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If the time required for a vehicle (particularly buses or elevators) to load passengers is an increasing function of the number of passengers loaded, then, on a route served by more than one vehicle, the vehicles tend to form pairs. If a vehicle runs behind (ahead of) schedule, it typically will pick up more (less) passengers and get even further behind (ahead of) schedule. The following is concerned with a shuttle type of route having just two vehicles and serving passengers who arrive at a constant rate. There is one control point at which vehicles can be intentionally delayed. The object is to devise a strategy of control that will minimize the average waiting time of the passengers. The strategy must correct for random fluctuations in trip time so that the headways will not become sufficiently unequal as to initiate effects of pairing. An approximate solution of the optimization problem suggests that the optimal control involves sufficiently tight control that the pairing effect has little influence on the waiting times. [ABSTRACT FROM AUTHOR]

Mathematical models of the delays incurred in a traffic link with reversible lanes, as a function of demands for service and allocation decisions, are constructed assuming that the state of the operation is reviewed periodically. There is a penalty associated with each allocation change that is manifested as a loss of capacity. Heuristic algorithms are derived that enable the determination of decision policies that minimize the delay per vehicle during some horizon. The first phase of the determination is performed upon a basic model, in which the reversal penalties are ignored, and results in a sequence of optimal periodwise decisions. This policy is then subjected to a second phase, performed upon the lost time model, in which reversal penalties are included. Progressively better policies are generated in this phase according to the heuristic notion that an optimal policy does not differ much from the policy obtained in the first phase. The solution of the models is illustrated in a case study using actual data for the Chesapeake Bridge. [ABSTRACT FROM AUTHOR]

The steady-state solution of a kinetic theory of vehicular traffic developed to describe the time and space evolution of the speed distribution of cars on a multiple-lane highway has been examined in the light of some observational data. A method of moments has been employed to compare the theory with the data. The order of magnitude agreement obtained between the theoretically predicted ratios of lower moments and the ratios determined from the provisional data indicates that the theoretical approach and assumptions are reasonable and consistent. [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]

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]

An experimental surveillance and control system was in operation for one lane of the Lincoln Tunnel in New York City, during most of the year 1967. The system shared in the use of an IBM 7040 computer located at the IBM Research Center, forty miles away from the tunnel. The computer received via a telephone line signals from pairs of detectors located at four observation points along the tunnel. From these signals were determined the number of vehicles in the three sections of the tunnel between the four observation points, as well as the speed and throughput over these four points. The control system reduced the input of traffic into the tunnel when needed in order to prevent congestion, which has been known to reduce appreciably the throughput of the tunnel. It has been shown that knowledge of the exact number of vehicles in the three sections of the tunnel permits much more timely action than has been possible in the past, resulting in longer periods of sustained high flow at comfortable speeds. A discussion is given of the algorithms used for control, and an analysis of the experimental data is presented showing the improvement of controlled versus uncontrolled traffic. [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]

A mathematical model is developed for predicting the expected duration of potential conflict situations at the intersection of air routes in the en route environment. Given the intersection angle of two routes and the average flows and speeds of aircraft, the model provides an estimate of the average duration of a potential conflict and the total time the aircraft would spend in potential conflict if no preventive action were taken by controllers or pilots. The model can be used in planning air route network geometry, as well as in providing guidelines to the establishment of suitable levels of traffic flow along various routes. [ABSTRACT FROM AUTHOR]

The response delay in clearing the queue of automobiles waiting at a traffic light can be modeled by allowing one car to leave at the end of each of a series of discrete intervals in time. The steady-state queue formed at a cycle traffic light is discussed for general stationary arrival processes. A method of solution for the case where arrivals are Poisson is described. General formulas are given for the probability of not clearing the queue during a cycle and for the expected wait at the light. [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]

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]

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]

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]

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]

The article focuses on the progress of traffic law enforcement. Traffic law enforcement alone does not have to carry the full responsibility for meeting the challenge. The burden is shared by two other fundamental factors in an effective control program: Engineering and Education. But the enactment of good traffic laws, and their proper enforcement, constitute a basic and indispensable element of highway safety. Now, in the face of imminent traffic changes ahead, the responsibility is once more clearly outlined. It is not pleasant to think what may happen if traffic is not effectively controlled during the next few years. Traffic regulations suffer from the national habit of passing a law and then forgetting that "there is no law without a sheriff." To be effective in this country, any law must carry the clear sanction of the majority of citizens. Beyond that, traffic laws must also be uniform. Conflicting rules of the road among local, county and state jurisdictions are impracticable in modern traffic.

At the University College London, professor R.J. Smeed put forward a theory giving the amount of traffic which can enter a city during peak periods. According to Smeed's theory, the amount of traffic that can enter a city center is proportional to its area rather than its circumference. At the Tewksbury Symposium on Urban Development held at Melbourne University recently, one speaker put forward a theory that the amount of traffic that can enter a city center is proportional to its area rather than its circumference. The data provided are of 35 cities of which 20 are in Great Britain. This data was collected by professor Smeed, and is contained in appendix 1 Figure 1 in the article shows the results, a linear regression line was fitted by least squares to the logarithmic values. The gradient was found to be very close to the 0.5 predicted by Smeed's theory.

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.

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]