Large Deviations of Square Root Insensitive Random Sums

Published Online:https://doi.org/10.1287/moor.1030.0082

References

  • Abate J., Whitt W. Asymptotics for M/G/1 low-priority waiting-time tail probabilities. Queueing Systems Theory Appl. (1997) 25(1–4):173–223CrossrefGoogle Scholar
  • Asmussen S. Subexponential asymptotics for stochastic processes: Extremal behavior stationary distributions and first passage probabilities. Ann. Appl. Probab. (1998) 8(2):354–374CrossrefGoogle Scholar
  • Asmussen S., Kalashnikov V., Konstantinides D., Klüppelberg C., Tsitiashvili G. A local limit theorem for random walk maxima with heavy tails. Statist. Probab. Lett. (2002) 56(4):399–404CrossrefGoogle Scholar
  • Asmussen S., Klüppelberg C., Sigman K. Sampling at subexponential times, with queueing applications. Stochastic Process. Appl. (1999) 79:265–286CrossrefGoogle Scholar
  • Asmussen S., Teugels J. Convergence rates for M/G/1 queues and ruin problems with heavy tails. J. Appl. Probab. (1996) 33:1181–1190CrossrefGoogle Scholar
  • Bingham N. H., Goldie C. M., Teugels J. L.Regular Variation (1987) (Cambridge University Press, Cambridge, MA) CrossrefGoogle Scholar
  • Borst S., Boxma O., Jelenković P. Coupled processors with regularly varying service times. Proc. IEEE Infocom. (2000) Tel Aviv, IsraelCrossrefGoogle Scholar
  • Borst S., Boxma O., Jelenković P. Reduced-load equivalence and induced burstiness in GPS queues with long-tailed traffic flows. Queueing Systems Theory Appl. (2003) 43(4):273–306CrossrefGoogle Scholar
  • Boxma O., Dumas V. The busy period in the fluid queue. Performance Evaluation Rev. (1998) 26:100–110CrossrefGoogle Scholar
  • Cohen J. W.The Single Server Queue (1982) (North-Holland, Amsterdam, The Netherlands) Google Scholar
  • de Meyer A., Teugels J. L. On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1. J. Appl. Probab. (1980) 17:802–813CrossrefGoogle Scholar
  • Foss S., Korshunov D. Sampling at random time with a heavy-tailed distribution. Markov Process Related Fields (2000) 6:543–568Google Scholar
  • Heyde C. C. A contribution to the theory of large deviations for sums of independent random variables. Z. Wahr. verw. Gebiete (1967) 7:303–308CrossrefGoogle Scholar
  • Jelenković P., Lazar A. Asymptotic results for multiplexing subexponential on-off processes. Adv. Appl. Probab. (1999) 31(2):394–421CrossrefGoogle Scholar
  • Jelenković P., Momčilović P. Large deviation analysis of subexponential waiting times in a processor sharing queue. Math. Oper. Res. (2003) 28(3):587–608LinkGoogle Scholar
  • Jelenković P., Momčilović P., Zwart B. Reduced load equivalence under subexponentiality. Queueing Systems Theory Appl.ForthcomingGoogle Scholar
  • Klüppelberg C., Mikosch T. Large deviations of heavy-tailed random sums with applications in insurance and finance. J. Appl. Probab. (1997) 34:293–308CrossrefGoogle Scholar
  • Nagaev A. V. Integral limit theorems taking large deviations into account when Cramér's condition does not hold. I, II. Theory Probab. Appl. (1969) 14:51–64–193–208Google Scholar
  • Nagaev A. V. On a property of sums of independent random variables. Theory Probab. Appl. (1977) 22(2):326–338CrossrefGoogle Scholar
  • Nagaev S. V. Large deviations of sums of independent random variables. Ann. Probab. (1979) 7(5):745–789CrossrefGoogle Scholar
  • Zwart B. Tail asymptotics for the busy period in the GI/G/1 queue. Math. Oper. Res. (2001) 26(3):485–493LinkGoogle Scholar
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