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

数学物理学报 ›› 2023, Vol. 43 ›› Issue (6): 1943-1960.

• • 上一篇

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

王勋,徐秀丽^*()

燕山大学理学院河北秦皇岛 066004

收稿日期:2022-09-15 修回日期:2023-05-17 出版日期:2023-12-26 发布日期:2023-11-16
通讯作者: *徐秀丽，E-mail: xxl-ysu@163.com
基金资助:
国家自然科学基金(62171143)

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

Wang Xun,Xu Xiuli^*()

School of Science, Yanshan University, Hebei Qinhuangdao 066004

Received:2022-09-15 Revised:2023-05-17 Online:2023-12-26 Published:2023-11-16
Supported by:
NSFC(62171143)

摘要/Abstract

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.

关键词: 流体模型, 双阶段休假, 启动时间, 有限容量, 库存量

Abstract:

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 two-dimensional 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.

Key words: Fluid model, Two-stage vacation, Set-up time, Finite capacity, Buffer content

中图分类号:

O226

王勋, 徐秀丽. 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[J]. 数学物理学报, 2023, 43(6): 1943-1960.

Wang Xun, Xu Xiuli. Performance Analysis of a Fluid Model Driven by Two-Stage Vacation Queue with Set-up Time and Optional Service[J]. Acta mathematica scientia,Series A, 2023, 43(6): 1943-1960.

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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

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