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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]

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 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]

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]

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]

In a recent paper, Ashton (1971) has proposed two methods for tho analysis of gap-acceptance data. It is not clear what parameters of driver behaviour and of the distribution of offered saps are being estimated in these two methods. A model is proposed for the gap-acceptance behaviour of drivers. Using this model it is shown that tho asymptotic values of Ashton's estimators are functions of both the parameters describing driver behaviour and those describing the stream of offered gaps. Consequently it is not valid to use these methods to compare driver behaviour for different traffic flows. References are given to recent work on alternative methods of gap-acceptance analysis. [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 presents a generalized analysis of the effects of on-ramp time varying flow on unidirectional n-lane freeways. The analysis incorporates the speed-density relations for every lane, which are then used to set up separate continuity equations for every lane and are coupled by some reasonable lane-changing hypotheses. The paper assumes the same wave velocities (uniform freeway) for the perturbed flow in each lane of a freeway. Using the generalized n-lane analysis, the paper then predicts the relative propagation of density perturbations in time and space in different lanes of a two-lane, three-lane, and four-lane freeway. The corresponding relaxation distances from the on-ramp, where the initial perturbation had started, have been defined and compared for the two-lane, three-lane, and four-lane freeway. The above studies have then incorporated the effects of con- trolled ramp flow by suitable mathematical expressions that simulate controlled ramp flow. [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]

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]

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.

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]

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]

Presents commentaries on issues related to operations research. Trends in organizations and size of operations research groups; Applications of multivariate statistical techniques to bombing problems; Symposium on the theory of traffic flow.

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]

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]

Car-following and continuum theories have been shown by other investigators to describe a number of aspects of the complex phenomenon of vehicular traffic flow in both quantitative and qualitative terms It is the purpose of this paper to suggest a variation in these theories in an effort to make them more accurate for traffic densities less than optimum The theory as modified for noncongested traffic may help to describe quantitatively the sudden change of state occurring in a traffic stream going from a relatively free-flowing condition to a crawling stop-and-go condition and back again. [ABSTRACT FROM AUTHOR]

This section presents abstracts of research papers on economics which were published as of June 1967. The Economics of Technological Change and the Demise of the Sharecropper summarizes a dynamic study of production, technological change, resource utilization, and labor demand in agriculture. It describes in nontechnical terms the recursive programming model that was developed for the Mississippi Delta farm economy, and summarizes the tests of the model. In An Analytical Technique for Estimating Weather Indexes From Meteorological Measurements, a model is developed to estimate crop yield response to weather and time trend. Weather is defined to be those meteorological variables directly affecting crop yields and direct measures of meteorological variables are included in the model. In the paper A Comparative Evaluation of Gravity and Systems Theory Models for Statewide Recreational Traffic Flows,the attendance pattern of campers at Michigan State Parks for the year 1964 was modelled in two ways: by a newly-developed systems theory model using concepts of systems engineering modelling theory, and by gravity model techniques. In Discontinuation of Holdings As Independent Units, the value of farm land parcelled out has been investigated. This investigation has been carried out on the farms which were parcelled out into built-up areas and industrial sites in the counties of Copenhagen, Frederiksborg, Odense, Vejle, Arhus and Alborg.

The automatic control of a string of high-speed, densely-packed vehicles is studied in a unified approach. Various input structures for the control schemes and their stability are studied and compared. The optimal decentralized regulation theory developed in a previous paper is applied to seek the best feedback control gains for various input structures. Value of information is defined to evaluate the relative merit of these inputs. The results can be easily applied for on-board computer designs in developing new transportation technology such as `personal rapid transit' systems. [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]

The article presents an analytical derivation of mean speed in the "Boltzmann-Like" traffic theory. In order to determine the speed distribution, it is, therefore, necessary to first determine the mean speed of the distribution. In this paper, the mean speed of the steady-state speed distribution is investigated. The mean speed is determined on the basis of the intersection of two functions; one of the functions is given by the desired speed distribution, which is a description of the goals that drivers want to attain in traffic; the other function is given by the concentration-dependent traffic parameters of the model. These parameters give a description of the restrictions that drivers exert on each other in the process of attaining their individual goals. Since the model is basically a description of the interaction between these two conflicting traffic characteristics, the effect on the mean speed due to each characteristic can hence be investigated separately through the properties of the corresponding function.

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 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]

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]

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]

When a traveler, or other user of a congested system, wishes to be reasonably sure of reaching a destination, or finishing a task, on time he must start early enough to compensate for random delays. This paper investigates the headstart decision policy arising if costs are attached both to lateness and to an otherwise undesirable early departure. The model encompasses a case in which the probability distribution of congestion delays is unknown, and must be inferred from previous experience. [ABSTRACT FROM AUTHOR]

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]

A simple mathematical model of a satellite town is presented in this paper. It is shown that the model contains the basic features of a satellite New Town as well as of a satellite Residential Town. The characteristics of commuter travel in a satellite Residential Town are investigated, and the size of the Central Area and of the satellite town, the distance traveled per unit area, and the average distance traveled, are evaluated. For an initial sample set of data, numerical results are presented and discussed. [ABSTRACT FROM AUTHOR]

Traffic flow past a point varies with time owing partly to statistical fluctuations and partly to a variation in the mean. Highway traffic surveys frequently include as a measure of this variation, peak short- time flows (1-, 5-, or 15-min flows) during a longer time (15, 30, or 60 mm). Near the peak of the rush hour, the expected flow should be nearly stationary and variation in short-time flows should be due mostly to statistical fluctuations. This paper describes methods for estimation of these peak flows under the assumption that the short- time flows are approximately a stationary Gaussian process with a variance-to-mean ratio of about 1. The theory suggests that one can predict the distribution of peak short-time flows (5-mm flows, for example) from the peak long-time flows (15 or 30 mm flows). Experimental data seem to confirm this. The implication is that these short-time peaks have no obvious relation to highway capacity beyond that already inferred from the longer-time flows. [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]

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]

This paper considers a modification of the single-car intersection delay problem in which the waiting driver, upon finding a suitable gap for crossing also examines the succeeding one, and uses it if it is larger. It is shown that the additional delay time caused by this method of gap acceptance is generally quite small. [ABSTRACT FROM AUTHOR]

Presents letters to the editor published in the July 1961 of the journal 'Operations Research.' Bibliography on theory of traffic flow publications up to October 1960; Table of generating functions; Formulation of the best route through a network.

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.

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]