程慧慧,田中连. 具有多重休假和两阶段服务的MX/G/1重试排队系统[J]. 科学技术与工程, 2020, 20(32): 13091-13098.
CHENG Hui-Hui,TIAN Zhong-lian.Mx/G/1 Retrial Queuing System with Multiple Vacation and Two-phase Services[J].Science Technology and Engineering,2020,20(32):13091-13098. |
| 具有多重休假和两阶段服务的MX/G/1重试排队系统 |
| Mx/G/1 Retrial Queuing System with Multiple Vacation and Two-phase Services |
| 投稿时间：2019-11-15 修订日期：2020-08-03 |
| DOI： |
| 中文关键词: 多重休假 启动时间 两阶段服务 稳定状态 随机分解 |
| 英文关键词:multiple vacations set-up time two-phaseservice steady-state the stochastic decomposition |
| 基金项目:国家自然科学基金(11201145；11501531) |
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| 中文摘要: |
| 研究具有服务多重休假和两阶段服务的重试排队系统, 其中休假结束后服台需要重新启动. 批次到达的顾客形成参数为的Poisson过程, 顾客进行两阶段的服务：必选服务和可选服务, 其中第二阶段的可选服务有多种服务可供选择. 首先通过嵌入马尔科夫链的方法得到了系统稳定性存在的条件, 然后通过引入补充变量求出系统稳定状态分布及相关指标. 最后在广义服务时间的定义下, 证明了系统随机分解性. |
| 英文摘要: |
| A retrial queue with multiple vacation and two-phase services is studied, in which the server is restarted after the vacation. Customers arriving in batches form a generalized Poisson process with the parameter \lambda. They are provided with two phase of service: the essential service and the optional service, and there are many services to choose from the second phase services. Firstly, the existence conditions of system stability are obtained by embedding Markov chains. Then the probability distribution and some performance measures of the system to be steady are obtained by introducing supplementary variables. Finally, under the definition of generalized vacation, the stochastic decomposition of the system is proved. |
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