P. Brill and M. Posner, Level Crossings in Point Processes Applied to Queues: Single-Server Case, Operations Research, vol.25, issue.4, pp.662-674, 1977.
DOI : 10.1287/opre.25.4.662

F. Baccelli, P. Boyer, and G. Hebuterne, Single-server queues with impatient customers, Advances in Applied Probability, vol.38, issue.04, pp.887-905, 1984.
DOI : 10.2307/3212710

A. Brandt and M. Brandt, On the Two-Class M/M/1 System under Preemptive Resume and Impatience of the Prioritized Customers, Queueing Systems, vol.47, issue.1/2, pp.147-168, 2004.
DOI : 10.1023/B:QUES.0000032805.73991.8e

C. Gromoll, P. Robert, and B. Zwart, Fluid Limits for Processor-Sharing Queues with Impatience, Mathematics of Operations Research, vol.33, issue.2, pp.375-402, 2008.
DOI : 10.1287/moor.1070.0298

URL : https://hal.archives-ouvertes.fr/inria-00001202

F. Iravani and B. Balcio?glubalcio?glu, On priority queues with impatient customers, Queueing Systems, vol.4, issue.2, pp.239-260, 2008.
DOI : 10.1007/s11134-008-9069-6

B. Ata and M. Tongarlak, On scheduling a multiclass queue with abandonments under general delay costs, Queueing Systems, vol.44, issue.7, pp.1-40, 2012.
DOI : 10.1007/s11134-012-9326-6

O. Boxma and P. De-waal, Multiserver Queues with Impatient Customers, Proceedings of ITC-14, pp.743-756, 1994.
DOI : 10.1016/B978-0-444-82031-0.50079-2

N. Boots and H. Tijms, A Multiserver Queueing System with Impatient Customers, Management Science, vol.45, issue.3, pp.444-448, 1999.
DOI : 10.1287/mnsc.45.3.444

W. Whitt, Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments, Management Science, vol.50, issue.10, pp.1449-1461, 2004.
DOI : 10.1287/mnsc.1040.0279

J. Dai and S. , Many-server queues with customer abandonment: A survey of diffusion and fluid approximations, Journal of Systems Science and Systems Engineering, vol.51, issue.1, pp.1-36, 2012.
DOI : 10.1007/s11518-012-5189-y

K. Glazebrook, P. Ansell, R. Dunn, and R. Lumley, On the optimal allocation of service to impatient tasks, Journal of Applied Probability, vol.25, issue.01, pp.51-72, 2004.
DOI : 10.1145/258623.258685

R. Atar, A. Mandelbaum, and M. Reiman, Scheduling a multi-class queue with many exponential servers: asymptotic optimality in heavy-traffic, The Annals of, Applied Probability, vol.14, pp.1084-1134, 2004.

J. Harrison and A. Zeevi, Dynamic Scheduling of a Multiclass Queue in the Halfin-Whitt Heavy Traffic Regime, Operations Research, vol.52, issue.2, pp.243-257, 2004.
DOI : 10.1287/opre.1030.0084

N. Argon, S. Ziya, and R. Righter, SCHEDULING IMPATIENT JOBS IN A CLEARING SYSTEM WITH INSIGHTS ON PATIENT TRIAGE IN MASS CASUALTY INCIDENTS, Probability in the Engineering and Informational Sciences, pp.301-332, 2010.
DOI : 10.2307/3212936

R. Atar, C. Giat, and N. Shimkin, Rule for Many-Server Queues with Abandonment, Operations Research, vol.58, issue.5, pp.1427-1439, 2010.
DOI : 10.1287/opre.1100.0826

D. Down, G. Koole, and M. Lewis, Dynamic control of a single-server system with??abandonments, Queueing Systems, vol.50, issue.4, pp.63-90, 2011.
DOI : 10.1007/s11134-010-9201-2

R. Atar, C. Giat, and N. Shimkin, On the asymptotic optimality of the c??/?? rule under??ergodic cost, Queueing Systems, vol.67, issue.2, pp.127-144, 2011.
DOI : 10.1007/s11134-010-9206-x

U. Ayesta, P. Jacko, and V. Novak, A nearly-optimal index rule for scheduling of users with abandonment, 2011 Proceedings IEEE INFOCOM, 2011.
DOI : 10.1109/INFCOM.2011.5935122

P. Whittle, Restless bandits: activity allocation in a changing world, Journal of Applied Probability, vol.1, issue.A, pp.287-298, 1988.
DOI : 10.1214/aop/1176994469

O. Garnett, A. Mandelbaum, and M. Reiman, Designing a call center with impatient customers, Manufacturing and Service Operations Management, pp.208-227, 2002.

C. Buyukkoc, P. Varaya, and J. Walrand, The cµ rule revisited, Advances in Applied Probability, vol.17, pp.237-238, 1985.

G. Weiss, On optimal draining of reentrant fluid lines, Stochastic Networks, pp.91-103, 1995.

N. Bäuerle and U. Rieder, Optimal control of single-server fluid networks, Queueing Systems, vol.35, issue.1/4, pp.185-200, 2000.
DOI : 10.1023/A:1019146111903

S. Meyn, Stability and optimization of queueing networks and their fluid models, Mathematics of Stochastic Manufacturing Systems Lectures in Applied Mathematics, pp.175-199, 1997.

N. Bäuerle, Asymptotic optimality of tracking policies in stochastic networks, The Annals of Applied Probability, vol.10, issue.4, pp.1065-1083, 2000.
DOI : 10.1214/aoap/1019487606

A. Gajrat and A. Hordijk, Fluid approximation of a controlled multiclass tandem network, Queueing Systems, vol.35, issue.1/4, pp.349-380, 2000.
DOI : 10.1023/A:1019162615537

C. Maglaras, Discrete-review policies for scheduling stochastic networks: trajectory tracking and fluid-scale asymptotic optimality, The Annals of Applied Probability, vol.10, issue.3, pp.897-929, 2000.
DOI : 10.1214/aoap/1019487513

I. M. Verloop and R. Núñez-queija, Asymptotically optimal parallel resource assignment with interference, Queueing Systems, vol.66, issue.1, pp.43-92, 2010.
DOI : 10.1007/s11134-010-9171-4

URL : https://hal.archives-ouvertes.fr/hal-00686248

J. Dai, On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models, The Annals of Applied Probability, vol.5, issue.1, pp.49-77, 1995.
DOI : 10.1214/aoap/1177004828

B. C. Chachuat, Nonlinear and dynamic optimization: from theory to practice, IC-32, 2006.

M. D. Larrañaga-is-a-ph, C. Student-in, and I. In, The research for her Master thesis was carried out at the Her main research interests are: optimal control theory, dynamic programming, stochastic processes, scaling methods, Toulouse since October 2012 under the supervision of Urtzi Ayesta and Ina Maria Verloop. She received her Master degree in Mathematics in September 2012 from the University of the Basque Country

I. M. Verloop-received-the and M. Sc, The Netherlands Her Ph.D. research was carried at the Probability, Networks and Algorithms Department of the Center for Mathematics and Computer Science (CWI) in Amsterdam, The Netherlands. From 2009 to 2011 she was a postdoc at the she has been a CNRS researcher at IRIT, 2005, and the Ph.D. degree from the Mathematics and Computer Her research interests are in the performance analysis of communication networks, scheduling and queueing theory, 2009.