Distribution-valued heavy-traffic limits for the $G/\mathit{GI}/\infty$ queue

Josh Reed; Rishi Talreja

doi:10.1214/14-aap1027

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arXiv · 0902.2236

Distribution-valued heavy-traffic limits for the $G/\mathit{GI}/\infty$ queue

Josh Reed·Rishi Talreja

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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.

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BibTeX RIS

Josh Reed, Rishi Talreja. 2009-02-13. Distribution-valued heavy-traffic limits for the $G/\mathit{GI}/\infty$ queue. https://doi.org/10.1214/14-aap1027

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