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As part of a continuing general investigation into the fundamental relations of traffic flow, the sampling properties of the variables speed, flow, and concentration of an ideal traffic stream, measured in rectangular space/time domains according to EDIE'S definitions, are evaluated and discussed. Although the speeds of drivers are independently distributed and maintained constant regardless of the proximity of other vehicles, it is shown that the speed and flow and the speed and concentration are both marginally correlated. Analytical expressions for the serial and cross-correlations of the flow and concentration in consecutive samples are given, and it is shown that the flow and concentration are distributed with both discrete and continuous probability components, with variance/mean ratios less than one. [ABSTRACT FROM AUTHOR]

Simultaneous recursive estimators for aggregate variables, section density, and mean speed, are derived. The estimators are simple and easily suitable for digital implementation. Performances of the estimators are evaluated utilizing the real traffic data obtained over a three-quarter mile section of the Long Island Expressway, New York, and data obtained from digital simulation of freeway traffic. [ABSTRACT FROM AUTHOR]

Presents a letter about the fifth International Symposium on the "Theory of Traffic Flow and Transportation."

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]

A transportation network is considered. The traffic demands associated with pairs of nodes and the traveling cost functions associated with the links are assumed given. An extended traffic assignment model where the traveling cost on a link becomes a function of the en- tire flow pattern in the network is introduced. The model appears particularly suitable for application to networks containing two-way streets, in view of its capability of taking into account delays to travelers of one lane caused by traffic on the opposite lane. It is also suitable for application to urban transportation networks, where the travel time on a link depends crucially on the delays occurring at the intersections. This in turn depends on the traffic volumes on the intersecting links. The concepts of system-optimizing and user-optitimizing traffic patterns are studied. Moreover, an algorithm for the construction of the above patterns is presented and applied in an example. [ABSTRACT FROM AUTHOR]

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]

A method for estimating costs and benefits to commuters, over a period of time, is developed in this paper. The method will account for the variation of traffic volumes over the period of time considered. The cost structure of a transport mode is taken as a function of the volume of traffic on that mode. The distribution of traffic volumes is then used to measure the costs and benefits to the user and the state over a year. Commuters are divided into different social classes according to the value they place on the attributes of the different transport modes. Next the method is used to evaluate different road pricing schemes. Finally the road system is examined both as a public utility and as a public enterprise. [ABSTRACT FROM AUTHOR]

A mathematical method is developed for minimizing the number of railcars that is needed for the peak operations of a suburban railway system by cutting railcars back from stations along the lines in an optimum way. A secondary objective is the minimization of the total driver time. A mathematical proof is given of the fact that the total number of railcars required is equal to the maximum number of railcars simultaneously in operation; and this theorem leads to the formulation of the minimization problem as a set of linear zero-one-programs. A case study demonstrates the practical usefulness of the method by applying it to an existing railway system. [ABSTRACT FROM AUTHOR]

The longitudinal vehicle control problem associated with any automated transportation scheme is discussed. The two fundamental aspects of the problem are the logical aspect and the control aspect. The logical aspect of the problem concerns the decision of where vehicles should be at a future time, based on present system conditions, so that the level of service delivered by the system is good. The control aspect is concerned with how to control vehicles to attain and maintain their desired positions while giving a comfortable ride, not taking too long, not exceeding car capabilities, and maintaining safety. Previous work dealing with both the logical and control aspects of the longitudinal vehicle control problem is briefly reviewed. One approach to handling the logical aspects of the merging problem in automated systems assumes that vehicles occupy positions on a guideway within hypothetical 'cells' that move at a constant velocity. This approach simplifies the logical aspect of the longitudinal control problem. The problem of controlling vehicles to attain and maintain an assigned cell on a guideway is modeled in the paper as a linear state regulator optimal control problem. The resulting vehicle control scheme requires less information feedback than alternative schemes, and exhibits good vehicle response characteristics. Alternative control strategies that lead to optimal control problems other than the linear state regulator are discussed, and the relative advantages of the scheme presented in the paper are pointed out. [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]

The flow of vehicles down one lane of a straight, signalized urban street with fixed cycle traffic lights at 500 ft intervals was simulated by means of a Fortran IV computer program. A car-following model and a simple model of lead-driver behavior were used to model driver responses. Flow and speed measurements were made for 'levels of congestion' in which, on average, 5, 10, 15, and 20 cars were queued at each traffic light; 10 ft cars, 20 ft cars, and mixtures of these two lengths were simulated. With 15 cars queued at each light a 70 per cent increase in flow can be obtained by the substitution of 10 ft cars for 20 ft cars. Average speed increases by about 57 per cent, from 3.5 ft/sec to 5.5 ft/sec. That the number of vehicles queued per light remains constant has been assumed. Complete results of our simulation are presented in Table III and Figs. 2, 3, and 4. Validation of the simulation model was provided by traffic flow counts and speed measurements on Walnut Street in downtown Philadelphia; correspondence between model and reality was close. [ABSTRACT FROM AUTHOR]

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]

The methods of analysis used in part I are extended to the analysis of a vehicle-actuated signal at the intersection of two two-way streets (four-way intersection) at which there is no turning traffic. The main conclusion is that the high efficiency of a vehicle-actuated signal as compared with a fixed-cycle signal for one-way streets as discussed in part I, does not necessarily extend to the case of two-way streets. In particular, if the flows in opposite direction on the two-way street are nearly equal and the intersection is nearly saturated, then it is very inefficient (even worse than a fixed-cycle) for a vehicle-actuated signal to follow a policy of holding a signal green until the last of the two discharging queues has vanished (it is even worse to switch when only one queue has vanished). In all cases, the competition between incompatible desirable policies for the two opposing traffic streams leads to compromise strategies that give considerably higher delays on all approaches than occurs on one-way streets. [ABSTRACT FROM AUTHOR]

A wide range of signal switching policies may be adopted for control of traffic flow between a pair of intersections. One of the most import,ant traffic situations is that in which rush-hour commuter traffic travels towards or away from a city center along radial roads. Under these circumstances opposing and tangential flow may be light. Earlier papers have shown that a modified form of the Dunne-Potts switching policy might be applied to pairs of intersections carrying commuter flow. Efficient and flexible operation of the system under a wide variety of flow conditions, and with the minimum of computer surveillance, was demonstrated. The present paper reports the results of further simulation experiments and discussed tentative solutions of some of the practical problems associated with the proposed scheme. [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]

In this article the author focuses on the problem of estimating the distribution of the minimum gap that a driver will accept before at tempting to cross a priority road. Drivers from a side-street arrive at a one-way main road where they are required to stop before attempting to enter or cross it. The time gaps between vehicles on the main road are independent, identically distributed random variables. Here authors obtain relation between the distributions and moments of certain observable random variables and the distribution, and show how these relations may be used to obtain statistics for estimating the parameters of interest. They provide two different procedures, depending on whether the distribution of the time gaps between successive vehicles on the priority road is known or unknown. Author also presents the information related to the sources of data used in the numerical studies by them. The drivers involved in the study were all waiting for gaps to turn right on a 6-lane divided road.

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]

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.

Hillier has described a method of selecting offsets to minimize delay in certain networks controlled by fixed-time signals. In this paper an attempt is made to extend the method by relaxing somewhat the restriction on the form of the network. The problem is expressed in terms of the theory of graphs, and an iterative process is developed for finding a set of offsets that minimizes delay over the whole network. At each stage, the part of the network already covered is extended by adding one or more links, and for the method to be viable these links must be chosen so that a certain set of intersections remains small. A method of selection of links that minimizes this set of intersections at each stage is developed. The selection of links and calculation of offsets have been programmed in Fortran. Having found one delay-minimizing set of offsets, some others that give the same total delay can be found if they exist. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for the behavior of right- turning (left-hand drive is the convention observed) vehicles at an uncontrolled intersection. The model is a development of the one proposed for this situation in a previous paper by the author. It relates to the intersection of a two-lane major road with a minor road at which vehicles on the major road have absolute priority. Completely random traffic is postulated on the major road, and congestion is caused by drivers of vehicles on the major road who wish to turn right and are unable to do so immediately because of oncoming traffic. It is not possible for following vehicles to filler to the left of a delayed vehicle. The delay distribution for vehicles in each lane of the major road is determined for the case of stochastically stationary behavior, and sonic numerical results for the mean and variance of this distribution are given. The gap acceptance mechanism used in this paper is similar to the one proposed by GAVER. Further references for this paper are discussed in the Introduction to the author's previous paper. [ABSTRACT FROM AUTHOR]

A probabilistic model to determine a variety of steady-state quantities describing the behavior of traffic on two-lane, four-lane, and six-lane highways is proposed. Faster cars form queues behind slower cars while waiting for an opportunity to pass; the occurrence of passing opportunities is governed by the characteristics of the traffic in adjacent lanes. The effects of entrances and exits, and of hills and curves on the traffic stream are also considered. Computational procedures are outlined and several sample calculations are made. [ABSTRACT FROM AUTHOR]

Examines the significant aspects of railroad traffic to geography. Level of traffic density on railroads; Pattern of rail traffic movements as revealed by local variations in density and directions of flow; Tempo of human activities in the areas served by the railway.

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]

In this paper a mathematical treatment of two-way traffic on a single line of railway is given. The traffic capacity, the cycle times of the trains, and the number of trains needed to accomplish the transports are studied for certain regular traffic systems. [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]

This paper proposes an algorithm for making a sensitivity analysis on a flow network, specifically, the problem of removing n arcs in a network such that the reduction in the maximum flow between an origin and destination node is maximized. Such an algorithm might be helpful in determining how sensitive a transportation system is to having its roads closed for repairs. [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]

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]

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 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 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]

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]