Note: Minimizing the variability of the waiting times in a globally gated elevator polling system

A polling system comprising n queues and a single server is considered. Service is performed according to an elevator scheme under the globally gated regime. The problem of arranging the channels to minimize a measure of the variability of the waiting times is addressed. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 605–611, 1997     

无标度网络上的队列资源重分配策略

在实际的通信系统中,由于物理条件的限制,每个节点都具有有限长度的队列。研究了在有限队列资源的条件下,队列资源对无标度数据流动力学的影响。提出了一种队列资源重分配策略,策略中节点的队列长度与节点的介数成正比。仿真结果表明,在无标度网络中使用最短路径路由的条件下,所提出的重分配策略可以有效地改进网络的容量。同时对有限队列资源条件下的网络容量进行了理论分析。     

Optimal staffing in nonstationary service centers with constraints

This paper considers optimal staffing in service centers. We construct models for profit and cost centers using dynamic rate queues. To allow for practical optimal controls, we approximate the queueing process using a Gaussian random variable with equal mean and variance. We then appeal to the Pontryagin's maximum principle to derive a closed form square root staffing (SRS) rule for optimal staffing. Unlike most traditional SRS formulas, the main parameter in our formula is not the probability of delay but rather a cost‐to‐benefit ratio that depends on the shadow price. We show that the delay experienced by customers can be interpreted in terms of this ratio. Throughout the article, we provide theoretical support of our analysis and conduct extensive numerical experiments to reinforce our findings. To this end, various scenarios are considered to evaluate the change in the staffing levels as the cost‐to‐benefit ratio changes. We also assess the change in the service grade and the effects of a service‐level agreement constraint. Our analysis indicates that the variation in the ratio of customer abandonment over service rate particularly influences staffing levels and can lead to drastically different policies between profit and cost service centers. Our main contribution is the introduction of new analysis and managerial insights into the nonstationary optimal staffing of service centers, especially when the objective is to maximize profitability. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 615–630, 2017     

Decentralized admission control of a queueing system: A game‐theoretic model

Consider a distributed system where many gatekeepers share a single server. Customers arrive at each gatekeeper according to independent Poisson processes with different rates. Upon arrival of a new customer, the gatekeeper has to decide whether to admit the customer by sending it to the server, or to block it. Blocking costs nothing. The gatekeeper receives a reward after a customer completes the service, and incurs a cost if an admitted customer finds a busy server and therefore has to leave the system. Assuming an exponential service distribution, we formulate the problem as an n‐person non‐zero‐sum game in which each gatekeeper is interested in maximizing its own long‐run average reward. The key result is that each gatekeeper's optimal policy is that of a threshold type regardless what other gatekeepers do. We then derive Nash equilibria and discuss interesting insights. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 702–718, 2003.     

Strategic spectrum occupancy for secondary users in cognitive radio networks with retrials

This article investigates joining strategies and admission control policy for secondary users (SUs) with retrial behavior in a cognitive radio (CR) system where a single primary user (PU) coexists with multiple SUs. Under a certain reward‐cost structure, SUs opportunistically access the PU band when it is not occupied by the PU. If the band is available upon arrival, an SU decides with a probability either to use the band immediately or to balk the system. If the band is occupied, the SU must decide whether to enter the system as a retrial customer or to leave the system. Once the PU requests for service, the service of SU being served, if any, will be interrupted, and the interrupted SU leaves the band and retries for service after a random amount of time. In this article, we study the equilibrium behavior of non‐cooperative SUs who want to maximize their benefit in a selfish, distributed manner with delay‐sensitive utility function. The socially optimal strategies of SUs are also derived. To utilize the PU band more efficiently and rationally, an admission control policy is proposed to regulate SUs who enter the system in order to eliminate the gap between the individually and socially optimal strategies.     

主动队列管理机制中PI算法的一种参数配置方法

研究了主动队列管理机制中PI控制器的参数配置方法。AQM中PI算法默认的参数以及一些文献提出的参数配置方法主要是从稳定性考虑,没有保证系统的动态性能指标。在控制论中,"二阶最优模型"是具有较好的动态性能和稳态性能的二阶系统。提出了一种PI控制器的参数配置方法,可以使TCP/AQM控制模型的开环传递函数具有"二阶最优模型"的形式。NS仿真结果表明采用该方法配置的参数可以提高PI控制器的动态性能并保证系统的稳态性能。最后指出PI控制器参数配置对网络状态的敏感性,以及今后的研究方向。     

一个输入依赖于系统状态的排队模型的瞬时队长分布

探讨了一个有如下特征的排队系统:该系统的第m个到达间隔αm-αm-1(m≥1)的分布依赖系统在时刻αm-1拥有的顾客数目。应用补充变量方法,这个系统的瞬时队长分布的积分表示被得到。在各到达间隔分布和诸服务时间分布均具有密度函数的条件下,这个积分表示的被积项能够递归地求取。     

A queueing system with vacations after N services

This article is devoted to the study of an M/G/1 queue with a particular vacation discipline. The server is due to take a vacation as soon as it has served exactly N customers since the end of the previous vacation. N may be either a constant or a random variable. If the system becomes empty before the server has served N customers, then it stays idle until the next customer arrival. Such a vacation discipline arises, for example, in production systems and in order picking in warehouses. We determine the joint transform of the length of a visit period and the number of customers in the system at the end of that period. We also derive the generating function of the number of customers at a random instant, and the Laplace–Stieltjes transform of the delay of a customer. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 646–658, 2015     

基于排队论的装备维修人员数量需求模型*

确定维修人员需求是对装备维修机构进行科学管理和对维修人员进行有计划培训的需要。在分析装备维修人员构成的随机服务系统特征的基础上,运用排队论理论建立了以平均等待时间为目标的维修人员需求的愿望模型,该模型可更加确切地描述各专业对维修人员的实际需求。通过对模型进行仿真,结果表明了模型的合理性。     

Scheduling policies for an antiterrorist surveillance system

This article concerns scheduling policies in a surveillance system aimed at detecting a terrorist attack in time. Terrorist suspects arriving at a public area are subject to continuous monitoring, while a surveillance team takes their biometric signatures and compares them with records stored in a terrorist database. Because the surveillance team can screen only one terrorist suspect at a time, the team faces a dynamic scheduling problem among the suspects. We build a model consisting of an M/G/1 queue with two types of customers—red and white—to study this problem. Both types of customers are impatient but the reneging time distributions are different. The server only receives a reward by serving a red customer and can use the time a customer has spent in the queue to deduce its likely type. In a few special cases, a simple service rule—such as first‐come‐first‐serve—is optimal. We explain why the problem is in general difficult and we develop a heuristic policy motivated by the fact that terrorist attacks tend to be rare events. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009