On busy periods of the unbounded Brownian storage

Queueing Systems

Volumn 39, Issue 4, 2001, Pages 317-333

  Salminen, Paavo ^a   Norros, Ilkka ^b  

^a ÅBO AKADEMI UNIVERSITY   (Finland)

^b VTT TECHNICAL RESEARCH CENTRE OF FINLAND   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN; BUSY PERIOD; EXPLICIT FORMULA; SERVICE RATES;

STORAGE AS A SERVICE (STAAS);

EID: 0035528309     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/A:1013953409012     Document Type: Article

References (19)

1. J. Abate and W. Whitt, Transient behavior of regulated Brownian motion, I: Starting at the origin, Adv. Appl. Prob. 19 (1987) 560-598.
2. J. Abate and W. Whitt, Transient behavior of regulated Brownian motion, II: Non-zero initial conditions, Adv. Appl. Prob. 19 (1987) 599-631.
3. J. Abate and W. Whitt, Transient behavior of the M/M/1 queue via Laplace transforms, Adv. Appl. Prob. 20 (1988) 145-178.
4. J. Abate and W. Whitt, Transient behaviour of the M/G/1 workload process, Operations Research 42 (1994) 750-764.
5. J. Abate and W. Whitt, Limits and approximations for the busy-period distribution in single-server queues, Prob. Eng. Inf. Sci. 9 (1995) 581-764.
6. A.N. Borodin and P. Salminen, Handbook of Brownian Motion - Facts and Formulae (Birkhäuser, Basel, Boston, Berlin, 1996).
7. E.B. Dynkin, Prostranstvo vyhodov markovskogo processa, Uspehi Mat. Nauk XXIV 4(148) (1969) 89-152 (in Russian).
8. A. Erdélyi, Tables of Integral Transforms (McGraw-Hill, New York, 1954).
9. R. Getoor, Excursions of a Markov process, Ann. Probab. 7(2) (1979) 244-266.
10. J.M. Harrison, Brownian Motion and Stochastic Flow Systems (Wiley, New York, 1985).
11. J.M. Harrison and R.J. Williams, On the quasireversibility of a multiclass Brownian service station, Ann. Probab. 18(3) (1990) 1249-1268.
12. K. Itô and H.P. McKean, Diffusion Processes and Their Sample Paths (Springer, Berlin, 1974).
13. P. McGill, P. Salminen and J.B. Walsh, Decomposing a diffusion via its local time, Unpublished.
14. N. O'Connell and M. Yor, Brownian analogues of Burke's theorem, Stochastic Process. Appl. 96(2) (2001) 285-304.
15. E. Reich, On the integrodifferential equation of Takács, I, Ann. Math. Stat. 29 (1958) 563-570.
16. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 3rd edition (Springer, Berlin, 2001).
17. L.C.G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales, Vol. II: Itô Calculus (Wiley, Chichester, New York, 1987).
18. P. Salminen, One-dimensional diffusions and their exit spaces, Math. Scand. 54 (1984) 209-220.
19. D. Williams, Path decompositions and continuity of local time for one-dimensional diffusions, Proc. London Math. Soc. 28 (1974) 738-768.