| 有启动失败和可选服务的M／G／1重试排队模型的一个特征值 |
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| 引用本文： | 仲彦军.有启动失败和可选服务的M／G／1重试排队模型的一个特征值[J].新疆师范大学学报(自然科学版),2014(4):53-59. |
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| 作者姓名： | 仲彦军 |
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| 作者单位： | 新疆师范大学 数学科学学院，新疆 乌鲁木齐830054; 中国科技大学 数学科学学院，安徽 合肥230026 |
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| 基金项目： | 基目]新疆维吾尔自治区自然科学基金( No．2013211B12)资助。 |
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| 摘 要： | 文章讨论具有可选服务的M／G／1重试排队模型，其中服务台有可能启动失败。系统外新到达的顾客服从参数为λ的泊松过程。重试区域只允许队首顾客重试，重试时间服从一般分布。所有的顾客都必须接受必选服务，然而只有其中部分接受可选服务，证明0是该模型主算子的几何重数为1的特征值。
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| 关 键 词： | M/G/1重试排队模型 初始启动失败 可选服务 特征值 几何重数 |
An Eigenvalue of M/G/1 Retrial Queueing Model with Second Optional Service and Starting Failures |
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| ZHONG Yan-Jun.An Eigenvalue of M/G/1 Retrial Queueing Model with Second Optional Service and Starting Failures[J].Journal of Xinjiang Normal University(Natural Sciences Edition),2014(4):53-59. |
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| Authors: | ZHONG Yan-Jun |
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| Institution: | ZHONG Yan-Jun(1. College of Mathematics Science, Xinjiang Normal University, Urumqi, Xinjiang, 830054, China ; 2. University of Science and Technology of China, Hefei, Anhui, 230026, China) |
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| Abstract: | This paper considers an M/G/1 retrial queue with second optional service and starting failures. We assume that customers arrive to the system according to a Poisson process with rate λ. Assuming that only the cus？tomer at the head of the orbit has priority access to the server, and the retrial time is an arbitrary distribution. All demand the first“essential” service, whereas only some of them demand the secomd“optional” service. We obtain that 0 is an eigenvalue of the operator with geometric multiplicity one. |
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| Keywords: | M/G/1 Retrial queueing Model Starting failures Optional service Eigenvalue Geometric mul-tiplicity |
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