基于启动时间和可选服务的双阶段休假排队系统的流体模型性能分析  

Performance Analysis of a Fluid Model Driven by Two-Stage Vacation Queue with Set-up Time and Optional Service

作　　者：王勋 徐秀丽[1] Wang Xun;Xu Xiuli(School of Science,Yanshan University,Hebei Qinhuangdao 066004)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《数学物理学报（A辑）》2023年第6期1943-1960,共18页Acta Mathematica Scientia

基　　金：国家自然科学基金(62171143)。

摘　　要：基于店铺的外卖经营模式,该文构建并分析了具有启动时间、可选服务和两种混合休假策略的M/M/1/N排队系统驱动的流体模型.首先,对驱动系统进行模型描述,并将此二维Markov过程的无穷小生成元写成块状雅克比矩阵形式,运用矩阵几何解方法求出驱动系统的稳态概率分布.其次,引入流体模型的净输入率结构,并利用概率分析方法得到流体库存水平在稳态条件下的微分差分方程组,进而运用Laplace变换(LT)和Laplace-Stieltjes变换(LST)方法得到稳态条件下库存量的均值及空库概率.最后,通过数值分析给出各参数变化对系统性能指标和费用的影响.Based on the take-out operation model of the store,this paper constructed and analyzed a fluid model driven by the M/M/1/N queueing system with set-up time,optional service and two types of mixed vacations.Firstly,the driving system is described and the infinite small generators of the twodimensional Markov process are decomposed into a blocky Jacobian matrix form.Then,the stationary probability distribution of the driving system is obtained by using matrix-geometric method.Secondly,based on the net input rate structure of the fluid model,the differential and difference equations satisfied by the fluid level in steady-state conditions are obtained using the probability analysis method.Then,the expected buffer content and the probability of the empty buffer under steady-state conditions are obtained by using Laplace transform(LT)and Laplace-Stieltjes transform(LST)methods.Finally,the influence of parameters changing on the performance indicators and cost function are illustrated in numerical analysis.

关 键 词：流体模型 双阶段休假 启动时间 有限容量 库存量 

分 类 号：O226[理学—运筹学与控制论]