Strong Approximation Method and the (Functional) Law of Iterated Logarithm for GI/G/1 Queue

GUO Yongjiang,HOU Xiyang

Journal of Systems Science & Complexity ›› 2017, Vol. 30 ›› Issue (5) : 1097-1106.

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PDF(186 KB)
Journal of Systems Science & Complexity ›› 2017, Vol. 30 ›› Issue (5) : 1097-1106. DOI: 10.1007/s11424-017-5226-5

Strong Approximation Method and the (Functional) Law of Iterated Logarithm for GI/G/1 Queue

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Abstract

In this paper, a unified method based on the strong approximation (SA) of renewal process (RP) is developed for the law of the iterated logarithm (LIL) and the functional LIL (FLIL), which 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 the GI/G/1 queue, the method 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.

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GUO Yongjiang , HOU Xiyang. Strong Approximation Method and the (Functional) Law of Iterated Logarithm for GI/G/1 Queue. Journal of Systems Science and Complexity, 2017, 30(5): 1097-1106 https://doi.org/10.1007/s11424-017-5226-5
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