## The Annals of Probability

### Translated Renewal Processes and the Existence of a Limiting Distribution for the Queue Length of the GI/G/s Queue

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 3, Number 3 (1975), 424-439.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996350

Digital Object Identifier
doi:10.1214/aop/1176996350

Mathematical Reviews number (MathSciNet)
MR402975

Zentralblatt MATH identifier
0311.60053

JSTOR