西北师范大学学报（自然科学版）2017，Vol.53Issue(3)：28-33,6.DOI:10.16783/j.cnki.nwnuz.2017.03.006
带服务台故障及启动期和备用服务台的GeomGeom1+1排队系统
The Geom/Geom/1+1 queue system with server breakdownsand a spare server with setup time
摘要
Abstract
Based on the classical Geom/Geom/1 discrete time queue system,a spare server with setup time is added into the system in this paper.The spare server will be used when the main server is in trouble,and the service rates of two servers are different.First of all,using the quasi birth and death process and the matrix-geometric solution method,the steady state distribution of the captain is given in this model,and then the analytical expressions which calculate the mean queue length and other performance indexes are also obtained.Secondly,the influence of parameters on the system indexes is analyzed by numerical examples.Finally,the average residual utility and social benefit function are constructed to analyze the social optimal strategy of the queue system.关键词
服务台故障/启动时间/备用服务台/拟生灭过程/矩阵几何解Key words
server breakdown/setup time/spare server/quasi birth and death process/matrix-geometric solution分类
数理科学引用本文复制引用
马占友,许敏杰,郑晓铭,王文博..带服务台故障及启动期和备用服务台的GeomGeom1+1排队系统[J].西北师范大学学报（自然科学版）,2017,53(3):28-33,6.基金项目
国家自然科学基金资助项目(61472342) （61472342）
河北省自然科学基金资助项目(A2014203096,G2013203169) （A2014203096,G2013203169）
河北省教育厅高等学校科技计划重点项目(ZD2017079) （ZD2017079）
燕山大学青年教师基金资助项目(13LGA017) （13LGA017）
河北省高等学校科学技术研究青年基金项目(QN2016016) （QN2016016）
