Queueing Syst.</i> <b>30</b> 149–201.

[18] Zeltyn, S. and Mandelbaum, A. (2005). Call centers with impatient customers: Many-server asymptotics of the <i>M</i>/<i>M</i>/<i>n</i>+<i>G</i> queue. <i>Queueing Syst.</i> <b>51</b> 361–402.

[19] Mandelbaum, A. and Zeltyn, S. (2009). Staffing many-server queues with impatient customers: Constraint satisfaction in call centers. <i>Oper. Res.</i> <b>57</b> 1189–1205.

[20] Parthasarathy, K. R. (1967). <i>Probability Measures on Metric Spaces. Probability and Mathematical Statistics</i> <b>3</b>. Academic Press, New York.

[21] Ramanan, K. and Reiman, M. I. (2003). Fluid and heavy traffic diffusion limits for a generalized processor sharing model. <i>Ann. Appl. Probab.</i> <b>13</b> 100–139.

[22] Whitt, W. (2006). Fluid models for multiserver queues with abandonments. <i>Oper. Res.</i> <b>54</b> 37–54.