Year: 2015
Type: article
Abstract: We study the $G/\mathit{GI}/\infty$ queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each customer in the system. In both cases, we use the continuous mapping theorem together with functional central limit theorem results in order to obtain fluid and diffusion limits for these processes in the space of tempered distribution-valued processes. We find that our diffusion limits are tempered distribution-valued Ornstein–Uhlenbeck processes.
DOI: 10.1214/14-aap1027
Authors: Josh Reed, Rishi Talreja
Language: English
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: bronze
OpenAlex ID: W1580901162