具有两类顾客和轨道搜索的重试排队系统的均衡策略分析
Equilibrium Strategies Analysis of a Retrial Queueing System with Two Classes of Customers and Orbital Search
时献玥 1刘力维 1闫俊娜2
作者信息
- 1. 南京理工大学数学与统计学院,南京 210094
- 2. 林州建筑职业技术学院基础教学部,林州 456500
- 折叠
摘要
文章考虑一个具有两类顾客和轨道搜索的M/M/1重试排队系统.到达系统的顾客如果服务受到阻碍,优先顾客可以排队等待,且在服务台前的等待空间有限;而普通顾客可以选择加入具有无穷容量的重试轨道,等待稍后重试.如果服务台在服务完一位顾客后发现系统中不存在优先顾客,但轨道中存在普通顾客,则服务台会以概率p保持空闲状态,等待顾客的到来;或者以概率1-p从轨道队列的队首开始搜索普通顾客.文章首先利用拟生灭过程的遍历条件推导出系统的稳态条件,并基于生成函数方法得到一些重要的系统性能指标.然后根据线性"收益-成本"结构,在完全不可见和部分可见情形下研究普通顾客的均衡策略.最后通过数值实例探究系统参数对均衡策略的影响.
Abstract
In this paper,we consider an M/M/1 retrial queueing system with two classes of customers and orbital search.If the service of arriving customers is ob-structed,priority customers can wait in line and have limited waiting space in front of the server;The ordinary customers can join an infinite-capacity retrial orbit and retry later.If the server finds that there is no priority customer in the system after serving a customer,but there are ordinary customers in orbit,the server will keep idle with probability p and wait for customers to arrive or start searching for customers from the head of the orbit with probability 1-p.We first derive the stability condition of the system using the ergodic condition of the quasi-birth-and-death(QBD)process and obtain some important system performance measures based on the generating function approach.Then,depending on a linear reward-cost structure,we study ordi-nary customers'equilibrium joining strategies in the fully unobservable and partially observable cases.Finally,the effects of the system parameters on the equilibrium strategies are explored through numerical examples.
关键词
两类顾客/抢占优先权/重试队列/轨道搜索/均衡策略Key words
Two classes of customers/preemptive priority/retrial queue/orbital search/equilibrium strategy引用本文复制引用
基金项目
国家自然科学基金(61773014)
河南省高等学校重点科研项目(20B110002)
出版年
2024
NETL
NSTL
万方数据