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Vehicles load passengers at a single service point and, after traversing some route, return for another trip. The travel times of successive trips are independent identically distributed random variables with a known distribution function. After a vehicle returns to the service point, one has the option of holding it, or dispatching it immediately. Passengers arrive at a uniform rate and the objective is to minimize the average wait per passenger. The problem of determining the optimal strategy (dispatch or hold) for a system of m vehicles is formulated as a dynamic programming problem. It is analyzed in detail for m = 1 and m = 2. For m = 1, the optimal strategy will hold a vehicle if it returns within less than about half the mean trip time. For m = 2, and for a small coefficient of variation of trip time C( T), the optimal strategy will control the vehicles so as to retain nearly equally spaced dispatch times, within a range of time proportional to C4/3(T). [ABSTRACT FROM AUTHOR]

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

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]

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

A model is developed to determine travel times between points in an urban area with a limited amount of input. The model uses a network consisting of grid shaped links and high speed, freeway links. The travel time over the grid shaped links is computed internally using a macroscopic description of travel velocities and paths. A minimum time algorithm is applied to the network to find the minimum travel times between all points in the network. A test of the procedure showed that the results of the grid travel time model closely agreed with travel times produced by the standard detailed network method. The grid model uses substantially less input and performs its computations in a very short period of time. It is possible to develop a model that closely agrees with the detailed network model with even greater simplification. The procedure developed seems to have promise for a number of applications in the transportation planning process. [ABSTRACT FROM AUTHOR]

The problem of determining a schedule for a traffic system of, e.g., bus or air lines that uses a minimum number of vehicles is treated. The various trips are required to start within given time intervals and have given origins, destinations, and travel times. It is shown that the problem can be formulated as an integer LP problem, but not of the simple network flow type. A rather simple branch-and-bound procedure is devised for its solution, which has been tested with favorable results. [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]

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.

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

The 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]

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]