We study a general k dimensional infinite server queues process. When the service times are fat tailed, we prove that the properly rescaled process converges to some limiting process: in particular we identify three regimes including slow arrivals, fast arrivals, and equilibrium, which lead to different limits in distribution. AMS 2000 subject classifications: Primary 60G50, 60K30, 62P05, 60K25. 查看全文>>