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Modifications are proposed for an algorithm that estimates the number of vehicles on a section of highway from a time series of flow and velocity measurements. The effect of alternate assumptions concerning the nature of the velocity field between points of measurement is explored. In addition a simplification is proposed to avoid solution by Successive approximation of certain transcendental equations. The net result is an algorithm that is more practical and provides generally superior performance than the original. Various algorithms are evaluated for both single and multilane traffic. [ABSTRACT FROM AUTHOR]

Numerical comparisons of several expressions for the average delay to traffic passing a fixed time traffic signal have been made for a wide range of values of the arrival rate, saturation flow, cycle time, proportion of the cycle effectively green, and variance-to-mean ratio of the number of arrivals per cycle (I-ratio). The values of average delay given by Miller's, Newell's, and Webster's simplified expressions, and by a new modification of the last incorporating the I-ratio are compared with the value given by Webster's full expression. The differences are not usually more than 10 per cent when I = 1, but the importance of the I-ratio is shown by the differences reaching about 50 percent at high degrees of saturation when I = 1.5. The differences between the values of the various expressions are also compared with the effects on the value of Webster's full expression of given errors in the parameters. These effects are found to be large enough to make it difficult to distinguish experimentally between the various expressions when the I -ratio is near to 1 except by extensive measurements. Because of this the choice between expressions is often a matter of convenience of computation, and this choice is briefly discussed. [ABSTRACT FROM AUTHOR]

The various theoretical analyses that have been made of delay to traffic at a fixed time traffic signal are critically reviewed. The more practicably applicable expressions for the average delay per vehicle, especially those derived by Webster, Miller, and Newell, are examined in some detail, and this paper provides an introduction to numerical comparisons to be reported by Hutchinson in the sequel. [ABSTRACT FROM AUTHOR]

Formulas are given for determining the cost and accuracy of a given sampling scheme. Home-based, work-based and roadside surveys are examined. As in any estimation problem, one may optimize either cost or accuracy but not both. For any required accuracy, formulas are given to minimize the survey cost. It is difficult to obtain a measure of accuracy that leads to tractable mathematics; however, a formula is given that will minimize a linear combination of the sample variances of the estimators of the traffic flows. Some approximations are made that lead to simple formulas for determining the sample size. An example for a home-based survey is worked assuming preliminary estimates given by the gravity model. [ABSTRACT FROM AUTHOR]

In a recent paper a traffic assignment model has been constructed in which the cost on a link may depend not only on its load, but also on the loads on other links of the network. In this paper it is shown that this model is also capable of handling the case of several classes of users in the same transportation network each of which has an individual cost function and, at the same time, contributes to its own and other classes' cost functions in an individual way. Typical applications arise not only in street networks where vehicles of different types share the same roads (e.g., trucks and passenger cars) but also in other types of transportation networks (e.g., telephone networks). An algorithm is constructed for finding the system-optimizing flow pattern for such a multiclass-user transportation network. [ABSTRACT FROM AUTHOR]

This paper concerns itself with the kinematic analysis of traffic flow on a signalized one-way artery. Using as mathematical model the continuum flow theory of LIGHTHILL -WHITHAM-RICHAJWS, the flow pattern is carefully investigated under the assumptions of parabolic volume-density diagram and constant flow on the artery. The interesting symmetry existing between fluid and congested regimes is noted and used in proving various results. The delay caused by an interruption of arbitrary regimes is analyzed as a function of space and time. It is shown that an interruption of an arbitrary regime is equivalent to a particular interruption of a corresponding uniform regime: this provides a very simple and general method for delay computation. The delay caused by a periodic interruption (traffic signal) is bounded by and is asymptotically equal to the duration of the red signal; more- over, both the maximum and the average delay at fixed distance from the signalized intersection are increasing functions of the cycle time. It is further shown that the results concerning the delay function apply to all convex volume-density diagrams. [ABSTRACT FROM AUTHOR]

The article discusses the three-dimensional representation of traffic flow. The traffic flow theory, particularly for single-lane traffic, contains many methods for displaying graphically the evolution of various traffic characteristics, such as flow, q, density, k, and velocity, v. Which graphical representation one uses depends upon which characteristics one wishes to analyze. Each method tends to display certain features in a convenient way, and others in a less convenient way. This three-dimensional surface is like a staircase, because cars are discrete, but people usually are not interested in such fine details. In the three-dimensional representation, the relation between these two families of curves is very simple. The x-t curves represent a contour map of the surface n (x, t), i.e., lines of constant height n (x, t) = j. The n-t curves also describe a contour map of the same surface but with the axes rotated so that the "base variables" are n and t. In the three-dimensional representation, these waves are paths of constant direction of the vector A and could be traced quite easily if one locates all points of the surface n (x, t) at which a plane of given orientation can be made tangent to the surface.

The general problem is that of locating a central facility in a network so as to minimize the sum of its distances from the sources of flow to it, each distance being appropriately weighted to reflect the associated flow volume and/or cost. In this paper, simple one-pass solution algorithms are given for two classes of topologically simple networks, namely those which are either acyclic or contain exactly one cycle. The first algorithm is based on a reduction procedure that may also yield useful simplification of problems involving general networks. [ABSTRACT FROM AUTHOR]

In periods of traffic congestion, residual queues at intersections or the blocking of lanes limit the efficiency of synchronized signalization. A computer control scheme is developed that concentrates upon providing real-time, traffic-responsive corrective action for a "critical intersection control (CIC)," defined as a point in the network at which primary driver routes cross or those where congestion has arisen for other reasons, such as in the aftermath of an accident or stall. The approach taken in this article assumes "synchronization" schemes form the background control with fast, real-time, traffic-responsive corrective action being applied to critical congestion situations. The downstream delay in included because it is futile to reduce vehicle delay at an intersection at the cost of accumulating more delay downstream than was saved at the controlled intersection. The inclusion of the downstream delay also maintains a degree of coordination with neighboring intersections. The CIC produced large reductions in total delay for the subnetwork being considered during congestion situations. This is particularly encouraging because the controller delay computations are based upon a number of simplifying assumptions on the traffic flow, whereas the simulation evaluations were conducted with full consideration given to such factors as turning movements, lane changing and headway and speed relations.

The distribution of hourly volumes is described and its form and characteristics are discussed. Theoretical models of the distribution are derived so that an estimate of the distribution may be obtained if only a fraction of the traffic data for the year is known. Depending on the size of this sample different estimation procedures are recommended. The hour has long been the conventional counting interval used for traffic counts over long periods. Other counting intervals are considered to determine if the hour is the best unit. The distribution of daily traffic volumes is found to be best represented by a displaced gamma distribution. [ABSTRACT FROM AUTHOR]

Before we can construct models for multilane traffic flow, we must be able to describe single-lane traffic. This paper considers some of these methods of description including the use of headway and counting distributions. Another method of describing point processes is by means of product densities. These are essentially joint probabilities of two or more vehicles passing a point at different specified times. Product densities have been used in many fields including particle physics, ecology, and road traffic. The idea of using product densities is simple and attractive, but they do have two major disadvantages: (i) except in simple cases, headway distributions are very difficult to derive from product densities, and (ii) product density estimates for different time lags are cor- related, so that tests of hypotheses are not easy to perform. An alternative to product densities is proposed. For want of a better name these are called termination rates. The termination rate after lag τ is the probability of a vehicle passing a point in a small interval of time, divided by the length of the small interval and conditional upon the last vehicle having passed a time τ previously. These are very similar to mortality rates for humans or scrap page rates for commodities with limited life-times. The interrelations between these statistics are quoted but not derived. Various sets of data are used to illustrate the less common statistics. Some analysis is given of a sample of data from the Congress (now Eisenhower) Expressway in Chicago. Variance to mean ratios are used to show that there is a strong correlation between lanes even though the autocorrelations of headways within lanes are very small. Bivariate termination rates have been estimated for each lane. Given a vehicle in one lane, it was found that the expected number of vehicles in a neighboring lane within 2 or 3 sec was enhanced by about 10-15 percent. [ABSTRACT FROM AUTHOR]

A problem that is of interest in transportation planning, as well as other fields, is the effect on some or all of the shortest routes through a network, of increasing the length of a link in the network, or removing a link completely. A method is described for handling this problem, by establishing a subset of links, one of which must be contained in any alternative shortest path. These are referred to as the competing links. It is shown that this method has applications going beyond the particular problem cited. It may be applied to measuring the effects of altering some of the links in a network subjected to congested flow. The results presented for the algorithm compare very favorably with alternative procedures. It is suggested that the algorithm could be used in the development of networks which are, in some sense, optimal. [ABSTRACT FROM AUTHOR]

Investigations of motorist delays at the intersection of a major and minor road have involved variations of one or the other of two merging strategies: (i) MILLER'S[8] model that assumes that a minor-road motorist makes consecutive decisions consistently, and (ii) that of WEISS AND MARADUDIN[7] that assumptions that a different, independent decision is made for each headway. In this paper we show that results for both models may be obtained easily, using the results of queuing theory, if certain reasonable assumptions are made. Simple expressions for the Laplace-Stieltjes transforms and means of the delays are derived in the case of independent major-road headways with a common, general distribution. For exponential headways, a numerical study shows the mean Miller delay to increase with the variation in the merge times, while the mean Weiss-Maradudin delay decreases. To illustrate the application of the expressions obtained, we investigate the reduction in the delay achieved by inserting a traffic island between two streams of major-road traffic. [ABSTRACT FROM AUTHOR]

The article focuses on the report of the fourth international symposium on the theory of traffic flow, that was held in Karlsruhe, Germany, in June, 1968. The symposium was attended by 154 participants from all over the world. Here, authors present brief comment on each paper discussed in the symposium. The paper entitled "A Study of Driver-Aided Car Following," by R. E. Fenton and W. B. Montano described recent experiments with a car controlled by a control, stick with a finger presenting a built-in kinesthetic tactile aid to the driver. The paper entitled "On Some Theoretical Traffic Problems" by J. Gustavsson, dealt with two topics, the asymptotic average speed of a vehicle on a long journey, and numerical examples illustrating the author's model for overtaking on a two-lane road. "An Analysis of Delays to Vehicle Platoons at Traffic Signals," by R.E. Allops examined the problem of the delay to a traffic platoon at an unsaturated traffic signal, the theoretical result being expressed in terms of the arrival pattern and duration of the platoon and the arrival time of the leading vehicle.

In this article, a generalized semi-Poisson model of traffic flow is postulated, its implication in terms of headway distributions outlined and its properties discussed briefly in relation to other models of traffic flow. The new headway distribution and certain other theoretical headway distributions are compared with over 10,000 headways covering a wide range of traffic flows. The parameters for the gamma semi-Poisson model are the most valuable of all because they are values that have not been shown to be inconsistent with the traffic stream when substituted in the appropriate distribution. The two semi-Poisson models are generalizations of some previous headway formulations, but they do not share all their deficiencies. Although they involve statistical difficulties and are somewhat complex mathematically, they can be related at least qualitatively to certain other traffic models. The new model or particularization of it describe headway distributions fairly well and appear to yield some insights into the nature of road traffic.

By a continuous circling technique, 35 mm air photo records were made during 10 peak traffic hours on two sections of an urban freeway, 5 on a four-lane, and S on a three-lane out bound section. Speeds, time headways, distance headways, and response times were analyzed from samples selected from the 1000 ft of projected films to include deceleration waves. Each sample included from 40 to 150 pictures spaced 1 sec apart yielding 20 to 30 individual measurements for a total of 3000 to 4500 in each sample. All measurements were corrected by electronic computer for continuously changing camera angle and slant range (including altitude). Of the samples analyzed, eight from the four-lane section and two from the three-lane section showed typical deceleration waves. Three on the latter showed dissipation of `slowdowns' with increasing speeds and decreasing headways. The four-lane section included speed control signals but the three-lane section did not. On the former, incoming ramp vehicles, visible slowing ahead and signals apparently caused drivers to operate in an uncertainty mode more than on the latter. Weaving vehicles were more numerous on the latter. Longer average time headways were found after deceleration waves. Longer headways related to driver uncertainty are consistent with previous reports and are of importance for traffic flow theory and for freeway design, control, and operation. [ABSTRACT FROM AUTHOR]

Consider a circular central business district of a city with n evenly spaced radial streets and m circular streets. We assume that during the evening rush hour driver origins are all inside the city and exits at the circumference with a joint distribution that depends only upon the relative angle between original and final radii, and the radial coordinate of the origin. Travel time on any directed link is assumed to be a function of the flow along that directed link and the radial coordinate of the link. For a flow of Q vehicles per hour leaving the city, our problem is to find an assignment of drivers to paths such that every driver follows a path of minimum travel time between his origin and exit. This extends some work of Smeed who considers a similar model with no flow dependence of the travel time and a uniform distribution of origins. It is first shown that this circularly symmetric system gives rise to a circularly symmetric optimal flow pattern. This flow pattern can be generated by assigning each driver to a path that uses at most one of the circular streets. Eventually the assignment is expressed explicitly as a function of 2(m - 1) unknown parameters that satisfy a system of equations and/or inequalities. The general solution of these equations were not found, but solutions were obtained for a number of special cases that showed the effect of congestion at the center and the effect of a belt expressway. Differential equations were also obtained for n → ∞ and m → ∞. [ABSTRACT FROM AUTHOR]

The problem of studying the stability of the reciprocal-spacing follow-the-leader model of traffic flow is first discussed and an approximate model is proposed. The mathematical functions that are suitable to describe lead-ear behavior are examined. The stability of a nonlinear car-following model is then defined rigorously, so that it can be studied in the framework of the Liapounov theory. Previous phase plane results show that the reciprocal-spacing model is barely stable, whereas an asymptotically stable model may describe the dynamics more closely. Using an extension of the Weber Ratio, such a model is derived. A phase plane study of the proposed model is presented together with some numerical results. The results corn pare favorably with existing data. Results are presented showing the relative behavior of the actual model with time delay and the proposed model, in which a truncated Taylor series has been used to approximate the time delay. [ABSTRACT FROM AUTHOR]

Delay formulas are derived for vehicles at an isolated intersection at which the vehicle arrivals are supposed generated by a binomial process, the departure rates are assumed constant, and the control strategy is to switch the lights when the favored queue empties. The mean delay is calculated using a discrete analog of the method used by Darroch, Morris, and Newell for the case of random arrivals. Later a probability generating function for delay is developed yielding, in particular, the variance of the delay. [ABSTRACT FROM AUTHOR]

In this paper the authors find the optimal allocation of servicing periods to a facility servicing N incoming traffic streams. In our model it is assumed that stream flows are deterministic, that there is a fixed amount of lime lost, τi , when the server switches attention from the ith to the i + 1st stream and that the objective is to minimize time average delay. [ABSTRACT FROM AUTHOR]

This article presents information on the third biennial conference of the Australian Road Research Board. The conference was held in Sydney from 5-9 September, 1966. It was attended by nearly 500 delegates and was opened by Mr. R.W. Askin, Premier of New South Wales. The conference comprised of 21 technical sessions of which 9 were dedicated to traffic or transport research. In one of the sessions, R.R. Allan presented his study on the binomial model of traffic flow. The time scale in Allan's binomial model for single-lane traffic flow was divided into equal cells and was extended slightly by allowing the times at which vehicles pass a point to have any distribution within the time cells. The model has been tested against a set of data used by D.J. Buckley. After introducing a displacement to give a minimum headway of about 0.45 sec, the three-parameter model fitted the data almost as well as Buckley's four-parameter model. However, an unsatisfactory feature of the model is that the counting distribution always had a variance less than the mean. The second study being presented by Allan in that particular session was a rigorous account of the use and properties of generating functions with particular reference to their application in deriving properties of models of road traffic.

This article focuses on legal aspects associated with various service industries. Railroad operations present a peculiarly complex application of the economic law of increasing returns, for not only is the initial capital outlay in permanent plant very great in comparison with operating costs, but also from one half to two thirds of the expenses of maintenance and operation are relatively constant and impervious to variations in the volume of traffic. Under such conditions it is obvious that up to the capacity of the plant every additional unit of traffic is always worth while, provided only that it affords any return, however small, over and above the actual out-of pocket expense of moving it.

The article reports that more than a century has elapsed since the founding of the first frontier constabularies. Out of the lawlessness of frontier days, such agencies formed the genesis of one of the great police movements in modem times: the establishment of state-wide police departments. But the causes which necessitated the development of the early frontier constabularies pale beside the multiplicity of demands, which compelled the establishment of present day, state police departments. Reformation of older techniques and the adoption of new enforcement methods symbolize the prevailing trends of the last three decades. Older functions have assumed specialty roles in their own right. New functions, such as traffic flow regulations, traffic accident reduction and juvenile delinquency correction, are taking accredited places in the police program. Moreover, as the universality of motor vehicles became increasingly apparent, a new era in transportation unfolded.

Let G be a directed graph such that ever5 edge v of G is associated with a positive integer, called the index of v. Then G is called a network graph if, at every vertex t of G, the sum of the indices of the edges terminating at v is equal to that of the edges incident from v. This paper obtains several theorems giving necessary and sufficient conditions for a directed graph to be a network graph, and applied the results to solving some problems of smoothing traffic flow. [ABSTRACT FROM AUTHOR]

The expected wait of a side-road driver at an unsignalized intersection or merge point is investigated. The method is that of numerical inversion of the Laplace transform of the time-dependent expected wait in a simple queuing model. The effect of various operational factors, such as mix of 'fast' and 'slow' side-road drivers, upon approach to conventional steady-state values is exhibited. The development of waits when the intersection is saturated is also illustrated. An approximation procedure is suggested; numerical evaluation suggests that it will often be adequate. [ABSTRACT FROM AUTHOR]

A commuter living outside a circular city arrives at a point on the circumference and is equally likely to wish to travel to every point of the interior. In the present paper we give the probability distribution for trip length, and the probability distribution for traffic weight at each point, under the assumption of six different routing systems. [ABSTRACT FROM AUTHOR]

The results of a series of experiments carried out to determine the characteristics of single-lane bus flow are reported. Using pairs of buses theoretical 'car-following' models of single-lane traffic flow, which had been shown by previous work to be valid for automobiles, are examined for this type of heavy vehicle and found to provide a good representation of the detailed manner in which one bus follows another. Flow characteristics of buses were also determined by using platoons of up to ten buses. Both of these approaches, which can be termed microscopic and macroscopic, respectively, indicated that a single lane of buses form a stable stream of traffic and have an optimal flow of about 1450 buses/hour at a speed of 33 miles/hour for an expressway type facility. [ABSTRACT FROM AUTHOR]

Some traffic service systems are characterized by service times that increase with the number of patrons undergoing service simultaneously. Two examples, the operation of a road traffic circle and the placement of toll telephone calls, are modelled to explore this property. The traffic circle model may yield information to determine whether a flow control system is justified. The telephone model leads to a doctrine for the rejection of calls during congested operation. Generally, the traffic capacity of such systems can be maximized only if some of the customers are thus rejected or retarded. [ABSTRACT FROM AUTHOR]

Traffic signals can be synchronized so that a car, starting at one end of a street and traveling at preassigned speeds, can go to the other end without stopping for a red light. The portion of a signal cycle for which this is possible is called the bandwidth for that direction. Ordinarily the band-width in each direction is single, i.e., is not split into two or more intervals within a cycle. We solve two problems for this case: (1) Given an arbitrary number of signals along a street, a common signal period, the green and red times for each signal, and specified vehicle speeds in each direction between adjacent signals, synchronize the signals to produce bandwidths that are equal in each direction and as large as possible. (2) Adjust the synchronization to increase one bandwidth to some specified, feasible value and maintain the other as large as is then possible. The method of calculation has been programmed for a digital computer and results have been used to synchronize signals on a street in Cleveland. [ABSTRACT FROM AUTHOR]

A vehicle waiting at an intersection with a major road makes a merging maneuver into the mainstream traffic, thus possibly requiring oncoming traffic to slow down. This paper examines the resulting disturbance that this forced entry may create in the main stream, assumed to be a renewal process. After showing that the disturbance propagation is formally equivalent to the busy period of a related queuing model, explicit results on the length of disturbance period and the number of vehicles affected are obtained for the case of Poisson traffic. It is shown that there is some minimal main-stream headway which should be forced in order to maximize the rate at which entries can be made from the secondary road. Finally, two measures of accident potential for the merging maneuver are discussed. [ABSTRACT FROM AUTHOR]

A linear control algorithm is proposed for the computer operation of a signalized traffic intersection. A theoretical analysis of the algorithm under the assumption of constant vehicular arrival and departure rates shows that the control is stable under unsaturated conditions, and with proper choice of control constants usually gives a rapid convergence to a limit cycle that minimizes the average delay. [ABSTRACT FROM AUTHOR]

A vehicle-actuated traffic light controls two intersecting traffic streams keeping the light green for lane i, i=1 or 2 until any existing queue has been discharged and a headway of duration at least βi is detected in the subsequent arrivals. The object of this paper is to investigate how one should choose the βi so as to minimize the average delay per vehicle at the intersection. A model is considered in which the arrival headways are exponentially distributed random variables, departure headways have any specified distribution, and there is a random lost time for each switch of the traffic light. Formulas are derived for the moments of the cycle times, the average wait per vehicle, and the optimal βi. [ABSTRACT FROM AUTHOR]

The problem of optimizing the control of two oversaturated traffic intersections is solved by using the semi-graphical methods employed in a previous paper for an isolated intersection. As in the case of a single intersection the optimum control involves values of the control variables that lie along edges of the control region, which in this case is defined by the permissible ranges of the green phase splits. An analytical formulation of the method using PONTRYAGIN's control theory is also given. [ABSTRACT FROM AUTHOR]

This paper studies some of the theoretical questions of large opemngs or gaps in a single stream of traffic A gap in the traffic stream is defined as a headway between vehicles greater than or equal to some minimum size -- say x Several authors have studied the probability distribution of the wait that a randomly located observer must endure before he finds a gap This paper, while briefly reviewing the solutions of this well-known problem, is primarily concerned with expressions for (i) the distribution of gap sizes, (ii) the distribution of spacings between vehicles and gaps, (iii) the mean and variance of intervehicle and intergap spacings, (iv) the stationary flow rates of gaps, and (v) the distribution of blocked and unblocked periods It is assumed that the origin of measurements may be located (i) with the passing of a vehicle, (ii) at the beginning of a gap, or (iii) at random It is also assumed that the distribution of intervehicle spacings are independently, but identically, distributed random variables. [ABSTRACT FROM AUTHOR]

The homogeneous time independent solution for a one-car speed distribution function is derived for a Boltzmann-like approach to the statistical theory of traffic flow Numerical results are discussed for a number of different desired speed-distribution functions Among these distribution functions, chosen for mathematical sunplicity are, for example, the exponential, linear, and parabolic Flow versus concentration curves and distribution function versus speed curves are given for several of the models. [ABSTRACT FROM AUTHOR]

In this paper the authors study the queues that build up in a minor stream of traffic waiting to cross or merge with a major stream The criterion for joining or crossing is that a gap between veincles in the major stream be greater than or equal to some constant value Several authors have studied the case where bulk service is provided for the minor stream queue with the appearance of each gap, in this paper the authors emphasize the higher flow rate situations where one car in the minor stream queue is released in a first-come first-serve fashinon with the appearance of a gap It is assumed that the minor stream is Poisson-fed while the intervehicle headways inq the major stream are arbitrary but identically and independently distributed random variables. [ABSTRACT FROM AUTHOR]

The approach to the traffic-flow problem based on an integral differential equation of the Boltzmann type which has been considered by one of us in a recent paper is further developed. The possibility of passing is explicitly introduced into the equation for the velocity distribution function. As in the previous paper, it is shown that at sufficiently high concentration a collective flow process must take place. In order to study more specifically the effects of one car on another, we define reduced n-car distribution functions giving the probability of finding a cluster of n cars all having the same velocity. We derive an equation for the evolution of this distribution function. Study of it yields some information as to the way traffic changes from relatively free flow to completely hindered, 'condensed' flow. [ABSTRACT FROM AUTHOR]

The steady-state flow is examined for a car-following model in which the acceleration at time t of a car attempting to follow a lead car is proportional to the relative velocity at a time t-Δ and in which the sensitivity &lamda; is no longer taken constant as in previous work but is inversely proportional to the car spacing. The characteristics of the steady-state flow for this model are described and compared with experimental data. [ABSTRACT FROM AUTHOR]

The authors have tried to improve the traffic dynamic theory of Professor Pipes and have found the fundamental equation of traffic dynamics for a case m which the velocity of the following vehicle is determined not only by the space between following and lead cars but also by the velocity of the lead car. The safety of the following car with respect to rear end collision when the lead car is in sinusoidal motion is quantified by introducing a safety index. At the same time, the authors describe the stability of the indicial response of the following car, and the stability of the propagation of a sinusoidal disturbance down a line of cars. [ABSTRACT FROM AUTHOR]

The manner in which vehicles follow each other on a highway (without passing) and the propagation disturbances down a line of vehicles has been investigated Experimental data is presented which indicates that the acceleration at time t of a car which is attempting to follow a leader is proportional to the difference in velocity of the two cars at a time (t-Δ) ,Δ being about 1 5 sec and the proportionality constant being about 037 sec-1 It is shown theoretically that the motion of a long line of vehicles becomes unstable when the product of the lag time and the proportionality constant exceeds one-half The experimental data implies that drying is done on the verge of instability A variety of other laws of following is analyzed theoretically [ABSTRACT FROM AUTHOR]

Recently developed techniques for traffic operational changes involving traffic signal control equipment are discussed Present practice is very largely based on intuition and qualitative analysis Quantitative analysis is limited because a general theory of traffic flow has not yet been developed Studies aimed at the eventual formulation of a theory of traffic flow are being conducted at the Road Research Laboratory (British), Brown University, the University of Michigan, and the University of California In combination with the flow theory the greatest promise appears to be in the simulation approach, some aspects of which are discussed [ABSTRACT FROM AUTHOR]

A simple theory of traffic flow is developed by replacing individual vehicles with a continuous 'fluid' density and applying an empirical relation between speed and density Characteristic features of the resulting theory are a simple 'graph-shearing' process for following the development of traffic waves in time and the frequent appearance of shock waves The effect of a traffic signal on traffic streams is studied and found to exhibit a threshold effect wherein the disturbances are minor for light traffic but suddenly build to large values when a critical density is exceeded [ABSTRACT FROM AUTHOR]

The article presents an alternative method for determining the state probabilities in the multiple-channel case with fixed holding times and random arrivals. The author of this article claims that this method is less mathematically sophisticated and possesses practical advantages from the point of view of simplicity and convenience. This method is used to calculate the equilibrium-state probabilities in congestion problems in railroads. The author of this article outlines how the equations for this method is solved, as well as its variables used.