| Abstract: |
| In this talk, we will show a unified method based on the strong approximation (SA) of renewal process (RP) and its applications in the law of the iterated logarithm (LIL) and the functional LIL (FLIL) of queueing models. The LIL and the functional LIL, for RP, quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For some queues, we can find the similar situation with the RP. For queues, the method based on the SA provides a complete analysis for both the LIL and the FLIL limits for four performance functions: the queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity, less than, equal and more than 1. |
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