Large deviations of square root insensitive random sums

Mathematics of Operations Research

Volumn 29, Issue 2, 2004, Pages 398-406

  Jelenković, Predrag R ^a   Momčilović, Petar ^b  

^a Columbia University ^*  (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Busy period; GI G 1 queue; Large deviation; Random sum; Square root insensitivity; Subexponential distribution

Indexed keywords

ASYMPTOTIC STABILITY; MARKOV PROCESSES; PROBABILITY DISTRIBUTIONS; WEIBULL DISTRIBUTION;

BUSY PERIOD; LARGE DEVIATION; RANDOM SUM; SQUARE ROOT INSENSITIVITY; SUBEXPONENTIAL DISTRIBUTION;

QUEUEING THEORY;

EID: 2342567266     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.1030.0082     Document Type: Article

References (21)

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