服务台不可靠的重试排队系统均衡分析

本文研究服务台不可靠的M/M/1常数率重试排队系统中顾客的均衡进队策略, 其中服务台在正常工作和空闲状态下以不同的速率发生故障。在该系统中, 服务台前没有等待空间, 如果到达的顾客发现服务台处于空闲状态, 该顾客可占用服务台开始服务。否则, 如果服务台处于忙碌状态, 顾客可以选择留下信息, 使得服务台在空闲时可以按顺序在重试空间中寻找之前留下信息的顾客进行服务。当服务台发生故障时, 正在被服务的顾客会发生丢失, 且系统拒绝新的顾客进入系统。根据系统提供给顾客的不同程度的信息, 研究队长可见和不可见两种信息情形下系统的稳态指标, 以及顾客基于收入-支出函数的均衡进队策略, 并建立单位时间内服务商的收益和社会福利函数。比较发现, 披露队长信息不一定能提高服务商收益和社会福利。

Combined response surface method with adaptive sampling for expensive black-box global optimization

A combined response surface method is presented for expensive black-box global optimization, which can adaptively take sampling points during iterations. Under the framework of response surface method, the convex combination of the cubic radial basis function and the thin plate spline radial basis function is adopted as the response surface. In the initial phase of the algorithm, the global optimizer of the auxiliary function formed by the product of the response surface model and the power of the distance indicator function will be taken as the new sample point. In the following iterations, if the distance between the two response surface models of the two consecutive iterations is smaller than a given threshold, then the global optimizer of the current response surface model will be taken as the next sample point, otherwise the sampling strategy of the initial phase will be adopted. The effectiveness of the proposed algorithm is demonstrated by the results of the numerical experiments carried respectively on 7 standard test problems and 22 standard test problems.