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A batch arrival retrial queue with starting failures, feedback and admission control

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Abstract

This paper is concerned with the analysis of a feedback M[X]/G/1 retrial queue with starting failures and general retrial times. In a batch, each individual customer is subject to a control admission policy upon arrival. If the server is idle, one of the customers admitted to the system may start its service and the rest joins the retrial group, whereas all the admitted customers go to the retrial group when the server is unavailable upon arrival. An arriving customer (primary or retrial) must turn-on the server, which takes negligible time. If the server is started successfully (with a certain probability), the customer gets service immediately. Otherwise, the repair for the server commences immediately and the customer must leave for the orbit and make a retrial at a later time. It is assumed that the customers who find the server unavailable are queued in the orbit in accordance with an FCFS discipline and only the customer at the head of the queue is allowed for access to the server. The Markov chain underlying the considered queueing system is studied and the necessary and sufficient condition for the system to be stable is presented. Explicit formulae for the stationary distribution and some performance measures of the system in steady-state are obtained. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, China

    Jinting Wang & Peng-Feng Zhou

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  1. Jinting Wang
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  2. Peng-Feng Zhou
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Correspondence to Jinting Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (10871020).

Jinting Wang is a full professor at Beijing Jiaotong University. He received his Ph.D. Degree in Operations Research and Cybernetics from Chinese Academy of Sciences (CAS) in 2000. His research interests include issues related to queueing theory, reliability and applied probability. He is author or co-author of several publications in Queueing Systems: Theory and Applications (QUESTA), Journal of Multivariate Analysis, European Journal of Operational Research, etc.

Peng-Feng Zhou is a Master student in the Department of Mathematics, School of Science at Beijing Jiaotong University. He received his B.Sc. in Mathematics from Beijing Jiaotong University. His research area includes retrial queues and reliability.

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Wang, J., Zhou, PF. A batch arrival retrial queue with starting failures, feedback and admission control. J. Syst. Sci. Syst. Eng. 19, 306–320 (2010). https://doi.org/10.1007/s11518-010-5140-z

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