具有插队和止步行为的M/M/c 排队系统

研究了具有插队和止步行为的M/M/c排队系统. 将到达顾客分为常规顾客和插队顾客, 常规顾客在队尾排队等待服务, 插队顾客总是尽可能的靠近队首插队等待服务. 插队行为由到达顾客的插队概率和队列中等待顾客对插队行为的容忍来描述. 利用负指数分布的性质、Laplace-Stieltjes变换和全概率公式, 给出了处于等待队列位置n的顾客、任意一个常规顾客和任意一个插队顾客的等待时间的表达式. 在此基础上, 讨论了系统相关指标随系统参数的变化情况.     

The Interarrival Hyperexponential Queues:Hk/M/c/N With Balking And Reneging

This paper treats the analytical solution of the truncated interarrival hyperexponential queue. H_k/M/c/N with balking and reneging for general values of k,c and N. The discipline considered here is FIFO. Some previously published results are shown to be special cases of the present results     

带有止步和中途退出的优先权排队系统

研究了一个带有止步和中途退出的优先权排队系统,其中系统中有两类顾客,第一类顾客具有优先权,而且可能中途退出,第二类顾客可能止步和中途退出.首先,建立了系统稳态概率满足的方程组.其次,采用分块矩阵的方法得到了两类顾客的稳态分布,并且得到了系统中两类顾客的的平均队长、平均中途退出率等性能指标.最后,进行了相应的性能分析与比较,为系统的优化设计提供了参考.     

基于Geo/Geo/1(E,SV)排队系统的均衡止步策略

基于单重休假Geo/Geo/1排队系统,研究顾客的均衡止步策略,首次将休假服务机制引入到离散时间排队经济学模型中. 顾客基于“收入--支出”结构,自主决定去留. 利用拟生灭过程理论,运用差分方程求解技巧,对系统进行了稳态分析,得到了顾客的平均逗留时间;进而构造适当的函数,给出了寻找均衡止步策略的具体方法并证明之;而后分析了在均衡策略下, 系统的稳态行为和社会收益;最后通过数值实验讨论了系统参数对均衡行为的影响.     

A single server queue with random arrivals and balking: Confidence interval estimation

This paper investigates a queueing system, which consists of Poisson input of customers, some of whom are lost to balking, and a single server working a shift of lengthL and providing a service whose duration can vary from customer to customer. If a service is in progress at the end of a shift, the server works overtime to complete the service. This process was motivated by the behavior of fishermen interviewed in the NY Great Lakes Creel Survey.We derive the distributions of the number of services (X), overtime and total server idle time (T), both unconditionally (for Poisson arrivals) and conditionally on the number (n) of arrivals per shift, assuming that the arrival times are not recorded in the data. These distributions provide the basis for estimation of the parameters from asingle realization of the queueing process during [0,L]. The conditional distributions also can be used to estimate common service time,w, when (n, X) or (n, T) are observed. Confidence intervals based onT are of shorter length, for all confidence coefficients, than the corresponding intervals based onX.This paper is Technical Report #BU-1019-M in the Biometrics Unit Series. The authors are grateful to N.U. Prabhu for suggestions on streamlining the distributional derivations and to D.R. Cox and C.E. McCulloch for helpful comments.     

A Diffusion Approximation for a GI/GI/1 Queue with Balking or Reneging

Consider a single-server queue with a renewal arrival process and generally distributed processing times in which each customer independently reneges if service has not begun within a generally distributed amount of time. We establish that both the workload and queue-length processes in this system can be approximated by a regulated Ornstein-Uhlenbeck (ROU) process when the arrival rate is close to the processing rate and reneging times are large. We further show that a ROU process also approximates the queue-length process, under the same parameter assumptions, in a balking model. Our balking model assumes the queue-length is observable to arriving customers, and that each customer balks if his or her conditional expected waiting time is too large.     

截超泊松排队:具有阻碍、放弃和不同服务员H_k/M/2/N系统(英文)

本文讨论具有阻碍、放弃,不同服务员Ｋｋ／Ｍ／２／Ｎ排队系统的解析解．对经典的一种先入先出的修改排队规则在较一般的条件下被采用了,得到了稳态概率和一些有效度量的显式．一些特殊情况也被化简了。     

考虑患者止步行为的动态入院接收决策模型

大型公立医院病床供需矛盾日益突出,医院作为服务系统有必要考虑由于病床需求响应速度不及时而引起的患者策略性行为。针对患者到达时间的随机性与住院时长的不确定性,本文提出考虑患者止步行为的动态入院接收决策问题,制定了适用于可等待慢性病患者的入院接收决策方法,旨在提高患者的就医满意度,有效权衡多类患者的接收数量,降低由于科室响应速度过慢引发的患者止步频率。首先,本文对考虑患者止步行为的动态入院接收决策问题进行数学描述及符号定义;然后,对患者止步行为的影响因素进行分析并构建止步概率函数;进一步地,构建考虑患者止步行为的动态入院接收马尔可夫决策过程(MDP)模型,并针对模型特点设计值迭代算法,最后通过数值算例验证本文所提方法的可行性与有效性。     

带有止步和状态相依的M/Ej/1/N排队系统的矩阵解法

研究了带有止步和服务率依赖于状态的M/Ej/1/N排队系统.顾客到达系统时,以一定的概率选择进入系统或止步(不进入系统).顾客接受服务的服务率依赖于系统中的顾客数,当系统中的顾客数不超过临界值k时,服务员慢速服务;否则,服务员快速服务.利用分块矩阵的方法,推出了稳态概率向量所满足的矩阵形式的迭代公式,给出了稳态概率的表达式和计算过程.作为特例,考虑了N=4时系统稳态概率的计算.在此基础上,还求出了系统的一些性能指标,并建立了以临界值k为控制变量的费用模型.通过数值分析,求出了使费用函数最小的最优临界值k*,并进一步研究了模型参数对最优临界值和最优费用的影响.     

Equilibrium and optimal strategies to join a queue with partial information on service times

In this paper, we study customer equilibrium as well as socially optimal strategies to join a queue with only partial information on the service time distribution such as moments and the range. Based on such partial information, customers adopt the entropy-maximization principle to obtain the expectation of their waiting cost and decide to join or balk. We find that more information encourages customers to join the queue. And it is beneficial for decision makers to convey partial information to customers in welfare maximization but reveal full information in profit maximization.