摘要
为了解决因维修台配置不合理而导致的专项汽修厂排队等待的问题,运用排队论等理论和方法,采用先到先修理与维修台带有优先权相结合的排队规则,将维修台配置数量问题转化为两类型服务台排队问题,建立了单队列M/M/s1+s2/K/∞/FCFS+PS排队模型.通过对某专项汽修厂相关的数据采集和分析,得到了模型所需的变量和参数,运用边际效益法进行优化,得到了节假日和非节假日客流高峰期的最优维修台配置数量.通过对系统服务强度、系统资源限制和服务时间段等因素的分析,既能保证排队系统可以在不同时间段内对维修台配置数量进行调整,又能缩小最优值的求解范围.
In order to solve the problem of queuing crowds in special auto repair plants caused by unreasonable maintenance station configuration,theories and methods such as queuing theory are used to adopt the first-come-first-served repair and maintenance station with priority queuing rules to configure the maintenance station.The quantity problem is transformed into two types of service desk queuing problems,and a single queue of M/M/s1+s2/K/∞/FCFS+PS queuing model is established.Through the data collection and analysis of a specific auto repair plant,the variables and parameters required by the model are obtained,and then the marginal benefit method is used for optimization,and the optimal number of maintenance stations during peak periods of holidays and non-holidays is finally obtained.Through the analysis of factors such as system service strength,system resource limitations and service time period,it can not only ensure that the queuing system can adjust the number of maintenance stations in different time periods,but also narrow the solution range of the optimal value.
作者
王鲁
杨玉中
WANG Lu;YANG Yu-zhong(School of Energy Science&Engineering,Henan Polytechnic University,Jiaozuo 454000,China)
出处
《数学的实践与认识》
2021年第3期143-151,共9页
Mathematics in Practice and Theory
基金
国家自然科学基金(51874121,51674102)。
关键词
排队论
生灭过程
先到先修理
优先级
边际效益法
queuing theory
birth and death process
first come first serve
priority
marginal benefit method
