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A preemptive priority retrial queue with two classes of customers and general retrial times

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Abstract

In this paper, we consider a continuous-time retrial queue with two classes of customers: priority customers and ordinary customers, where priority customers don’t queue and have an exclusive preemptive priority to receive their services over ordinary customers. If an arriving ordinary customer finds the server busy, it enters a retrial group (called orbit) according to FCFS discipline. Only the ordinary customer at the head of the retrial queue is allowed to access the server. Firstly, we obtain the necessary and sufficient condition for the system to be stable by embedded Markov chain approach. Secondly, using supplementary variable method, we obtain the stationary probability distribution and some performance measures of interest. Thirdly, we give the analysis of the sojourn time in the system of an arbitrary ordinary customer. Lastly, numerical examples are given to show the effect of system parameters on several performance measures.

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Acknowledgments

The authors would like to thank the anonymous referees for their helpful comments and suggestions, which improved the content and the presentation of this paper. This work is supported by the National Natural Science Foundation of China (Nos. 11171179, 11301306), the Natural Science Foundation of Anhui Higher Education Institutions of China (No. KJ2014ZD21), the National Statistical Science Research Project of China (No. 2014191) and Program for Science Research of Fuyang Normal College (No. 2014LY088).

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  1. School of Mathematics and Statistics, Fuyang Normal College, Fuyang, 236032, People’s Republic of China

    Shan Gao

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  1. Shan Gao
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Correspondence to Shan Gao.

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Gao, S. A preemptive priority retrial queue with two classes of customers and general retrial times. Oper Res Int J 15, 233–251 (2015). https://doi.org/10.1007/s12351-015-0175-z

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