Interoutput times in processor sharing queues with feedback

While properties of the flows in isolated processor sharing queues are well understood, little is known about the flows in networks with processor sharing nodes. This paper analyzes the internal traffic processes in processor sharing queues with instantaneous Bernoulli feedback. The internal traffic does not inherit the insensitivity to the shape of the service requirement distribution from the external traffic. The interoutput time distribution is studied in the single server and infinite server processor sharing queues. For the systems we study, we show that when service requirement distributions with the same means are convexly ordered, so are interoutput time distributions.This work was partially supported by the National Science Foundation under Grant ECS-8501217 and by the Graduate School of the University of Massachusetts under Faculty Research Grant 1-03205.     

The finite capacity multi-server queue with inhomogeneous arrival rate and discrete service time distribution — and its application to continuous service time problems

The finite capacity multi-server queueing model with inhomogeneous arrival rate and discrete service time distribution is developed. The system is formulated as an inhomogeneous Markov chain in discrete time. An algorithm is described to solve the model numerically. A method is then proposed for using this model to approximate the time dependent behaviour of multi-server queues with inhomogeneous arrival rate and continuous service time distribution. Empirical results are presented to show that this approximation will produce results that are accurate enough for most practical purposes.     

An extension of Tanner's results on uncontrolled intersections

A delay formula is developed for the problem, analyzed by Tanner in 1962, where two streams of traffic have conflicting demands at an intersection. The situation is such that the major stream has absolute priority and the minor stream vehicles can only enter the intersection when sufficiently large gaps appear in the major stream. This paper extends Tanner's work by considering a generalised stochastic structure on the arrival streams. The paper also links Tanner's work to other papers of this author where the utilitarian value of this generalised model has been established in a wide range of traffic problems.     

Comparison conjectures about the M/G/s queue

We conjecture that the equilibrium waiting-time distribution in an M/G/s queue increases stochastically when the service-time distribution becomes more variable. We discuss evidence in support of this conjecture and others based partly on light-traffic and heavy-traffic limits. We also establish an insensitivity property for the case of many servers in light traffic.     

A general model of road traffic accidents

A general model that relates road traffic accidents to the number of vehicles involved, and the number of primary causes of such accidents, is presented. The model considers traffic accidents as failures of a road traffic network system to meet social and economic constraints, and therefore as a measure of the unreliability of such a system. The equations apply to accidents in the real time domain as well as to mean values per unit of vehicle exposure time or vehicle distance. They also apply to single vehicles and drivers, groups of drivers and fleets of vehicles, and the entire vehicle and driving population. They can be used for sections of a network or for a whole network.The equations used have a large number of terms, hence bias errors are common in road accident investigations.     

基于模糊理论的交通安全评价方法的研究

道路交通安全系统的内部结构极为复杂,影响因素众多,各因素都具有模糊性.在综合研究分析国内外道路交通安全评价方法的基础上,对以往发生的道路交通事故资料进行分析,利用模糊评价理论,选取合理评价指标,建立了基于模糊的道路交通安全评价模型,对道路交通的安全性进行合理评价.     

An optimal mechanism charging for priority in a queue

We derive a revenue-maximizing scheme that charges customers who are homogeneous with respect to their waiting cost parameter, for a random fee in order to become premium customers. This scheme incentivizes all customers to purchase priority, each at his/her drawn price. This is repeated for the case where customers are heterogeneous. The mechanisms are based on the fact that once some customers get priority, its value of the other gets even higher.     

Delay performance in stochastic processing networks with priority service

We evaluate the delay performance of an open multi-class stochastic processing network of multi-server resources with preemptive-resume priority service. We show that the stationary distribution of aggregate queue lengths has product form. For each service class we derive explicit expressions for the following stationary performance measures: The mean and, under feedforward routing, the Laplace transform of the delay distribution at each resource. We show that these measures are the same as if the resources were operating in isolation.     

A finite capacity multi-queueing system with priorities and with repeated server vacations

In this paper, we study an M/G/1 multi-queueing system consisting ofM finite capacity queues, at which customers arrive according to independent Poisson processes. The customers require service times according to a queue-dependent general distribution. Each queue has a different priority. The queues are attended by a single server according to their priority and are served in a non-preemptive way. If there are no customers present, the server takes repeated vacations. The length of each vacation is a random variable with a general distribution function. We derive steady state formulas for the queue length distribution and the Laplace transform of the queueing time distribution for each queue.     

Developments in operational research: R.W. Eglese and G.K. Rand (eds.) Pergamon, Oxford, 1984, vii + 110 pages, $20.00

A practical method of calculating the distribution of the number of customers in the single server queueing system with inhomogeneous arrival rate and discrete service time distribution is proposed. The system is formulated as an inhomogeneous Markov chain in discrete time, leading to recurrence relations for the state probabilities. The recurrence relations are then solved numerically. Various measures of performance, such as mean and variance of the number of customers in the system and virtual waiting time can be obtained from these results. Examples are presented to demonstrate the scope of the method, including time-dependent behaviour of homogeneous queues; cyclic behaviour of queues with cyclic arrival rates; and a previously published study of an airport runway in which the author had to resort to crude interpolation to obtain results. The method can be further extended to provide a reasonably accurate approximation for some systems with continuous distributions of service times.     

道路行车系统中人的可靠性研究

随着人-车-路-环境系统复杂性的增加和交通事故数量的上升,新型交通设备对其使用者的素质与适应性提出了全面的要求,要提高道路行车系统的整体可靠性,必须对人的可靠性进行分析研究.从人的生理、心理、教育训练、驾车技能等因素对驾驶员可靠性的相关影响进行了探讨.分析了影响驾驶员的可靠性因素,研究了驾驶员的可靠性模型,提出建立有助于驾驶员可靠性分析研究的综合数据库,最后从理论上分析总结了提高驾驶员可靠性的措施从而得出提高道路行车安全的有效途径.     

基于BP神经网络的道路交通事故预测

道路交通事故预测是交通研究的一个重要课题.以我国交通安全状况为研究对象,依据我国道路交通事故的特点,利用神经网络具有自学习、自组织、自适应能力特性,运用神经网络的方法及我国多个年度道路交通事故统计数据,建立了道路交通事故神经网络宏观预测模型,预测精度符合道路交通事故预测的要求.     

基于可靠性视角的交通堵塞模型

本文从可靠性角度研究了交通堵塞模型.首先,通过合理的假设,建立了道路系统的可靠性模型.然后,利用补充变量方法及拉普拉斯变换技术,得到了道路系统的畅通率、稳态堵塞频度和首次堵塞前系统的平均畅通时间等道路系统评价指标.     

基于DEA模型测算交通信息化对道路畅通性改善的贡献研究

交通信息化建设和应用在改善城市道路问题等方面的社会效益受到广泛关注,但实际中较少对其贡献价值进行研究.通过应用DEA方法,结合回归分析,从投入产出角度选取指标建立交通信息化对道路畅通性的贡献测算模型,并以北京市为例进行实证分析.研究结果显示,北京市2005-2014年交通信息化对道路畅通性改善的年平均贡献值为17.47%.研究结论为交通信息化绩效的评估提供理论支撑,辅助交通信息化建设和应用的规划制定.     

考虑信息熵模型的道路交通安全态势模型

分析道路交通事故统计中的交通事故数、死亡人数和受伤人数,并且将这三种统计数据和某地区的机动车辆数和机动车驾驶人数相结合,分别得到万车交通事故数和万人死亡人数和万人受伤人数,建立信息熵模型(information entropy model)对以上数据进行分析研究,从而得出评价交通安全程度的指标.这种方法突破了以往仅停留在万车死亡人数的指标上,且以往的研究方法还需采用专家评价法或德尔菲等定性评价方法,此评价方法对道路交通安全的分析更客观.最后以北京和天津近三年的交通事故统计数据为案例进行分析,研究结果表明:2012年至2014年间北京道路交通安全评价指标主要以交通事故起数认定所在年的道路交通安全状况,天津道路交通安全评价指标主以交通事故造成的受伤人数认定所在年的道路交通安全状况,且北京三个指标的G_i均高于天津,因此北京交通安全水平要低于天津.     

Reserve capacity of signal-controlled road network

For a signal control road network subject to equilibrium flows, the maximum possible increase in travel demands is considered in this paper. Using the concept of reserve capacity of signal-controlled junctions, the problem of finding the maximum increase in traffic demands can be formulated as a mathematical program with equilibrium constraints (MPEC). In this paper, we present a projected gradient approach to obtain the maximum increase in travel demands based on the TRANSYT traffic model. Numerical computations are made on a grid network where good results are obtained.     

A dynamic programming approach for the airport capacity allocation problem

In most of the optimization models developed to manage airportsoperations, arrivals and departures capacities are treated asindependent variables: that is the number of flights allowedto take off does not affect the number of landings in any unitof time, and vice versa. This assumption is seldom verifiedin most of the congested airports, where many interactions betweenarrivals and departures take place. In this paper, we face the problem of finding the optimal trade-offbetween the number of arrivals and departures in order to reducea delay function of all the flights, using a more realisticrepresentation of the airport capacity, i.e. the capacity envelope. Under the assumption of piecewise linear convex capacity envelopesand of the exact interpolation of all the Pareto-optimal operationalpoints, we show that the problem can be formulated as a linearprogramming model. For general airport capacity envelopes, wepropose a dynamic programming formulation with a correspondingbackward solution algorithm, which is robust, easy to implementand has a linear computational complexity. The algorithm performancesare evaluated on different realistic scenarios, and the optimalsolutions are compared with those computed by a greedy algorithm,which can be seen as an approximation of the current decisionprocedures. The percentage deviation of the cost of these twosolutions ranges from 3.98 to 35.64%.     

Analysis and design of rate-based congestion control of high speed networks,I: stochastic fluid models,access regulation

The paper gives models and analytic techniques for addressing critical issues of the Broadband Integrated Services Digital Network which will use the Asynchronous Transfer Mode. The traffic is expected to be highly bursty and variable at the source and consequently a key issue is admission control. We study a 4-parameter device called a regulator which acts as a policing device as well as a traffic shaper. The device is a generalized leaky bucket with a data buffer, a token buffer supplied by a constant-rate token stream, and a peak rate controller; the outputs of the device are streams of priority and marked cells. The composite system comprising of the source and the regulator is represented in a stochastic fluid model since fluid flow has been found to have properties well matched to the ATM environment, and the Markov Modulated Fluid Source allows bursty characteristics to be accurately modelled. A complete procedure based on spectral expansions for calculating the system's stationary state distribution is given. It is shown that with proper design the regulator effectively controls a three-way trade-off between throughput, delay and burstiness. Numerical results reveal that performance is sensitive to source characteristics such as the squared coefficient of variation of burst and silent periods. The second part of the paper characterizes the output of the regulator. The distributions of the time periods spent in the various states by the output process are calculated exactly. From this an approximate Markovian characterization is obtained. The output streams of priority and marked cells are coupled to capture their correlations. For the simple case of two-state on-off sources, the approximate Markovian characterization of the regulator's output rate processes is explicitly given and it is distinguished by the property that all moments are identical to those of the actual processes. With this characterization an original goal of analyzing a composite system of access regulation and statistical multiplexing is separated, decomposed and thereby made tractable.