Limits and approximations for the M/G/1 LIFO waiting-time distribution

Operations Research Letters

Volumn 20, Issue 5, 1997, Pages 199-206

  Abate, Joseph ^a   Whitt, Ward ^b  

^a ATandT Labs Research ^*  (United States)

^b AT AND T LABS RESEARCH   (United States)

Author keywords

Asymptotic normal approximation; Asymptotics; Catalan numbers; Heavy traffic; Last in first out service discipline; M G 1 queue; Moments; Waiting time

Indexed keywords

EID: 0000476241     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-6377(97)00016-3     Document Type: Article

References (19)

1. J. Abate, G.L. Choudhury, W. Whitt, Calculating the M/G/1 busy-period density and LIFO waiting-time distribution by direct numerical transform inversion, Oper. Res. Lett. 18 (1995) 113-119.
2. J. Abate, W. Whitt, Transient behavior of regulated Brownian motion, I: starting at the origin, Adv. Appl. Probab. 19 (1987) 560-598.
3. J. Abate, W. Whitt, Transient behavior of the M/M/1 queue via Laplace transforms, Adv. Appl. Probab. 20 (1988) 145-178.
4. J. Abate, W. Whitt, Transient behavior of the M/G/1 workload process, Oper. Res. 42 (1994) 750-764.
5. J. Abate, W. Whitt, Limits and approximations for the busy-period distribution in single-server queues, Prob. Eng. Inform. Sci. 9 (1995) 581-602.
6. J. Abate, W. Whitt, An operational calculus for probability distributions via Laplace transforms, Adv. Appl. Probab. 28 (1996) 75-113.
7. P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
8. D.R. Cox, W.L. Smith, Queues, Methuen, London, 1961.
9. A. Erdélyi, Asymptotic Expansions, Dover, New York, 1956.
10. I. Iliadis, S.W. Fuhrmann, Moment relationships for queues with Poisson input, Queueing Systems 12 (1992) 243-256.
11. J.F.C. Kingman, Queue disciplines in heavy traffic, Math. Oper. Res. 7 (1982) 262-271.
12. F.W.J. Olver, Asymptotics and Special Functions, Academic Press, New York, 1974.
13. J. Riordan, Delays for last-come first-served service and the busy period, Bell System Tech. J. 40 (1961) 785-793.
14. J. Riordan, Stochastic Service Systems, Wiley, New York, 1962.
15. J. Riordan, Combinatorial Identities, Wiley, New York, 1968.
16. L. Takács, Delay distributions for one line with Poisson input, general holding times, and various orders of service, Bell System Tech. J. 42 (1973) 487-503.
17. E. Vaulot, Delais d'attente des appels telephoniques dans l'ordre inverse de leur arrive, C.R. Acad. Sci. Paris 238 (1954) 1188-1189.
18. W. Whitt, Weak convergence theorems for priority queues: preemptive-resume discipline, J. Appl. Probab. 8 (1971) 74-94.
19. D.M. Wishait, Queueing systems in which the discipline is last-come first-served, Oper. Res. 8 (1960) 591-599.