Distributions for Gaps in Road Traffic

The importance of both counting and gap distributions in roadtraffic flow has been recognized for some years. One reasonfor their importance is that they are linked to three importantaspects of road traffic viz. flow, concentration and capacity.The flow-rate is the reciprocal of the mean time-gap betweenvehicles and concentration is the reciprocal of the mean distance-gapbetween vehicles. Capacity is, in one sense or another, themaximum flow, and is thus related to the minimum time-gap betweenvehicles. Another reason for the importance of these distributionsis that the distribution of vehicles on a road can be consideredas a succession of moving gaps and dealt with on that basis. The displaced exponential distribution has been known for sometime to be a reasonably good model for low-medium flow-ratesof up to about 800 vehicles per hour (v/h) in one lane, butit breaks down for higher flows. A number of alternatives tothe displaced exponential are considered in this paper. A substantial amount of data, collected in New Zealand, hasbeen used in fitting the distributions. There is no real evidenceto show that the displaced exponential can be improved uponmuch as a model, although overall the use of a mixed exponentialimproves the fit somewhat. However, all the alternative distributionsare easy to sample from, and can be used in simulation studies.     

T-SPH排队队长平稳分布的尾部分析

在复杂随机模型的研究中,经常会出现水平和位相都是无限的拟生灭过程,对这类过程,平稳分布的计算仍然是一个未很好解决的难题.然而对一类比较特殊三对角无限位相拟生灭过程,简记为T-QBD过程,文献[1]指出,在一定条件下可以估计其平稳分布的尾部特征.本文对文献[1]1中提出的方法在某一环节上作了改进,使之更适合于实际计算,并用此方法分析了两个具有实际应用背景的排队模型,即T-SPH/M/1排队和M/T-SPH/1排队,分析结果表明,在一定条件下,这两类排队系统的队长分布的尾部都具有几何衰减的特性.     

Tail Asymptotics for HOL Priority Queues Handling a Large Number of Independent Stationary Sources

In this paper we study the asymptotics of the tail of the buffer occupancy distribution in buffers accessed by a large number of stationary independent sources and which are served according to a strict HOL priority rule. As in the case of single buffers, the results are valid for a very general class of sources which include long-range dependent sources with bounded instantaneous rates. We first consider the case of two buffers with one of them having strict priority over the other and we obtain asymptotic upper bound for the buffer tail probability for lower priority buffer. We discuss the conditions to have asymptotic equivalents. The asymptotics are studied in terms of a scaling parameter which reflects the server speed, buffer level and the number of sources in such a way that the ratios remain constant. The results are then generalized to the case of M buffers which leads to the source pooling idea. We conclude with numerical validation of our formulae against simulations which show that the asymptotic bounds are tight. We also show that the commonly suggested reduced service rate approximation can give extremely low estimates.     

Delay-minimizing Settings for Fixed-time Traffic Signals at a Single Road Junction

The operation of traffic signals at road junctions is controlledwholly or partly by preset schedules. Expressions for the delayat fixed-time traffic signals have previously been used in severalmethods of calculating signal settings. These methods give satisfactoryresults in many cases, but have a number of drawbacks whichare largely overcome in a new method described in this paper.This method finds settings that minimize the estimated averagedelay per unit time to all traffic passing through the roadjunction, subject to certain constraints imposed by the trafficengineer. It first determines whether there are any settingsthat both satisfy these constraints and allow all the approachingtraffic to pass through the junction in the long run. If thereare, it is shown that delay-minimizing settings exist and areessentially unique, and an iterative procedure is given whichcan be shown to converge to the delay-minimizing settings. Acomputer program for carrying out the procedure is briefly described,and a few illustrative results are given.     

Transient and First Passage Time Distributions of First- and Second-order Multi-regime Markov Fluid Queues via ME-fication

We propose a numerical method to obtain the transient and first passage time distributions of first- and second-order Multi-Regime Markov Fluid Queues (MRMFQ). The method relies on the observation that these transient measures can be computed via the stationary analysis of an auxiliary MRMFQ. This auxiliary MRMFQ is constructed from the original one, using sample path arguments, and has a larger cardinality stemming from the need to keep track of time. The conventional method to approximately model the deterministic time horizon is Erlangization. As an alternative, we propose the so-called ME-fication technique, in which a Concentrated Matrix Exponential (CME) distribution replaces the Erlang distribution for approximating deterministic time horizons. ME-fication results in much lower state-space dimensionalities for the auxiliary MRMFQ than would be with Erlangization. Numerical results are presented to validate the effectiveness of ME-fication along with the proposed numerical method.

     

城市道路交通环境质量的模糊可拓评价方法

分析了影响城市道路环境质量的各种因素,并将模糊数学和可拓学结合,提出了城市道路环境质量的模糊可拓评价方法,建立了相应的多指标的环境质量评价模型.     

Description and Shortcomings of Some Urban Road Traffic Models

In the sense of this paper "traffic models" are formulae for predicting the number of journeys made between one place and another, usually between one part of a town and another. Some models are described and are applied to hypothetical examples. The models are divided into two main classes, "gravity models" and "opportunity models". Gravity models are based on the assumption that the amount of traffic between two areas varies with the size or importance of the areas and with the distance between them in a manner analogous to the inverse square law of gravitation. The idea of opportunity models arises from the supposition that travellers consider possible destinations or opportunities in order of distance from their origin, accepting or rejecting them in a certain proportion. It is inferred that the basic form of gravity model tends to overestimate traffic in high-density areas, whereas the opportunity model has the opposite tendency. However, either type of formula can be adapted so that these defects are overcome. Much of the section on gravity models relates to the work of J. C. Tanner of the Road Research Laboratory.     

道路维修施工路段交通分流信控优化模型

针对道路维修施工期间常采用的部分路面封闭施工且利用辅路进行分流的情形,探讨了交通分流信控优化模型。借助交通流波动理论,分析了施工路段及其前后车流拥挤排队及疏散特征和规律,分析了对车流进行控制需满足的约束,并分析了车流的延误计算公式。以总的车辆行驶时间最小化目标,原路径及分流路径的绿时分配及信号周期为优化参数,考虑交通分流控制的各种约束,建立了道路施工路段交通分流信控优化模型。分析了该模型属于非凸问题,因此提出了一种近似求解最优解的办法。通过一个示例对模型和求解算法进行了验证,并对一些规律性结果进行了分析。     

城市道路交通发展规划的数学模型

指出城市道路交通拥堵的原因 .确立城市交通中诸关键因素之间相互关系的数学模型     

The Decay Parameter and Invariant Measures for Markovian Bulk-Arrival Queues with Control at Idle Time

We consider properties regarding decay parameter and invariant measures for unstable Markovian bulk-arrival Queues with control at idle time. The exact value of the decay parameter, denoted by λ _Z , is firstly revealed. An elegant criterion regarding λ _Z -recurrence and λ _Z -positive is obtained. The corresponding subinvariant and invariant measures are considered and the structure of all the subinvariant and invariant measures are presented.     

Distributional Form of Little's Law for FIFO Queues with Multiple Markovian Arrival Streams and Its Application to Queues with Vacations

This paper considers stationary queues with multiple arrival streams governed by an irreducible Markov chain. In a very general setting, we first show an invariance relationship between the time-average joint queue length distribution and the customer-average joint queue length distribution at departures. Based on this invariance relationship, we provide a distributional form of Little's law for FIFO queues with simple arrivals (i.e., the superposed arrival process has the orderliness property). Note that this law relates the time-average joint queue length distribution with the stationary sojourn time distributions of customers from respective arrival streams. As an application of the law, we consider two variants of FIFO queues with vacations, where the service time distribution of customers from each arrival stream is assumed to be general and service time distributions of customers may be different for different arrival streams. For each queue, the stationary waiting time distribution of customers from each arrival stream is first examined, and then applying the Little's law, we obtain an equation which the probability generating function of the joint queue length distribution satisfies. Further, based on this equation, we provide a way to construct a numerically feasible recursion to compute the joint queue length distribution.     

北京市道路交通事故致死率的分析与预测

根据北京市道路交通事故的统计资料,以交通事故致死率为指标,对北京市目前道路交通安全情况进行评价.并基于灰色预测理论,建立北京市道路交通事故死亡人数的灰色GM(1,1)预测模型.预测结果显示,北京市未来几年道路交通事故死亡人数虽处于下降趋势,但死亡人数仍在千人左右,平均每起事故死亡人数仍处于上升趋势,道路交通事故致死率仍然偏高.道路交通管理部门应加大惩治道路交通违法行为力度,以控制道路交通事故的严重后果.     

高负荷下非强占优先排队网络系统中队长过程的扩散逼近

本文是在高负荷下非强占优先排除网络系统中给出了队长过程的扩散逼近 .证明了其队长过程的扩散极限是半鞅反射的布朗运动 .     

加权马尔可夫模型在道路交通受伤人数预测中的应用

为提高交通事故预测的可靠性,首先应用有序聚类的方法建立交通受伤人数的分级标准;然后针对事故受伤人数为相依随机变量的特点,采取以规范化的各阶自相关系数为权重,用加权的马尔可夫链模型来预测未来交通事故受伤人数的升降变化状况;最后以北京市1970-2010年共41年的事故受伤人数为例对该方法进行了具体应用,取得了较为满意的结果,为交通事故受伤人数的预测分析提供了新的途径.     

关于圆形和方形城市工作区道路交通面积的解析与比较

对于城市规划来讲，事先预测其工作区内所需道路面积，以尽量避免实际交通网络中发生拥挤阻塞，具有重要意义，在本文，我们通过考虑一个城市通勤高峰时期的车辆交通情况，并通过利用走行中的车辆占用道路面积这一概念，基于一个相对现实的模型，从理论上对圆形方形城市工作区推导了所需的道路面积，并将两者加以比较，以发现与其交通网络结构相关的工作区的相对有效形状。     

安徽省道路交通事故影响因素分析及其预测研究

以安徽省道路交通安全状况为研究对象,探讨分析安徽省道路交通事故致因要素及未来发展趋势.首先利用灰色关联度法分析道路交通事故数与相关致因要素之间的关联度,得出人口因素是主导因素,其次为环境因素,包括社会经济环境和道路环境.在此基础上,运用灰色GM(1,1)及其残差改进模型,对事故起数及其主导因素进行预测研究,结果证明灰色预测可以很好地预测人口发展趋势,但对事故起数这样波动较大的数据更适宜残差修正模型.     

北京市道路交通事故灰色预测模型的构建与应用

利用灰色预测理论,根据北京市1999～2006年道路交通事故的统计资料,建立了北京市道路交通事故发生次数的灰色GM(1,1)预测模型,并根据实际数据的特点,对所建立的模型进行了改进.经证实,改进后的GM(1,1)模型预测精度高,预测结果与实际相符.GM(1,1)模型的预测结果可为北京市道路交通管理部门制定预防交通事故的措施提供重要的数据支持和理论依据,这对加强北京市的道路交通管理、改善北京市的道路交通安全状况将具有一定的现实意义.     

Korn's Inequalities for Junctions of Spatial Bodies and Thin Rods

The dependence on the small parameter ε of constants in Korn's inequalities is investigated for domains which are obtained by joining thin rods to an elastic spatial body. The external ends of the rods are clamped. The asymptotic accuracy of the derived inequalities is achieved by certain distribution of weight multipliers and powers of ε in L₂-norms of displacements and their derivatives while the introduced weights differ for longitudinal and transversal components of displacement fields in the rods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.     

Diagonalization of Weyl Transforms and Heat Equations for Time-Dependent Hermite Operators

Weyl transforms with radial symbols are diagonalized in terms of explicit formulas for the eigenvalues with respect to the Hermite basis for L²(\mathbbR){L^2(\mathbb{R})} . The exact solutions of heat equations governed by time-dependent Hermite operators are analyzed in detail. Formulas for the heat kernels of these time-dependent Hermite operators are derived.     

基于新老司机道路选择行为的交通流均衡研究

针对新上路司机数量的爆发式增长带来的交通流均衡变化问题,本文在对司机进行分类和道路选择行为分析的基础上,应用决策树方法构建了基于新老司机道路选择行为的交通流均衡模型,并用实际案例研究了主要参数的敏感性。研究发现:路况通过联合系统车流量的分配情况、车速预期和司机学习过程等因素共同对司机比例产生影响;当某一条道路达到均衡时,车流量对司机比例的敏感程度受到路况差异的影响;司机在驾驶经验、对道路的熟悉程度以及学习能力等方面存在差异,但这种差异仅存在于对交通信息的感知方面。该研究有助于加深对城市交通流变化规律的认识和理解,对于发展出有效的交通管制措施有积极的理论价值和现实意义。