Calculating transient characteristics of the Erlang loss model by numerical transform inversion

Communications in Statistics. Part C: Stochastic Models

Volumn 14, Issue 3, 1998, Pages 663-680

  Abate, J ^a   Whitt, W ^b  

^a AT and T Labs Research ^*  (United States)

^b AT AND T LABS RESEARCH   (United States)

Author keywords

Blocking probability; Covariance function; Erlang loss model; First passage time; Numerical transform inversion; Reflected Ornstein Uhlenbeck diffusion process; Scaling; Transient behavior

Indexed keywords

EID: 0009007208     PISSN: 08820287     EISSN: None     Source Type: Journal    
DOI: 10.1080/15326349808807494     Document Type: Article

References (29)

1. Abate, J., Choudhury, G. L. and Whitt, W. (1996) On the Laguerre method for numerically inverting Laplace transforms, INFORMS J. Computing, 8, 413-427.
2. Abate, J. and Whitt, W. (1992) The Fourier-series method for inverting transforms of probability distributions, Queueing Systems 10, 5-88.
3. Abate, J. and Whitt, W. (1995) Numerical inversion of Laplace transforms of probability distributions, ORSA J. Computing 7, 36-43.
4. Beneš, V. E. (1961) The covariance function of a simple trunk group with applications to traffic measurements. Bell System Tech. J. 40, 117-148.
5. Beneš, V. E. (1965) Mathematical Theory of Connecting Networks and Telephone Traffic, Academic Press, New York.
6. Borovkov, A. A. (1984) Asymptotic Methods in Queueing Theory, Wiley, New York.
7. Choudhury, G. L., Lucantoni, D. M. and Whitt, W. (1994) Multidimensional transform inversion with application to the transient M/G/1 queue, Ann. Appl. Prob. 4, 719-740.
8. t/1 queues, Oper. Res., 45, to appear.
9. Choudhury, G. L. and Whitt, W. (1996) Probabilistic scaling for the numerical inversion of non-probability transforms, INFORMS J. Computing, submitted.
10. Darling, D. A. and Siegert, J. F. (1953) The first passage problem for a continuous Markov process, Ann. Math. Statist. 24, 624-639.
11. Davis, J. L., Massey, W. A. and Whitt, W. (1995) Sensitivity to the service-time distribution in the nonstationary Erlang loss model, Management Sci. 41, 1107-1116.
12. Green, L., Kolesar, P. and Svoronos, A. (1991) Some effects of non-stationarity on multiserver Markovian queueing systems, Oper. Res. 39, 502-511.
13. Jagerman, D. L. (1974) Some properties of the Erlang loss function. Bell System Tech. J. 53, 525-551.
14. Jagerman, D. L. (1975) Nonstationary blocking in telephone traffic, Bell System Tech. J. 54, 625-661.
15. Jagerman, D. L. (1978) An inversion technique for the Laplace transform with applications, Bell System Tech. J. 57, 669-710.
16. Keilson, J. (1979) Markov Chain Models - Rarity and Exponentiality, Springer-Verlag, New York.
17. Keilson, J. and Ross, H. F. (1975) Passage Time distributions for Gaussian Markov (Ornstein-Uhlenbeck) Statistical Processes, Selected Tables in Mathematical Statistics, 3, 233-327.
18. Knessl, C. (1990) On the transient behavior of the M/M/m/m Loss model. Stochastic Models 6, 749-776.
19. Koopman, B. O. (1972) Air terminal queues under time-dependent conditions, Oper. Res. 20, 1089-1114.
20. Kosten, L., Manning, J. R. and Garwood, F. (1949) On the accuracy of measurements of probabilities of loss in telephone systems, J. Roy. Statist. Soc., Ser. B 11, 54-67.
21. Lucantoni, D. M., Choudhury, G. L. and Whitt, W. (1994) The transient BMAP/G/1 queue, Stochastic Models 10, 145-182.
22. Mitra, D. and Weiss, A. (1989) The transient behavior in Erlang's model for large trunk groups and various traffic conditions, Teletraffic Science for new cost-Effective Systems, Networks and Services, ITC-12, M. Bonatti (ed.), Elsevier-Science Publishers, Amsterdam 1367-1374.
23. Ong, K. L. and Taaffe, M. R. (1989) Nonstationary queues with interrupted Poisson arrivals and unreliable/repairable servers, Queueing Systems 4, 27-46.
24. Riordan, J. (1962) Stochastic Service Systems, Wiley, New York.
25. Shwartz, A. and Weiss, A. (1995) Large Deviations for Performance Analysis, Chapman and Hall, London.
26. Srikant, R. and Whitt, W. (1996) Simulation run lengths to estimate blocking probabilities ACM J. TOMACS, 6, 7-52.
27. Taaffe, M. R. and Ong, K. L. (1987) Approximating Ph(t)/M(t)/S/C queueing systems, Annals Oper. Res. 8, 103-116.
28. Takács, L. (1962) Introduction to the Theory of Queues, Oxford University Press, New York.
29. Whitt, W. (1984) Heavy traffic approximations for service systems with blocking, AT&T Bell Lab. Tech. J. 63, 689-708.