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At a transfer station arriving trucks dump collected refuse, and larger capacity trucks haul the refuse to a final disposal point. Transfer of refuse from collection to haul trucks is direct at some such facilities, while at others a storage area serves as a buffer into which refuse is dumped and from which it is loaded for shipment. A (single) deterministic queuing model is formulated for idealized forms of both direct and indirect transfer. The model takes into account a time-dependent arrival rate of refuse, the number of haul trucks, the hauling time, the number of collection loads per haul load, the storage capacity, numbers of dumping and loading channels, and dumping and loading times. Arrivals and departures of both types of vehicles are treated as fluid flows. Mathematical relations that describe physical behavior are derived, and interpreted graphically. Quantities represented graphically include storage level, and queues and delays of both kinds of vehicles. Optimal haul schedules are obtained for 'typical' examples. The San Francisco (indirect) and Orange County (direct) transfer stations are discussed, based on direct observation. The model is applied directly to the former facility; a variation of the model is outlined for the latter. [ABSTRACT FROM AUTHOR]

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]

The semi-Poisson headway distribution model introduced by Buckley ["Road Traffic Headway Distributions," Proc. Australian Road Research Board 1, 153-183 (1962); "A semi-Poisson Model of Traffic Flow," Trans. Sci. 2, 107-133 (1968)] involves the decomposition of the headway distribution into components which can be regarded as corresponding to 'free' and 'constrained' vehicles. This model is reformulated here in order to derive am integral equation by means of which the components can be calculated directly from the observed headway distribution, thereby avoiding an arbitrary parametric representation of the constrained distribution component. The model is applied to traffic observations under high flow conditions from a British and an American freeway. The model results are interpreted as an indication of whether the freeway lane is operating at its maximum possible capacity. It is found that one lane of the British freeway had a flow very near the maximum given by the model, but the greatest observed flow on the American freeway was stilt less than the calculated maximum. [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]

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]

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.

Modifications are proposed for an algorithm that estimates the number of vehicles on a section of highway from a time series of flow and velocity measurements. The effect of alternate assumptions concerning the nature of the velocity field between points of measurement is explored. In addition a simplification is proposed to avoid solution by Successive approximation of certain transcendental equations. The net result is an algorithm that is more practical and provides generally superior performance than the original. Various algorithms are evaluated for both single and multilane traffic. [ABSTRACT FROM AUTHOR]

The literature of various disciplines including engineering, operations research, and management science contains many problems that would have widespread application if methods could be found for solving problems of reasonable size. In general, these problems are combinatoric in nature; moderate to large-scale problems in this class have resisted solution by currently existing algorithms and heuristics. A partial list of these well known problems includes the traveling-salesman problem, the generalized truck-dispatching problem, board wiring, and the construction of minimum cost communication networks with various survival or redundancy demands. The authors report on a man-machine approach for solving the generalized truck-dispatching problem. Their results indicate that the technique is more accurate than previously reported heuristics. They further comment on application of the man-machine technique to other routing, scheduling, and network problems. [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 methodology of the discrete-time, extended Kalman filter is applied for the estimation of densities and the control of critical traffic links. The methodology is tested using traffic data obtained at the Lincoln tunnel of New York City. Two algorithms are tested, one involving density estimation alone and one combining density estimation with a formalism for the determination of optimal control. The results indicate that the first algorithm gives very good density estimates. The second algorithm yields a less accurate density estimate, but has the advantage over the first that it is amenable to an analytical optimization investigation. [ABSTRACT FROM AUTHOR]

A model is developed for determining the optimal timing of investment in the capacity of a transportation network for which there is a finite planning horizon. The model is long term and macroscopic in nature and is limited to single-mode transportation systems in which there is a unique path connecting each origin-destination pair. The form of the optimal solution for the special case of a two-link serial network is presented. Conditions, that may be checked in application, are developed that allow the optimal solution to be calculated by solving a sequence of independent, unconstrained optimization problems. If these conditions are met, the necessity for forecasting cost and demand data for the whole planning period is eliminated. [ABSTRACT FROM AUTHOR]

Numerical comparisons of several expressions for the average delay to traffic passing a fixed time traffic signal have been made for a wide range of values of the arrival rate, saturation flow, cycle time, proportion of the cycle effectively green, and variance-to-mean ratio of the number of arrivals per cycle (I-ratio). The values of average delay given by Miller's, Newell's, and Webster's simplified expressions, and by a new modification of the last incorporating the I-ratio are compared with the value given by Webster's full expression. The differences are not usually more than 10 per cent when I = 1, but the importance of the I-ratio is shown by the differences reaching about 50 percent at high degrees of saturation when I = 1.5. The differences between the values of the various expressions are also compared with the effects on the value of Webster's full expression of given errors in the parameters. These effects are found to be large enough to make it difficult to distinguish experimentally between the various expressions when the I -ratio is near to 1 except by extensive measurements. Because of this the choice between expressions is often a matter of convenience of computation, and this choice is briefly discussed. [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]

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]

Circuit constraints on the phasing of fixed-time synchronized signal networks are defined. A method, based on a graph-theoretic approach, for deriving a fundamental set of equations characterizing these constraints is presented. [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 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 article discusses the three-dimensional representation of traffic flow. The traffic flow theory, particularly for single-lane traffic, contains many methods for displaying graphically the evolution of various traffic characteristics, such as flow, q, density, k, and velocity, v. Which graphical representation one uses depends upon which characteristics one wishes to analyze. Each method tends to display certain features in a convenient way, and others in a less convenient way. This three-dimensional surface is like a staircase, because cars are discrete, but people usually are not interested in such fine details. In the three-dimensional representation, the relation between these two families of curves is very simple. The x-t curves represent a contour map of the surface n (x, t), i.e., lines of constant height n (x, t) = j. The n-t curves also describe a contour map of the same surface but with the axes rotated so that the "base variables" are n and t. In the three-dimensional representation, these waves are paths of constant direction of the vector A and could be traced quite easily if one locates all points of the surface n (x, t) at which a plane of given orientation can be made tangent to the surface.

Exogeneous events occurring as a Poisson process are assumed to cause stoppages in the normal operation of convoys, road vehicles, or equipments. The operational delay experienced by each stoppage is assumed to have an exponential distribution. By introducing appropriate state variables, a hyperbolic partial differential equation is set up; expressions are obtained for the probability that at a given time the operation has registered at most a given number of cumulative performance units (e.g., distance) and for the probability that the operation has registered a given number of cumulative performance units on or before a specified time. [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]

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.

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]

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]

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]

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]