Reliability indices of discrete-time Geox/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations |
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Authors: | Yinghui Tang Miaomiao Yu Xi Yun Shujuan Huang |
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Affiliation: | 1. School of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, China 2. School of Science, Sichuan University of Science and Engineering, Zigong, 643000, China 3. School of Mathematics, University of Electronic Science and Technology of China, Chengdu, 610054, China
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Abstract: | This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed: 1) The probability that the server is in a “generalized busy period” at time n; 2) The probability that the service station is in failure at time n, i.e., the transient unavailability of the service station, and the steady state unavailability of the service station; 3) The expected number of service station failures during the time interval (0, n], and the steady state failure frequency of the service station; 4) The expected number of service station breakdowns in a server’s “generalized busy period”. Finally, the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper. |
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