| A RepairableGeoX/G/1 Retrial Queue with Bernoulli Feedback and Impatient Customers |
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| 作者姓名： | Shan GAO Zai-ming LIU |
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| 作者单位： | Department of Mathematics,Fuyang Normal College;School of Mathematics and Statistics,Central South University |
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| 基金项目： | Supported by the National Natural Science Foundation of China(Nos.11171019,11171179,and 11271373);Program for New Century Excellent Talents in University(No.NCET-11-0568);the Fundamental Research Funds for the Central Universities(No.2011JBZ012);Tianyuan Fund for Mathematics(Nos.11226200 and 11226251);Program for Science Research of Fuyang Normal College(2013FSKJ01ZD) |
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| 摘 要： | Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each customer after service either immediately returns to the orbit for another service with probabilityθor leaves the system forever with probability 1θ(0≤θ1).On the other hand,if the server is started unsuccessfully by a customer(external or repeated),the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 q(0≤q1).Firstly,we introduce an embedded Markov chain and obtain the necessary and sufcient condition for ergodicity of this embedded Markov chain.Secondly,we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary time.We also derive a stochastic decomposition law.In the special case of individual arrivals,we develop recursive formulae for calculating the steady-state distribution of the orbit size.Besides,we investigate the relation between our discrete-time system and its continuous counterpart.Finally,some numerical examples show the influence of the parameters on the mean orbit size.
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| 关 键 词： | 客户 排队 嵌入式马尔可夫链 伯努利 离散时间系统 反馈 稳态分布 服务器 |
A repairable Geo
X
/G/1 retrial queue with Bernoulli feedback and impatient customers |
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| Shan GAO,Zai-ming LIU.A RepairableGeoX/G/1 Retrial Queue with Bernoulli Feedback and Impatient Customers[J].Acta Mathematicae Applicatae Sinica,2014,30(1):205-222. |
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| Authors: | Shan Gao Zai-ming Liu |
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| Institution: | 1. Department of Mathematics, Fuyang Normal College, Fuyang, 236037, China
2. School of Mathematics and Statistics, Central South University, Changsha, 410075, China
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| Abstract: | discrete-time queue retrial queue starting failure steady state Bernoulli feedback |
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| Keywords: | discrete-time queue retrial queue starting failure steady state Bernoulli feedback |
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