# Distribution-valued heavy-traffic limits for the $G-mathit{GI}-infty$ queue - Mathematics > Probability

Distribution-valued heavy-traffic limits for the $G-mathit{GI}-infty$ queue - Mathematics > Probability - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We study the $G-\mathit{GI}-\infty$ queue in heavy-traffic using tempereddistribution-valued processes which track the age and residual service time ofeach customer in the system. In both cases, we use the continuous mappingtheorem together with functional central limit theorem results in order toobtain fluid and diffusion limits for these processes in the space of tempereddistribution-valued processes. We find that our diffusion limits are tempereddistribution-valued Ornstein-Uhlenbeck processes.

Autor: Josh Reed, Rishi Talreja

Fuente: https://arxiv.org/