Discrete-time GI/D-MSP/1/N queuing system with negative customer arrival and RCH killing policy

YU Miao-miao, TANG Ying-hui, FU Yong-hong, LIU Qiang-guo

Systems Engineering - Theory & Practice ›› 2011, Vol. 31 ›› Issue (9) : 1753-1762.

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Systems Engineering - Theory & Practice ›› 2011, Vol. 31 ›› Issue (9) : 1753-1762. DOI: 10.12011/1000-6788(2011)9-1753

Discrete-time GI/D-MSP/1/N queuing system with negative customer arrival and RCH killing policy

  • YU Miao-miao1,2, TANG Ying-hui1, FU Yong-hong3, LIU Qiang-guo2
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Abstract

Applying the supplementary variable technique and embedded Markov chain method based on the iteration of conditional probability matrix, we studied a discrete-time GI/D-MSP/1/N queuing system with negative customer arrival and RCH killing policy. Three kinds of queue length distributions, namely the queue length distribution at positive customer pre-arrival, arbitrary and outside observer's observation epochs, are obtained. Furthermore, we also considered the waiting time distribution of the accessible positive customer. Finally, we presented several numerical examples under some special cases to demonstrate the correctness of the theoretical analysis of this algorithm.

Key words

supplementary variable technique / embedded Markov chain / discrete-time Markovian service process / negative customer / RCH killing policy

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YU Miao-miao, TANG Ying-hui, FU Yong-hong, LIU Qiang-guo. Discrete-time GI/D-MSP/1/N queuing system with negative customer arrival and RCH killing policy. Systems Engineering - Theory & Practice, 2011, 31(9): 1753-1762 https://doi.org/10.12011/1000-6788(2011)9-1753

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