Showing papers in "Transportation Science in 1976"

Optimal Control of Oversaturated Store-and-Forward Transportation Networks

Abstract: A general method is developed for the dynamic optimization of multi-commodity flows in an oversaturated, store-and-forward transportation network. The network is characterized by time-varying inputs, and the existence of queues in front of certain nodes where the incoming flows exceed the capacity to discharge them, during a certain period of oversaturation. The method consists of discretizing in time and solving a linear programming LP problem, in order to obtain the order of exhaustion of the various queues and an approximation to their, optimum time variation. The LP solution may be refined to any degree of desired accuracy, or used as a first step in a two-step procedure, where the order of exhaustion of the queues of the LP solution is used in a variational scheme to obtain the exact solution. The method is demonstrated by optimizing the operation of a two-node, four-queue network.

Models of Single Lane Time Headway Distributions

Abstract: The movement of traffic past a point is compared to the output of a queuing system having random input. A generalization of the queue output model leads to a suitable headway model: this model is a mixture of two distributions, representing following and nonfollowing headways, in appropriate proportions. Thin model is compared with several others that have been suggested; when used with a lognormal distribution of following headways, it gives the best overall fit to data from the M4 motorway, England, and two-way roads in Indiana, USA. For each site, the parameters of the following headway distribution can be assumed constant. The mean following headways are 1.3 sec and 1.6 sec for the M4 fast and slow lanes respectively, and 2 sec for the Indiana sites. The standard deviation of logarithms of following headways is 0.4 for both M4 lanes and 0.45 for the Indiana sites. For most samples, the reciprocal of the mean interbunch gap λ can be approximated by λ = λ*-1/2 λ*3/2, where λ* is the flow rate, and the proportion of the following vehicles ψ can be approximated by ψ = ρ-1/2ρ-1λ*3/2, where ρ is the traffic intensity.

An Application and Validation of Equilibrium Trip Assignment Methods

Abstract: We describe an application of an equilibrium trip assignment method to the 1970 road network of the City of Winnipeg, Manitoba, Canada. We discuss in detail the validity of the method. The results are encouraging and demonstrate the suitability of the method for planning purposes.

Route Constrained Fleet Scheduling

Abstract: This paper attempts to provide some insight into the structure of a large class of fleet scheduling problems. Scheduling under fixed due date constraints is shown to be easily solved using a new formulation of the problem. Scheduling under flexible due date constraints is shown to be inherently complex, and strong evidence is given for asserting that no efficient polynomial bounded algorithm exists for solving this problem exactly. A fast heuristic approach is described which has worked well in some school bus scheduling applications.

An Optimization Approach to Routing Aircraft

Abstract: The optimal solution for an aircraft routing model is developed for use in the route construction process of an airline operating in long haul markets The problem is to determine the sequence of stops for each aircraft from one base through a network of cities terminating at the original or second base A mixed integer linear programming model is formulated to maximize the profit derived from each routing The special structure of the mixed integer model is solved by an application of Benders' Decomposition Method Methods to improve the computational efficiency of the technique are examined and tested Finally, an implementation plan for incorporating the routing model into the airline scheduling process is presented

Multivariate Analysis of Traffic Factors Related to Fuel Consumption in Urban Driving

Abstract: The influence of various urban driving conditions on automobile fuel consumption was studied in an experiment involving 383 km of driving in the Detroit metropolitan area. The detailed speed, acceleration, and fuel consumption records were analyzed by multivariate statistical techniques. The objective of the study was to identify pertinent measures of traffic related speed-time characteristics that influence fuel consumption in urban driving. The results showed that average trip time per unit distance was the single most important factor in explaining the variability of fuel consumption. The results can be explained in terms of the physical properties of the engine-vehicle system and the interrelationships among the traffic related variables.

Minimax Multifacility Location with Euclidean Distances

Abstract: The problem considered is that of locating N new facilities among M existing facilities with the objective of minimizing the maximum weighed Euclidean distance among all facilities. The application of nonlinear duality theory shows this problem can always be solved by maximizing a continuously differentiable concave objective subject to a small number of linear constraints. This leads to a solution procedure which produces very good numerical results. Computational experience is reported.

The Traveling Salesman Location Problem

Abstract: The problem of locating a single new facility relative to m existing facilities has been studied extensively under the assumption that trips are always made between the new facility and a single existing facility each time a trip occurs A variation of the problem is the traveling salesman location problem, which involves a traveling salesman who services m customers Each time a trip occurs the salesman visits one or more customers during the trip Thus, 2m-1 different itineraries can be formed, each occurring with a given probability The new facility, which is the starting and ending point of each itinerary, is to be located such that the expected distance traveled per unit time is minimized An iterative procedure is presented for solving the traveling salesman location problem; computational experience with the procedure is provided

On the Fastest Route for Convoy-Type Traffic in Flowrate-Constrained Networks

Abstract: Flows of convoy-type traffic through networks whose arcs are characterized by both travel times and flowrate constraints are investigated. Suggested here, in particular, is the notion of a “flowrate-constrained fastest path”---a path by means of which the entirety of a volume of traffic, initially located at a source, node, can arrive at a sink in as short a time as possible when all traffic must flow along the same path and rates of flow along arcs are limited by flowrate constraints. Unlike the usual fastest path problems those in networks without flowrate constraints, flowrate-constrained fastest times and paths both depend, in general, upon the initial volume of traffic at the source node. Several theorems about flowrate-constrained fastest times and paths are stated and proved; it is shown, for example, that such paths are independent of source volume whenever this volume is sufficiently large. Two algorithms for finding flowrate-constrained fastest times and paths are given.

The Influence of Forward Vision and Target Size on Apparent Inter-Vehicular Spacing

Abstract: When one car follows another, the driver of the following car makes spacing judgments based on observing the lead ear within his field of vision. This visual field depends on a variety of design features of the following car, such as hood geometry, and is difficult to quantify simply. One quantity which relates to the driver visual field is the amount of roadway obscured from his view by his automobile. It is possible that the amount of this obscuration could influence spacing judgments. Furthermore, it is possible the size of the lead car, as characterized by the rear bumper length, might influence, spacing judgments. A laboratory experiment using color slides was devised to investigate if the amount of forward obscuration or target size influenced apparent spacing. The color slides showed the view of a driver seated in one car following another. Two different models of cars, with different values of forward obscuration and target size, served as lead and following cars. The influence of forward obscuration was also investigated by elevating the rear of one of the following cars. It was found that the lead ear target size did not systematically influence apparent spacing. On the other hand, changes in forward obscuration, whether caused by different following cars, or by elevating the rear of the same car, did influence apparent spacing; the same spacing appeared greater for smaller forward obscuration. These findings are related to reported test-track results.

A Round-Trip Location Problem on a Tree Graph

Abstract: The problem considered is to locate one new facility with respect to a finite number of pairs of existing facilities on, a tree graph, which typically represents a road network, so as to minimize the maximum cost, where cost are linear increasing functions of the round-trip distance a vehicle based at the new facility travels via a pair of existing facilities. Based on an attainable lower bound for the minimax problem, an algorithm is developed that yields all optimal solutions to the problem.

Reduction and Solution of Large Scale Vehicle Routing Problems

Abstract: This paper discusses the General Routing Problem approach to solving large scale routing problems. The General Routing Problem on network G = N; A requires finding the minimum cost cycle that visits every node in subset Q ⊆ N and that traverses every arc in a subset R ⊆ A. Utilizing special problem characteristics and the structure of real transportation networks, large reduction in effective problem size and complexity can often be made. This permits a very effective heuristic to produce optimum and near optimum solutions quickly.

Statistical aspects of injury severity; part i: comparison of two populations when there are several grades of injury; part ii: the case of several populations but three grades of injury

Abstract: A method is proposed of comparing the average levels of injury sustained in two conditions. It consists of plotting the proportion of cases in one population that exceed an arbitrary threshold of severity against the proportion of cases in the other population that exceed the same threshold, as the threshold varies. The further this curve is from the 45 degree line, the greater is the difference in severity between the populations. The precise shape of the curve depends on the particular model considered: two examples are derived from considering the distributions of injury severity, respectively, each to be (i) normally distributed with the same variance, or (ii) exponentially distributed; the means of the distributions differing. A number of applications ot his type of theory are outlined. Those types of accidents in which a high proportion of casualities are killed are usually those in which also a high proportion are seriously injured. This paper is concerned with the quantification of this correlation. In particular, it was found (using British data) that the variation in injury severity in a number of situations can be described by alternations in the exponent of a exponential distribution of severity, with the boundary between slight and serious injury occurring at one-third the distance from the origin of the boundary between serious and fatal injury. /Author/

Statistical Aspects of Injury Severity Part I: Comparison of Two Populations When There Are Several Grades of Injury

Abstract: A method is proposed of comparing the average levels of injury sustained in two conditions. It consists of plotting the proportion of cases in one population that exceed an arbitrary threshold of severity against the proportion of cases in the other population that exceed the same threshold, as the threshold varies. The further this curve is from the 45 degree line, the greater is the difference in severity between the populations. The precise shape of the curve depends on the particular model considered: two examples are derived from considering the distributions of injury severity, respectively, each to be i normally distributed with the same variance, or ii exponentially distributed; the means of the distributions differing. A number of applications of this type of theory are outlined.

Some Issues Relating to Metering or Closing of Freeway Ramps Part I. Control of a Single Ramp

Abstract: A hypothetical transportation corridor consists of two parallel routes. One route has properties typical of a congested freeway, the other is considered to be the composite of all alternative routes on city streets. Transfer between the two routes is permitted only at discrete points entrance or exit ramps. At these points, various methods of traffic control are possible. It is postulated that the control objective is to minimize the total cost of travel to all trips, subject to the hypothesis that travelers choose the route of minimum personal cost. Emphasis is placed on two control methods; metering the flow at entrance ramps, or closing the ramps. Two specific models are considered. In this study Part I, backtracking is forbidden but the origin-destination characteristics are fairly general. In a second study Part II, backtracking is permitted but the origin-destination characteristics have translational symmetry. In both cases it is found that, if the queuing costs are included in the total travel cost, ramp closure is often a more efficient method of control than ramp metering.

Some Issues Relating to Metering or Closing of Freeway Ramps Part II. Translationally Symmetric Corridor

Abstract: As an idealization of a long freeway imbedded in a network of parallel streets, we consider a hypothetical freeway with equally spaced entrance and exit ramps joining an adjacent slower speed parallel route. The origin-destination pattern of trips is assumed to be translationally symmetric on the adjacent route. Each ramp can be metered causing a queue to form, closed, or left uncontrolled. Two extreme strategies are considered. In the first, the ramps have a spacing short compared with the average trip length, but all ramps are metered at the same rate. In the second, the spacing between ramps is adjusted by closing ramps, but those which are open are not metered. Flow on the freeway is reduced because travelers will on the average travel a certain fraction of their journey on the alternate route, enroute to a ramp. The latter strategy typically gives a lower total travel cost, for flows on the freeway close to its capacity.

Statistical Aspects of Injury Severity Part II: The Case of Several Populations but Only Three Grades of Injury

Abstract: Those types of accident in which a high proportion of casualties are killed are usually those in which also a high proportion are seriously injured. This paper is concerned with the quantification of this correlation. In particular, it was found using British data that the variation in injury severity in a number of situations can be described by alterations in the exponent of an exponential distribution of severity, with the boundary between slight and serious injury occurring at one-third the distance from the origin of the boundary between serious and fatal injury.

An Optimization Model for Freeway Stationary Emergency Service Systems

Abstract: This study is concerned with the analysis of a stationary emergency service system, and includes the application of this analytic procedure to the Los Angeles Freeway Surveillance and Control Project. The stationary emergency service system is interpreted as an ordinary queuing system and is approximated by an M/G/∞ model. In conjunction with queuing theory, dynamic programming is used to determine the best locations for service facilities, the optimal number of service vehicles at each service location, and the service area covered by an individual service location.

A Theory of Household Automobile Allocation Decisions

Abstract: A theory of the decision-making behavior of urban households in allocating the use of their automobiles among essential travel purposes is developed. This theory begins to assess interdependence of household members with respect to their tripmaking behavior. The nature of trips to be made is predetermined by fixing the extent to which essential purposes must be served. Also, limits on household automobile availability and the importance of trip timing are recognized. Mathematical programs are developed based upon the assumption that households attempt to minimize travel costs in terms of both time and money required to achieve essential purposes subject to constraints on automobile availability.

An Abbreviated Procedure for Estimating Equilibrium Queue Lengths in Rural Two Lane Traffic

Abstract: On two-lane two-way roads overtaking opportunities are limited by the opposing traffic. For fixed volumes of traffic in both directions the opportunities for vehicles in one lane to overtake depend on the mean length of queues in the second lane, so that the mean queue length in the first lane is a function of the mean queue length in the second lane and vice versa. This paper takes an earlier procedure for determining the mean queue lengths in the two lanes at equilibrium and simplifies it by assuming that the distribution of queue lengths is known. The results,obtained by assuming that the underlying distribution is Miller, Borel-Tanner, or geometric are then compared by a numerical evaluation.

Letter to the Editor---Savings Approach to the Multiple Terminal Delivery Problem

Abstract: For the solution of the multiple terminal delivery problem a formula for the actual savings is presented and a method of solution based on these actual savings is described. This method is simple both conceptually and computationally and gives results that appear to be “good.”

Queuing Models for Multiple Chamber Locks

Abstract: Several models for predicting mean waiting times of river traffic at a multiple chamber lock were developed and tested. Mean waiting times predicted by the M/G/1 model differed significantly from observed times. Analysis of possible causes of failure of this model suggested a limited queue length M/G/1 model for one chamber, from which more accurate predictions were derived. For the two chamber system, an M/G/1 model with random batch size was developed. This model yields a lower bound for mean waiting time. These last two models can be used to predict system performance under various operating conditions.

A Model to Predict Benefits of Priority Lanes on Freeways

Abstract: An interactive computer-based model is described which permits a reasonable assessment of the decrease in the number of vehicle miles driven when one or several lanes of a freeway are devoted to the exclusive use of “carpools”: vehicles carrying at least a specified number of people. The vehicle miles driven are obtained by finding the equilibrium distribution of pool sizes as a function of distance driven, on both regular and priority lanes. A simple but believable economic model incorporating the cost of time and the “utility” of having a vehicle for one's exclusive use is the basis for determining what individuals will do in their self-interest. The economic model is partly verified using existing pooling data without priority lanes. The idea of the priority lane or lanes is, of course, that they move faster than the regular lanes. However, an attractive feature of the priority lane concept is that, in typical cases, traffic flow is actually improved even for those who choose not to pool. Simple runs of the model show that in some cases it can be better for all concerned if two lanes are reserved for carpools rather than one lane, and if vehicles with two occupants are allowed to use the priority lanes rather than requiring three occupants. A 12.5-mi stretch of the Santa Monica Freeway in the Los Angeles area is used as a computational example for the theory. Further refinements to the model are suggested.

Letter to the Editor---A Further Note on a Minimax Location Problem

Abstract: Elzinga and Hearn Trans. Sci. 7, 100--103 have presented a simplified formulation of a multifacility location problem with rectangular distances as a linear program. This paper describes a further simplification which permits a closed-form solution. It is shown that the former simplification can be beneficially used to solve a different version of the problem.

Traveling salesman location problem

Abstract: The problem of locating a single new facility relative to existing facilities has been studied extensively under the assumption that trips are always made between the new facility and a single existing facility each time a trip occurs. An iterative procedure is presented for solving the traveling salesman location problem; computational experience with the procedure is provided.

The Unpublished Schedule of Urban Peak Period Traffic

Abstract: Urban peak period traffic is unique in that a significant portion of all trips are made by persons making daily trips to and from work. The effect that such an underlying daily schedule may have upon the stochastic properties of urban traffic demand is discussed, and the existence of such a schedule is investigated empirically for five locations.