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A repairable discrete-time retrial queue with recurrent customers, Bernoulli feedback and general retrial times

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Abstract

This paper relates to a repairable Geo/G/1 retrial queue with general retrial times, Bernoulli feedback, the server subjected to starting failures and two types of customers: transit and a fixed number of recurrent customers. After service completion, recurrent customers always return to the orbit and transit customers either immediately return to the orbit for another service with probability \(\theta (0\leq\theta<1)\) or leave the system forever with probability 1 − θ. We construct the mathematical model and present some performance measures of the model in steady-state. We provide a stochastic decomposition law and analyze the relationship between our discrete-time system and its continuous-time counterpart. Finally, some numerical examples show the influence of the parameters on the performance characteristics of the system.

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Authors and Affiliations

  1. School of Mathematics, Central South University, Changsha, 410075, People’s Republic of China

    Shan Gao, Zaiming Liu & Hua Dong

  2. Department of Mathematics, Fuyang Normal College, Fuyang, 236032, People’s Republic of China

    Shan Gao

Authors
  1. Shan Gao
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  2. Zaiming Liu
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  3. Hua Dong
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Correspondence to Shan Gao.

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Gao, S., Liu, Z. & Dong, H. A repairable discrete-time retrial queue with recurrent customers, Bernoulli feedback and general retrial times. Oper Res Int J 12, 367–383 (2012). https://doi.org/10.1007/s12351-010-0098-7

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  • DOI: https://doi.org/10.1007/s12351-010-0098-7

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