R. Aalto and U. Ayesta, Mean delay optimization for the M/G/1 queue with Pareto type service times, Extended abstract in ACM SIGMETRICS 2007, pp.383-384, 2007.

D. Bertsimas and J. Nino-mora, Restless Bandits, Linear Programming Relaxations, and a Primal-Dual Index Heuristic, Operations Research, vol.48, issue.1, pp.80-90, 2000.
DOI : 10.1287/opre.48.1.80.12444

C. Buyukkoc, P. Varaya, and J. Walrand, The cµ rule revisited, Adv. Appl. Prob, vol.17, pp.237-238, 1985.

A. [. Crovella and . Bestavros, Self-similarity in World Wide Web traffic: evidence and possible causes, IEEE/ACM Transactions on Networking, vol.5, issue.6, pp.835-846, 1997.
DOI : 10.1109/90.650143

M. Dacre, K. Glazebrook, and J. Niño-mora, The achievable region approach to the optimal control of stochastic systems, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.61, issue.4, pp.61747-791, 1996.
DOI : 10.1111/1467-9868.00202

G. [. Frostig and . Weiss, Four proofs of Gittins??? multiarmed bandit theorem, Annals of Operations Research, vol.25, issue.12, 1999.
DOI : 10.1007/s10479-013-1523-0

]. J. Git89 and . Gittins, Multi-armed Bandit Allocation Indices, 1989.

]. L. Kle75 and . Kleinrock, Queueing systems, 1975.

]. L. Kle76 and . Kleinrock, Queueing systems, 1976.

N. Osipova-[-kli74 and ]. G. Klimov, Time-sharing service systems. i. Theory of Probability and Its Applications, pp.532-551, 1974.

]. G. Kli78 and . Klimov, Time-sharing service systems. ii. Theory of Probability and Its Applications, pp.314-321, 1978.

M. Nabe, M. Murata, and H. Miyahara, Analysis and modeling of World Wide Web traffic for capacity dimensioning of Internet access lines, Performance Evaluation, vol.34, issue.4, pp.249-271, 1998.
DOI : 10.1016/S0166-5316(98)00040-6

D. [. Nain and . Towsley, Optimal scheduling in a machine with stochastic varying processing rate, IEEE Transactions on Automatic Control, vol.39, issue.9, pp.1853-1855, 1994.
DOI : 10.1109/9.317111

]. K. Sev74 and . Sevcik, Scheduling for minimum total loss using service time distributions, Journal of the ACM, vol.21, pp.66-75, 1974.

D. [. Shanthikumar and . Yao, Multiclass Queueing Systems: Polymatroidal Structure and Optimal Scheduling Control, Operations Research, vol.40, issue.3-supplement-2, pp.293-299, 1992.
DOI : 10.1287/opre.40.3.S293

]. J. Tsi93 and . Tsitsiklis, A short proof of the Gittins index theorem, IEEE CDC, pp.389-390, 1993.

. P. Vwb, J. Varaiya, C. Walrand, and . Buyukkoc, Extensions of the multiarmed bandit problem : the discounted case, journal = IEEE Transactions on Automatic Control, vol.30, pp.426-439, 1985.

]. R. Web92 and . Weber, On the Gittins index for multiarmed bandits, Annals of Appllied Probability, vol.2, issue.4, pp.1024-1033, 1992.

]. P. Whi88 and . Whittle, Restless bandits : activity allocation in a changing world, Journal of Applied Probability, vol.25, pp.287-298, 1988.

]. C. Wil01 and . Williamson, Internet traffic measurement, IEEE Internet Computing, vol.5, pp.70-74, 2001.

]. S. Yas92 and . Yashkov, Mathematical problems in the theory of shared-processor systems, Journal of Mathematical Sciences, vol.58, pp.101-147, 1992.

I. Unité-de-recherche-inria-sophia and . Antipolis, route des Lucioles -BP 93 -06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université -ZAC des Vignes 4, 2004.

I. Unité-de-recherche and . Lorraine, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt, Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex

I. De-voluceau-rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399