On a random variable associated with excursions in an M/M/∞ system

Queueing Systems

Volumn 32, Issue 4, 1999, Pages 305-318

  Guillemin, Fabrice ^a   Pinchon, Didier ^b  

^a ORANGE LABS   (France)

^b UNIVERSITÉ PAUL SABATIER   (France)

Author keywords

Continued fractions; Excursions; Laplace transform; M M system; Stieltjes transform

Indexed keywords

DISTRIBUTION FUNCTIONS; POLES; RANDOM VARIABLES;

CONTINUED FRACTION; EXCURSIONS; EXPONENTIAL DECAYS; LAPLACE TRANSFORM INVERSIONS; NUMERICAL VALUES; STIELTJES TRANSFORM; TRANSIENT CHARACTERISTIC; TRICOMI FUNCTIONS;

LAPLACE TRANSFORMS;

EID: 0033235197     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/A:1019199306934     Document Type: Article

References (11)

1. J. Abate and W. Whitt, Numerical inversion of Laplace transforms of probability distributions, ORSA J. Comput. 7(1) (1995) 36-43.
2. J. Abate and W. Whitt, Computing Laplace transforms for numerical inversion via continued fractions, Inform. J. Comput., to appear.
3. R. Askey and M.B.H. Ismail, Recurrence Relations, Continued Fractions, and Orthogonal Polynomials, Memoirs of the American Mathematical Society, Vol. 300 (Amer. Math. Soc., Providence, RI).
4. G. Bordes and B. Roehner, Applications of Stieltjes theory for S-fractions to birth and death processes, Adv. in Appl. Probab. 15 (1983) 507-530.
5. F. Guillemin and D. Pinchon, Continued fraction analysis of the duration of an excursion in an M/M/∞ system, J. Appl. Probab. 35 (1998) 165-183.
6. F. Guillemin and D. Pinchon, Excursions of birth and death processes, orthogonal polynomials, and continued fractions, J. Appl. Probab., to appear.
7. F. Guillemin and A. Simonian, Transient characteristics of an M/M/∞ system, Adv. in Appl. Probab. 27 (September 1995) 862-888.
8. P. Henrici, Applied and Computational Complex Analysis, Vol. 2 (Wiley, New York, 1977).
9. M.B.H. Ismail and D. Kelker, Special functions, Stieltjes transforms, and infinite divisibility, SIAM J. Math. Anal. 10(5) (1979) 884-901.
10. S. Karlin and J. Mc Gregor, The differential equation of birth and death processes, and the Stieltjes moment problem, Trans. Amer. Math. Soc. 85 (1957) 489-546.
11. N.N. Lebedev, Special Functions and Their Applications (Dover, New York, 1972).