Continued fraction analysis of the duration of an excursion in an M/M/∞ system

Journal of Applied Probability

Volumn 35, Issue 1, 1998, Pages 165-183

  Guillemin, Fabrice ^a   Pinchon, Didier ^b  

^a ORANGE LABS   (France)

^b UNIVERSITÉ PAUL SABATIER   (France)

Author keywords

Continued fractions; Laplace transforms; M M system; Orthogonal polynomials; Stieltjes transforms

Indexed keywords

EID: 0001741669     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1032192560     Document Type: Article

References (16)

1. ASKEY, R. AND ISMAIL, M. (1984). Recurrence relations, continued fractions, and orthogonal polynomials. Mem. Amer. Math. Soc. 300, 12.
2. DOSHI B. (1993). Deterministic rule based traffic descriptors for broadband ISDN: worst case behavior and connection acceptance control. In Proc. Globecom’93. Houston, TX.
3. GUILLEMIN, F. AND SIMONIAN, A. (1995). Transient characteristics of an M/M/m system. Adv. Appl. Prob. 27, 862-888.
4. GUILLEMIN, F., RUBINO, G., Sericola, B. and SIMONIAN, A. (1997). Transient analysis of statistical multiplexing of data connections on an ATM link. In Proc. ITC’15. Washington, DC.
5. GUILLEMIN, F. AND PINCHON, D. (1996). On a random variable associated with excursions in an M/M/m queueing system. Submitted.
6. HENRICI, P. (1977). Applied and Computational Complex Analysis. Vol. 2. Wiley, New York.
7. INCE, E.L. (1956). Ordinary Differential Equations. Dover, New York.
8. Ismail, M., Letessier, J., Masson, D. and Valent, G. (1990). Birth and death processes and orthogonal Polynomials. In Orthogonal Polynomials. ed. P. Nevai. Kluwer, Dordrecht. pp. 229-255.
9. ISMAIL, M., Letessier, J. and Valent, G. (1988). Linear birth and death models and associated Laguerre and Meixner polynomials. J. Approx. Theory 55, 337-348.
10. ISMAIL, M. and Kelker D. (1979). Special functions, Stieltjes transforms and infinite divisibility. SIAM J. Math. Anal. 10, 884-901.
11. KARLIN, S. AND McGregor, J. (1957). The differential equations of birth and death processes and the Stieltjes moment problem. Trans. Amer. Math. Soc. 85, 456-489.
12. KARLIN, S. AND McGregor, J. (1958). Linear growth birth and death processes. J. Math. Mech. 7, 643-662.
13. LEBEDEV, N. (1965). Special Functions and their Applications. Prentice Hall, New York.
14. MORRISON, J., Shepp, L. and VAN WYK, C. (1987). A queueing analysis of hashing with lazy deletion. SIAMJ. Comput. 16,1155-1164.
15. SLATER, L. J. (1960). Confluent Hypergeometric Functions. Cambridge University Press, Cambridge.
16. SZEGO, G. (1975). Orthogonal Polynomials. American Mathematical Society, Providence, RI