Geodesic
Asymptotics of the Exit Distributionfor Markov Jump Processes; Application to Atm
Canadian journal of mathematics, Tome 46 (1994) no. 6, pp. 1238-1262

Voir la notice de l'article provenant de la source Cambridge University Press

We approximate the exit distribution of a Markov jump process into a set of forbidden states and we apply these general results to an ATM multiplexor. In this case the forbidden states represent an overloaded multiplexor. Statistics for this overload or busy period are difficult to obtain since this is such a rare event. Starting from the approximate exit distribution, one may simulate the busy period without wasting simulation time waiting for the overload to occur.
DOI : 10.4153/CJM-1994-070-5
Mots-clés : 60J27, 60K30, Exit distribution, Perron-Frobenius, Dirichlet eigenvalue, ATM, asymptotics 
Iscoe, I.; Mcdonald, D.; Qian, K. Asymptotics of the Exit Distributionfor Markov Jump Processes; Application to Atm. Canadian journal of mathematics, Tome 46 (1994) no. 6, pp. 1238-1262. doi: 10.4153/CJM-1994-070-5
@article{10_4153_CJM_1994_070_5,
     author = {Iscoe, I. and Mcdonald, D. and Qian, K.},
     title = {Asymptotics of the {Exit} {Distributionfor} {Markov} {Jump} {Processes;} {Application} to {Atm}},
     journal = {Canadian journal of mathematics},
     pages = {1238--1262},
     year = {1994},
     volume = {46},
     number = {6},
     doi = {10.4153/CJM-1994-070-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-070-5/}
}
TY  - JOUR
AU  - Iscoe, I.
AU  - Mcdonald, D.
AU  - Qian, K.
TI  - Asymptotics of the Exit Distributionfor Markov Jump Processes; Application to Atm
JO  - Canadian journal of mathematics
PY  - 1994
SP  - 1238
EP  - 1262
VL  - 46
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-070-5/
DO  - 10.4153/CJM-1994-070-5
ID  - 10_4153_CJM_1994_070_5
ER  - 
%0 Journal Article
%A Iscoe, I.
%A Mcdonald, D.
%A Qian, K.
%T Asymptotics of the Exit Distributionfor Markov Jump Processes; Application to Atm
%J Canadian journal of mathematics
%D 1994
%P 1238-1262
%V 46
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-070-5/
%R 10.4153/CJM-1994-070-5
%F 10_4153_CJM_1994_070_5

[Aldous, D. (1989)] Probability approximations via the Poisson clumping heuristic, Springer-Verlag, New York Inc. Google Scholar

[Iscoe, I. and McDonald, D. (1994)] Asymptotics of exit times for Markov jump processes I, Ann. Probab. (1) 22,372–397. Google Scholar

[Iscoe, I., McDonald, D. and Qian, K. (1993)] Capacity of ATM switches, Ann. Appl. Probab. (2) 3, 277–295. Google Scholar

[Kato, T. (1949)] On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan 4, 334–339. Google Scholar

[Liggett, T. M. (1989)] Exponential L2 convergence of attractive reversible nearest particle systems, Ann. Prob. (2) 17, 403–432. Google Scholar

[Olver, F. (1974)] Asymptotics and special functions, Academic Press, New York, San Francisco, London. Google Scholar

[Reed, M. and Simon, B. (1978)] Methods of modern mathematical physics Vol. IV: Analysis of operators, Academic Press, New York, San Francisco, London. Google Scholar

Cité par Sources :