Some ideas from the theory of weak convergence of probability measures on function spaces are modified and extended to show that the queue-length of the GI/G/s system converges in distribution as time passes, for the case of atomless interarrival and service distributions. The key to this result is the concept of the uniform $\sigma$-additivity of certain sets of renewal measures on a space endowed with incompatible topology and $\sigma$-field.
Publié le : 1975-06-14
Classification:
GI/G/s queue,
renewal process,
weak convergence of measures on nonseparable metric spaces,
uniform $\sigma$-additivity,
60K25,
60B10,
60K05
@article{1176996350,
author = {Miller, Douglas R. and Sentilles, F. Dennis},
title = {Translated Renewal Processes and the Existence of a Limiting Distribution for the Queue Length of the GI/G/s Queue},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 424-439},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996350}
}
Miller, Douglas R.; Sentilles, F. Dennis. Translated Renewal Processes and the Existence of a Limiting Distribution for the Queue Length of the GI/G/s Queue. Ann. Probab., Tome 3 (1975) no. 6, pp. 424-439. http://gdmltest.u-ga.fr/item/1176996350/