Journal of Systems Science and Complexity

, Volume 30, Issue 5, pp 1097–1106 | Cite as

Strong approximation method and the (functional) law of iterated logarithm for GI/G/1 queue

  • Yongjiang GuoEmail author
  • Xiyang Hou


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.


GI/G/1 queue renewal process (RP) strong approximation (SA) method the functional LIL (FLIL) the law of the iterated logarithm (LIL) 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.Automatic SchoolBeijing University of Posts and TelecommunicationsBeijingChina

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