We introduce a family of heavy-traffic regimes for large scale service systems, presenting a range of scalings that include both moderate and extreme heavy traffic, as compared to classical heavy traffic. The heavy-traffic regimes can be translated into capacity sizing rules that lead to Economies-of-Scales, so that the system utilization approaches 100% while congestion remains limited. We obtain heavy-traffic approximations for stationary performance measures in terms of asymptotic expansions, using a non-standard saddle point method, tailored to the specific form of integral expressions for the performance measures, in combination with the heavy-traffic regimes.
@article{arxiv.1411.5251,
title = {Novel heavy-traffic regimes for large-scale service systems},
author = {A. J. E. M. Janssen and Johan S. H. van Leeuwaarden and Britt W. J. Mathijsen},
journal= {arXiv preprint arXiv:1411.5251},
year = {2014}
}