批量到达、服务台可修的M^X/G/1重试排队系统  

Repairable Retrial Queuing System With Batch Arrival

作　　者：朱春鹏[1] 

机构地区：[1]徐州工程学院数学与物理科学学院,江苏徐州221111

出　　处：《重庆科技学院学报（自然科学版）》2016年第6期104-107,119,共5页Journal of Chongqing University of Science and Technology：Natural Sciences Edition

基　　金：国家自然科学基金数学天元基金项目“KAM理论中光滑性问题的研究”(11526177);2014年江苏省高校自然科学基金项目“树指标随机过程的极限理论及其应用”(14KJB110025));徐州工程学院青年教师科研项目“基于排队论方法优化物流运输的研究”(XKY2012302)

摘　　要：讨论顾客批量到达且服务台会出现故障的重试排队模型。当新顾客批量到达服务台时,如果服务台忙,则新到达的顾客会进入重试组继续寻求服务或离开系统;当服务台出现故障时,会立刻得到修理并继续进行服务。利用补充变量法,结合服务时间、修理时间、重试时间研究排队队长。给出了系统稳态时的遍历条件,求解系统的稳态方程组,分析系统的各项性能指标。This paper relates to a retrial queuing model with unreliable server and batch arrivals. When customers arrive at the server which is busy, the new arrivals will enter the retry group to continue to search for a service or leave the system. We assumed that the server may fail while providing service and must be repaired immediately. We research the queue size by using supplementary variables methods corresponding to service time, repair time and retrial time. We also present the ergodic condition for the system to be stable and derive analytical results for the stationary distribution as well as some performance measures of the system.

关 键 词：批量到达 重试 可修 补充变量 稳态 

分 类 号：O226[理学—运筹学与控制论]