A Large Deviation Principle for Join the Shortest Queue

References

• Alanyali M., Hajek B. On large deviations in load sharing networks. Ann. Appl. Probab. (1998) 8:67–97Crossref, Google Scholar
• Alanyali M., Hajek B. On large deviations of Markov processes with discontinuous statistics. Ann. Appl. Probab. (1998) 8:45–66Crossref, Google Scholar
• Atar R., Dupuis P. Large deviations and queueing networks: Methods for rate function identification. Stochastic Process. Appl. (1999) 84(2):255–296Crossref, Google Scholar
• Blinovskii V. M., Dobrushin R. L. Process level large deviations for a class of piecewise homogeneous random walks. The Dynkin Festschrift: Markov Processes and Their Applications (1994) (Birkhäuser, Boston, MA) 1–59Crossref, Google Scholar
• Borovkov A. A., Mogul'skĭ A. A. Large deviations for Markov chains in the positive quadrant. Uspekhi Mat. Nauk (2001) 56(5(341)):3–116Crossref, Google Scholar
• Boué M., Dupuis P., Ellis R. S. Large deviations for small noise diffusions with discontinuous statistics. Probab. Theory Related Fields (2000) 116(1):125–149Crossref, Google Scholar
• Chen H., Mandelbaum A. Discrete flow networks: Bottleneck analysis and fluid approximations. Math. Oper. Res. (1991) 16(2):408–446Link, Google Scholar
• Clarke F. H.Optimization and Nonsmooth Analysis (1983) (Wiley, New York) Google Scholar
• Dembo A., Zeitouni O.Large Deviations Techniques and Applications (1998) 2nd ed.(Springer, New York) Crossref, Google Scholar
• Dupuis P., Ellis R. S. Large deviations for Markov processes with discontinuous statistics. II.. Probab. Theory Related Fields (1992) 91:153–194Crossref, Google Scholar
• Dupuis P., Ellis R. S.A Weak Convergence Approach to the Theory of Large Deviations (1997) (Wiley, New York) Crossref, Google Scholar
• Dupuis P., Ellis R. S. The large deviation principle for a general class of queueing systems, I. Trans. Amer. Math. Soc. (1995) 347:2689–2751Google Scholar
• Dupuis P., Ellis R. S., Weiss A. Large deviations for Markov processes with discontinuous statistics. I. Ann. Probab. (1991) 19:1280–1297Crossref, Google Scholar
• Ethier S. N., Kurtz T. G.Markov Processes. Characterization and Convergence (1986) (Wiley, New York) Crossref, Google Scholar
• Fleming P. J., Simon B. Heavy traffic approximations for a system of infinite servers with load balancing. Probab. Engrg. Inform. Sci. (1999) 13:251–273Crossref, Google Scholar
• Foley R. D., McDonald D. R. Join the shortest queue: Stability and exact asymptotics. Ann. Appl. Probab. (2001) 11(3):569–607Crossref, Google Scholar
• Garcia J. An extension of the contraction principle. J. Theoret. Probab. (2004) 17(2):403–434Crossref, Google Scholar
• Ignatiouk-Robert I. Large deviations of Jackson networks. Ann. Appl. Probab. (2000) 10(3):962–1001Crossref, Google Scholar
• Ignatiouk-Robert I. Large deviations for processes with discontinuous statistics. Ann. Probab. (2005) 33(4):1479–1508Crossref, Google Scholar
• Jacod J., Shiryaev A. N.Limit Theorems for Stochastic Processes (1987) (Springer, Berlin, Germany) Crossref, Google Scholar
• Korostelëv A. P., Leonov S. L. An action functional for a diffusion process with discontinuous drift. Theory Probab. Appl. (1992) 37(3):543–550(In Russian: Teor. Veroyatn. eë Primen. 37 (3) 570–576)Crossref, Google Scholar
• Korostelëv A. P., Leonov S. L. Action functional for diffusions in discontinuous media. Probab. Theory Related Fields (1993) 94(3):317–333Crossref, Google Scholar
• Liptser R. S., Shiryaev A. N.Theory of Martingales (1989) (Kluwer, Dordrecht, The Netherlands) Crossref, Google Scholar
• Majewski K. Large deviation bounds for single class queueing networks and their calculation. Queueing Syst. (2004) 48(1–2):103–134Crossref, Google Scholar
• Puhalskii A., Sazonov V., Shervashidze T. On functional principle of large deviations. New Trends in Probability and Statistics (1991) 1(VSP/Moks'las, Vilnius, Lithuania) 198–218Google Scholar
• Puhalskii A. The method of stochastic exponentials for large deviations. Stochastic Process. Appl. (1994) 54(1):45–70Crossref, Google Scholar
• Puhalskii A.Large Deviations and Idempotent Probability (2001) (Chapman & Hall/CRC, Boca Raton, FL) Crossref, Google Scholar
• Puhalskii A. A. The action functional for the Jackson network. Markov Process: Related Fields (2007) 13(1):99–136Google Scholar
• Ramanan K., Dupuis P. Large deviation properties of data streams that share a buffer. Ann. Appl. Probab. (1998) 8(4):1070–1129Crossref, Google Scholar
• Ridder A., Shwartz A. Large deviations without principle: Join the shortest queue. Math. Methods Oper. Res. (2005) 62(3):467–483Crossref, Google Scholar
• Shwartz A., Weiss A.Large Deviations for Performance Analysis (1995) (Chapman & Hall, London, UK) Google Scholar
• Turner S. R. E., McDonald D. R., Turner S. R. E. Large deviations for join the shorter queue. Analysis of Communication Networks: Call Centres, Traffic and Performance (Toronto, Ontario, 1998), Vol. 28, Fields Institute Communications (2000) (American Mathematical Society, Providence, RI) 95–108Google Scholar