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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]

The purpose of this paper is to provide a solution to a linear difference differential equation with time lag which governs the motion of a line of traffic. The idea of using operational calculus in solving such types of equations is not new, but the result may be of interest. In addition, a special problem is considered and some consequences derived from the solution. [ABSTRACT FROM AUTHOR]

A little-used method of estimating road traffic flows between two points is to record the registration numbers of vehicles passing each point in one direction and then compare the two lists of registration numbers to discover how many appear in both lists. One of the disadvantages of the method is that some inaccuracy in recording the numbers is inevitable and inaccuracy causes the numbers not to match when they should. This paper describes the application of the registration number method to a long-distance traffic survey and develops an estimate of traffic flow which compensates for inaccurate recording. [ABSTRACT FROM AUTHOR]

The article discusses the mission and objectives of The Institute of Management Sciences (TIMS). The author discusses the two-person game theory of John von Neumann, and the fact that von Neumann's breakthroughs came from his study of quantum mechanics rather than management science. The author states that von Neumann was one of the earliest scientists to recognize the importance of electronic computers. Leslie Edie, of the Port of New York Authority, was awarded the Lanchester Prize by the Operations Research Society of America for his paper on "Traffic Delays at Toll Booths." An article by Smiddy and Naum that addresses the evolution of management science in the U.S. is cited. Frederick Winslow Taylor is referenced for promoting an archaic, engineering-based form of management science.

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]

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]

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]

This paper presents a study of several aspects of the theory of car queues. In it we consider a situation in which there is traffic on a main highway and a queue of cars on a side road waiting to merge. First we consider a case in which the lead driver chooses to merge on the basis of whether the gap in main highway traffic exceeds a service time that is chosen from a probability density. An expression for the generating function of the steady-state distribution and the waiting-time distribution are derived. Secondly, the critical input to the side road is determined such that for all larger inputs the queue is transient. In particular we consider the effect of the move up time (of the second car in a queue) on this parameter. Finally, we present the results of a study by simulation techniques for the analysis of traffic queuing models. A discussion of the use of importance sampling in improving simulation studies is given, and a comparison made between theoretical and simulation results. [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 develops an analytic model of the mean running time for trains on a single track railway. Trains operating at several different speeds in each direction are permitted. Priority systems are included in the model to control train behavior when meets and overtakes occur and delay times due to implementing these priority schemes are calculated. It is assumed that the departing times for trains are independent random variables that are uniformly distributed over the time period of interest. The resulting mean running times, including delays, for each speed class in each direction are found by solving a set of linear equations. [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]

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]

Alternative methods of analysing gap acceptance data are considered with a view to removing the bias implicit in the situation in which minor road vehicle drivers exhibit consistent behavior and all accepted and rejected gaps are taken into account. Simulation techniques are used to show that some of these suggested methods are invalid, but verification is obtained for a method derived by the author in an earlier paper that simply requires the displacement of the gap acceptance curve time scale by an amount equal to the product of the variance of the observed gap acceptance distribution (sec²) and the major road volume (veh/sec). This, it is contended, is easier to apply than an alternative method of estimating the critical gap distribution parameters given by MCNEIL AND MORGAN. A theoretical relation is determined between the mean of the critical gap distribution and the Raff critical lag that shows the two to be equal only when the gap acceptance curve takes the form of a step function. [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]

Satisfactory solutions to congestion within and at the access routes of an airport may require data beyond the response to standard origin- destination questions and for all subgroups of airport users. An airport is considered as a closed system generating vehicle and person trips sampled within randomly or systematically selected observation time periods. Sampling at airport egress points may be most effective, but least feasible administratively. An alternative presented in this paper consists of developing a model for estimating the hourly volume of vehicle and person trips from machines counts at egress points and surveying four strata of airport users for collecting additional data with estimation based on post-stratification. [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 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]

A traffic counting distribution is derived in which a minimum spacing or headway between units of traffic is taken into account A comparison is made between this probability distribution and the Type I Counter distribution derived by W FELLER Explicit expressions are derived forthemean and variance of count as well as the probability that the interval of interest is completed filled by vehicles. [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.

This article focuses on various problems which are associated with the innovation adoption process in road safety, and/or traffic safety. There is a difference between an innovation which involves a purchase of equipment, and an innovation which merely calls for a change in behavior, although a decision is called for in each case. The author considers various ways in which research could help in solving some of the behavioral problems that are relevant to innovation adoption. With discussing the relevant value of the innovation it is argued that a seat belt greatly reduces the chances of injury in accidents; driving with dipped headlights in dimly-lit streets considerably improves the chances of the car being seen; and a pair of wing mirrors will improve a driver's view to the rear. A recent survey found that more cars had fog lights than seat belts; it may be that this is partly because drivers experience fog several times in a year and because a fog light may prevent an accident, whereas a seat belt can only help to mitigate the consequences of an accident.

IT is now becoming generally realised that the most important transport problem in Britain today is not surplus capacity on the railways but excess demand on the roads. There are some, such as Professor Kolbuszewski of Birmingham, who have suggested that the problem of urban road congestion is so intractable that big-city life may eventually have to be abandoned. But in the meanwhile many partial solutions and remedies for urban congestion have been put forward. Amongst these is the special contribution of economists, the suggestion that a tax should be imposed on vehicles using congested roads.[2] The purpose of this article is to examine the case for a congestion tax as it is put forward in the Report of the Ministry of Transport Panel which met under the chairmanship of Dr. R. Smeed.[3] The aim of a congestion tax is to obtain a more efficient use of road space. If a congestion tax was imposed on all vehicles using congested roads, it is argued, some drivers would use alternative, less-congested routes, some would travel at a different time, some transfer from private to public transport, and others would decide that their journey was not really necessary. The basis of the theoretical case for a congestion tax is that at present there are some road users who would value the benefit gained from their use of road space at less than the "social" marginal costs which they impose on other road users. When the traffic flow on a road increases beyond a certain point vehicle operating costs per mile (fuel consumption, brake, tyre and engine wear) will rise. More importantly, average speeds will be reduced and journey times lengthened. Since people value the scarce resource of time, a slower journey may be said to be a more costly journey, and the "costs" of lost time added to increased operating costs give total congestion costs. [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]

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]

This article presents annotated bibliography of scientific research in road traffic and safety. It presents investigation of relations between theoretical models and data that is supposed to be described by the models. There are a few entries without annotation; these have not been inspected. Parentheses enclose symbols of secondary importance. The main stream of research reflected in the present bibliography falls into the first subject category, "Traffic," and it is with respect to this category that the bibliography purports to be complete. Selection of publications has been more difficult in the other four areas. The subject matter blends into several fields that the journal wish specifically to exclude; chief among these are: the construction and maintenance of highways and the furniture of highways; the various mechanical and electrical properties of vehicles; physiological and psychological aspects of the driving population; instruments and instrumental systems, including computers; economic and financial analysis, and medical and legal questions of all kinds.

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]

Fluid and diffusion queuing approximations are used to analyze the behavior of vehicle-actuated signals at the intersection of two one-way streets at which there is no turning traffic. The arriving traffic is assumed to be a stationary stochastic process with a flow rate just slightly below that which saturates the intersection. Certain qualitative properties of the queues suggests that to minimize delay the signal should (in most cases) switch as soon as the queue vanishes, defined roughly as the time when the expected flow rate across the intersection drops below the discharge rate of a queue. The mean and variance of the cycle time and the mean delay are evaluated for this strategy. The average delay per car is shown to be less than for a fixed-cycle signal by about a factor of 3. The distribution of cycle time is shown to have approximately a Γ distribution. [ABSTRACT FROM AUTHOR]

The interchange of traffic density between lanes moving in the same direction is investigated on the basis of a simple mathematical model Emphasis is placed on the question of stability, i e, attenuation of disturbances from an 'equilibrium density distribution' A solution is obtained for a system of differential difference equations with a time lag corresponding to the interaction of two lanes This solution is directly applicable to other problems described by similar equations, such as the follow-the-leader problem The solution is generalized to n lanes, and it is found that the inherent instability is twice as great for n approaching infinity as it is for two lanes. [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]

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 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 operating speed y of a car is a function of desired speed x and traffic density λ, where x and y are random variables, and λ a real parameter. Relationships are proposed between the distributions of x and y and quantities which occur in empirical studies of traffic. It is postulated that for large λ queuing theory may be usefully employed, and several necessary modifications are discussed A résumé of literature is included. [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]

This article focuses on the study that presents the results of an investigation of conformity of motorists in a traffic control situation, and to present certain critical considerations of the J-curve hypothesis of conforming behavior as stated by F.H. Allport, a social psychologist. In the studies referred to, the behavior took place in the presence of various types of traffic controls--stops signs, police officers, red lights, and white lines establishing traffic lanes. The modal form of the behavior, which furnished the backbone of the J curve and, according to the hypothesis, represents the complete fulfillment of the purpose of the regulation, is that of stopping completely. In the studies reported by Allport a double incentive to stop existed either in the form of cross traffic at right angles to that observed, together with a boulevard stop sign, or in the form of a police officer together with a red light. In a traffic situation in which the only external conformity inducing agency is a stop sign, the modal pattern is slowing rather than stopping. When the deviating behaviors are distributed on a telic continuum representing degrees of conformity, the resultant curve is skewed, but is not in form.