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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]

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 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]

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]

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]

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]

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]

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]

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]

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 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.

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]

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]

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]

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 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]

A problem that is of interest in transportation planning, as well as other fields, is the effect on some or all of the shortest routes through a network, of increasing the length of a link in the network, or removing a link completely. A method is described for handling this problem, by establishing a subset of links, one of which must be contained in any alternative shortest path. These are referred to as the competing links. It is shown that this method has applications going beyond the particular problem cited. It may be applied to measuring the effects of altering some of the links in a network subjected to congested flow. The results presented for the algorithm compare very favorably with alternative procedures. It is suggested that the algorithm could be used in the development of networks which are, in some sense, optimal. [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]

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]

An algorithm for control of queue lengths at oversaturated intersections oriented towards delaying spillback across upstream inter- sections as long as possible is described. It is based on determining the change in queue and the allotment of available green time so as to keep the ratio of the actual queues to the maximum link storage space on both phases equal. The mathematical development of the algorithm is described in terms of a Z transform analysis, and the conditions for stability are derived. The resulting mathematical model is linear with the exception of a saturation type nonlinearity caused by the physical requirement to limit split. A describing function analysis is used to demonstrate loop stability in the presence of the nonlinearity. [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]

We study the highway merging problem with acceleration area. We suppose there is an acceleration area beside a highway and that a vehicle which arrives at an entrance from a rampway wails for a chance to merge as it accelerates on the acceleration area. The velocity of the merging vehicle at time t is a known function v(t), where the time origin is the moment when the merging vehicle arrives at the entrance. We derive the probability density function of the delay to the merging vehicle, i.e., the time between its arrival at the entrance and the moment it merges into the highway. We also discuss a properly of the probability density function of the 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]

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]

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 problem of studying the stability of the reciprocal-spacing follow-the-leader model of traffic flow is first discussed and an approximate model is proposed. The mathematical functions that are suitable to describe lead-ear behavior are examined. The stability of a nonlinear car-following model is then defined rigorously, so that it can be studied in the framework of the Liapounov theory. Previous phase plane results show that the reciprocal-spacing model is barely stable, whereas an asymptotically stable model may describe the dynamics more closely. Using an extension of the Weber Ratio, such a model is derived. A phase plane study of the proposed model is presented together with some numerical results. The results corn pare favorably with existing data. Results are presented showing the relative behavior of the actual model with time delay and the proposed model, in which a truncated Taylor series has been used to approximate the time delay. [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]

We consider a one-way street that intersects ii one-way (side) streets. Traffic approaching the first street is steady as are the flows on all side streets. Traffic signals are idealized as perfect on-off switches and traffic is treated as a fluid moving with a constant velocity on the main street. Total delay and total number of stops are evaluated for several types of signal coordination schemes. Some conclusions are: 1. For any given common cycle time and given splits at each inter- section, there is a choice of offsets (phases) that simultaneously minimizes both the total delay and stops, but it is not necessarily the one that produces a `through band' of maximum bandwidth. 2. There are signal settings for which some signals operate on half or a third the cycle time of other lights, which give a main Street delay equal to that for the optimal common cycle time setting but give less delay to the side street. 3. Similar models are commonly used to find maximum through bands for two-way traffic, but it is not obvious that this is a suitable objective even for one-way streets. [ABSTRACT FROM AUTHOR]

In order to ascertain whether neighboring intersections can be effectively coupled on the basis of traffic behavior, observational information on vehicular platoons was collected at four sites in London, England. This information is analyzed with particular emphasis on the phasing or synchronization of neighboring inter-sections for minimum delay. At each of the four sites studied, arrival time data was collected at four positions downstream from the signalized intersection from which the vehicular platoons were emerging. This data gives a measure of how platoons diffuse as they move from one intersection to the next. The analysis indicates that the diffusion process can be taken into account in the setting of signals. In particular, total delay in vehicle-hours per hour of green as a function of offset time is calculated, and in turn, the optimal offset time that would minimize delay is shown to be a linear function of the distance from the issuing traffic signal. [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]

This article presents information on the third biennial conference of the Australian Road Research Board. The conference was held in Sydney from 5-9 September, 1966. It was attended by nearly 500 delegates and was opened by Mr. R.W. Askin, Premier of New South Wales. The conference comprised of 21 technical sessions of which 9 were dedicated to traffic or transport research. In one of the sessions, R.R. Allan presented his study on the binomial model of traffic flow. The time scale in Allan's binomial model for single-lane traffic flow was divided into equal cells and was extended slightly by allowing the times at which vehicles pass a point to have any distribution within the time cells. The model has been tested against a set of data used by D.J. Buckley. After introducing a displacement to give a minimum headway of about 0.45 sec, the three-parameter model fitted the data almost as well as Buckley's four-parameter model. However, an unsatisfactory feature of the model is that the counting distribution always had a variance less than the mean. The second study being presented by Allan in that particular session was a rigorous account of the use and properties of generating functions with particular reference to their application in deriving properties of models of road traffic.

Traffic obstruction involves a financial loss to the community, the amount cf which it is difficult to determine. In the present article the author estimates the value of the time lost by different classes of vehicle and, on a basis of this assessment, shows that a small repair operation in a busy thoroughfare cost the public over £300 a day for eight weeks. [ABSTRACT FROM AUTHOR]

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.

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.

The realism of an approximation to the running time of an elevator car during morning up-peak is studied. It is shown that the difference between maximum and minimum running times is very small for cases of practical interest. This small range not only verifies that the approximation gives realistic values for running time but also eliminates the need for complicated probability calculations for up-peak elevator studies. [ABSTRACT FROM AUTHOR]

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.