On the discrete-time Geo/G/1 queue with randomized vacations and at most J vacations

This paper examines a discrete-time Geo/G/1 queue, where the server may take at most J − 1 vacations after the essential vacation. In this system, messages arrive according to Bernoulli process and receive corresponding service immediately if the server is available upon arrival. When the server is busy or on vacation, arriving messages have to wait in the queue. After the messages in the queue are served exhaustively, the server leaves for the essential vacation. At the end of essential vacation, the server activates immediately to serve if there are messages waiting in the queue. Alternatively, the server may take another vacation with probability p or go into idle state with probability (1 − p) until the next message arrives. Such pattern continues until the number of vacations taken reaches J. This queueing system has potential applications in the packet-switched networks. By applying the generating function technique, some important performance measures are derived, which may be useful for network and software system engineers. A cost model, developed to determine the optimum values of p and J at a minimum cost, is also studied.     

Critical periods of perturbations of reversible rigidly isochronous centers

In this paper we discuss bifurcation of critical periods in an m-th degree time-reversible system, which is a perturbation of an n-th degree homogeneous vector field with a rigidly isochronous center at the origin. We present period-bifurcation functions as integrals of analytic functions which depend on perturbation coefficients and reduce the problem of critical periods to finding zeros of a judging function. This procedure gives not only the number of critical periods bifurcating from the period annulus but also the location of these critical periods. Applying our procedure to the case n=m=2 we determine the maximum number of critical periods and their location; to the case n=m=3 we investigate the bifurcation of critical periods up to the first order in ε and obtain the expression of the second period-bifurcation function when the first one vanishes.     

Tail asymptotics for the fundamental period in the MAP/G/1 queue

This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802–813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions. I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.     

含重边星形箭图偏周期预投射代数的希尔伯特级数

设△是一个有限无圈的箭图.引入了由△所决定的偏周期预投射代数,它是一个定义在周期为p的稳定平移箭图Z△/(r^p)上的代数,记为Π_(Q(△,p),J).推广了Eting和Eu的方法并得到无圈的连通星形箭图△所决定的偏周期预投射代数Π_((Q(△,p)),J)的希尔伯特级数的计算公式.     

基于Copula-EVT模型的干旱灾害风险评估

干旱历时和干旱强度是影响干旱灾害风险的主要因素。根据干旱灾害发生的极端过程特点,用极值理论刻画干旱灾害风险两个特征变量的边缘分布,用Archimedes Copula函数捕捉旱灾风险两个特征变量之间的极值相依结构,本文构建的基于Copula-EVT的旱灾风险评估模型较好地反映了旱灾形成的极端过程和影响因子。实证分析以淮河流域蚌埠站为例,证实了ClaytonCopula-EVT模型能较好地拟合蚌埠站干旱灾害风险的历史经验分布,计算得出:蚌埠站干旱历时大于5个月,干旱强度超过7.45的极端干旱灾害风险概率为3%,重现期T_∩(t,d)为32.4年,对干旱历时和干旱强度的条件重现期研究得出干旱强度的取值对干旱灾害风险重现期的影响较大。     

A Regularly Preemptive Model and its Approximations

A regularly preemptive model D,MAP/D ₁,D ₂/1 is studied. Priority customers have constant inter-arrival times and constant service times. On the other hand, ordinary customers' arrivals follow a Markovian Arrival Process (MAP) with constant service times. Although this model can be formulated by using the piecewise Markov process, there remain some difficult problems on numerical calculations. In order to solve these problems, a novel approximation model MAP/MR/1 with Markov renewal services is proposed. These two queueing processes become different due to the existence of idle periods. Thus, a MAP/MR/1 queue with a general boundary condition is introduced. It is a model with the exceptional first service in each busy period. In particular, two special models are studied: one is a warm-up queue and the other is a cool-down queue. It can be proved that the waiting time of ordinary customers for the regular preemption model is stochastically smaller than the waiting time of the former model. On the other hand, it is stochastically larger than the waiting time of the latter model.     

Periodic Solutions of Classical Hamiltonian Systems without Palais-Smale Condition

In this paper, we study the existence of periodic solutions for classical Hamiltonian systems without the Palais-Smale condition. We prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions. Moreover, we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function V.     

HCHO-(DL-苹果酸)-BrO-3-Mn2+-H2SO4体系化学振荡反应动力学研究

研究了HCHO参与下的(DL-苹果酸)-BrO-3-Mn2+-H2SO4化学振荡反应体系的非线性动力学行为,考察了该体系中各反应物的初始浓度范围及主要影响因素. 结果表明,在5.0×10-5～1.0×10-2 mol·L-1范围内, HCHO对振荡反应的诱导期和周期有较大影响,且HCHO浓度的对数lnc(HCHO)与诱导期倒数的对数ln(1/tin)及周期倒数的对数ln(1/tp)均存在线性关系. 诱导期和周期的表观活化参数分别为70.87,55.71 kJ·mol-1. 另外还对HCHO参与下的可能振荡反应机理进行了探讨.     

基于DID模型的ITS对北京交通拥堵改善的研究:评价期的视角

采用双重差分模型,基于智能交通系统(ITS)效用发挥滞后时间为3年,选择2010年和2014年作为评价时点对ITS实施效果和北京交通拥堵之间的相关性进行分析.DID模型计量分析的最终结果显示,ITS效果的发挥明显改善了北京交通拥堵问题.为了验证评价结果的可信度,通过改变评价时点这一参数对评价结果进行稳健性检验,结果仍显示ITS效应发挥对北京交通拥堵改善有很大的促进作用.     

仓库容量有限条件下的随机存贮管理问题的评注

给出2005年全国部分高校研究生数学建模竞赛D题的研究背景,对参赛论文作了简要评注,并提供了一种参考解答.