RELIABILITY INDICES OF DISCRETE-TIME GeoX/G/1 QUEUEING SYSTEM WITH UNRELIABLE SERVICE STATION AND MULTIPLE ADAPTIVE DELAYED VACATIONS

Yinghui TANG, Miaomiao YU, Xi YUN ,Shujuan HUANG

系统科学与复杂性(英文) ›› 2012, Vol. 25 ›› Issue (6) : 1122-1135.

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系统科学与复杂性(英文) ›› 2012, Vol. 25 ›› Issue (6) : 1122-1135. DOI: 10.1007/s11424-012-1062-9

RELIABILITY INDICES OF DISCRETE-TIME GeoX/G/1 QUEUEING SYSTEM WITH UNRELIABLE SERVICE STATION AND MULTIPLE ADAPTIVE DELAYED VACATIONS

    Yinghui TANG1, Miaomiao YU2, Xi YUN3 ,Shujuan HUANG3
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RELIABILITY INDICES OF DISCRETE-TIME GeoX/G/1 QUEUEING SYSTEM WITH UNRELIABLE SERVICE STATION AND MULTIPLE ADAPTIVE DELAYED VACATIONS

    Yinghui TANG1, Miaomiao YU2, Xi YUN3 ,Shujuan HUANG3
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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  erspective 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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Yinghui TANG, Miaomiao YU, Xi YUN ,Shujuan HUANG. RELIABILITY INDICES OF DISCRETE-TIME GeoX/G/1 QUEUEING SYSTEM WITH UNRELIABLE SERVICE STATION AND MULTIPLE ADAPTIVE DELAYED VACATIONS. 系统科学与复杂性(英文), 2012, 25(6): 1122-1135 https://doi.org/10.1007/s11424-012-1062-9
Yinghui TANG, Miaomiao YU, Xi YUN ,Shujuan HUANG. RELIABILITY INDICES OF DISCRETE-TIME GeoX/G/1 QUEUEING SYSTEM WITH UNRELIABLE SERVICE STATION AND MULTIPLE ADAPTIVE DELAYED VACATIONS. Journal of Systems Science and Complexity, 2012, 25(6): 1122-1135 https://doi.org/10.1007/s11424-012-1062-9
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