bluuebunny/crossref_metadata_2025 huggingface dataset:
Unconstrained Extremal Formulation of Some Transportation Equilibrium Problems
Authors: Daganzo Carlos F.
Published: October 2008

This paper presents transportation equilibrium results that apply to both discrete choice models and network problems. Specifically, it shows that many network equilibrium problems admit an unconstrained extremal formulation and that unconstrained optimization algorithms may be used for their solution. Similar results are derived for equilibrium problems involving discrete choice models. It also shows that a certain class of stochastic networks exhibit unique equilibria and that simulation algorithms with fixed step sizes converge almost surely to the equilibrium point.
An Empirical Study of Travel Time Variability and Travel Choice Behavior
Authors: Jackson W. Burke , Jucker James V.
Published: October 2008

Although reliability of travel modes has generally been found to be one of the most important attributes of transportation systems, few attempts have been made to make these findings operational. The impact of a specific measure of reliability, the variability of travel time, on the route-to-work choice is investigated in this research through the use of a survey instrument posing hypothetical commute alternatives. A mean-variance model of travel choice is used to estimate an individual's tradeoff between time and variability (i.e., risk aversion). The principal tool of analysis was LINMAP, a linear programming technique for multidimensional analysis of preferences, which yielded estimates of each respondent's risk aversion coefficient (λ). A pretest was conducted to determine an appropriate format for the commute choices and to investigate external validity concerns.
PMAKE Analysis: Predicting Rail Yard Time Distributions Using Probabilistic Train Connection Standards
Authors: Martland Carl D.
Published: October 2008

Any study of rail freight service or freight car utilization must eventually address the reliability of train connection performance. In a series of case studies over the past 10 years, the MIT Rail Group developed PMAKE analysis as an effective means of doing this. The PMAKE methodology has been used extensively in service planning by a number of railroads and has been used in two major rail network models. The Freight Car Utilization Program has supported two demonstration projects showing how to incorporate PMAKE analysis in railroad terminal control systems. The paper reviews three other major modeling approaches used in rail yard studies: simulation, queuing, and capacity planning. These approaches have had limited effectiveness in prediction train connection performance and in supporting management control systems. PMAKE analysis improves upon these approaches by making it easier to (a) calibrate models of yard performance and (b) incorporate analytic techniques within the operating control system. In short, PMAKE analysis builds a bridge between operations research technique and management control. The paper includes the parameters of PMAKE functions calibrated for various rail yards. It also includes the mathematical basis for PMAKE analysis and shows several means of calibrating PMAKE functions. This paper, therefore, provides a complete description of PMAKE analysis, including its development, its relation to other methods of terminal analysis and its use by the rail industry.
Travel Time Variability—The Case of Two Public Modes
Authors: Taylor M. A. P.
Published: October 2008

The variability of travel times on a given route for a particular journey is known to be an important factor in influencing the choice of mode and route for trips, particularly for those trip types where constraints may exist on arrival time at the destination. Previous work in this area has concentrated on daily variability for journeys by private car. This paper describes some results obtained from a study of travel time reliability for a work trip using two alternative and directly comparable public transport modes, bus and underground rail (metro), in Paris, France. Data were collected to permit the study of the distributions of variations in daily travel times, relationships between measures of variation and congestion, and to compare the characteristics of the two modes. It was found, for instance, that while the bus offered a potentially quicker and more direct service in terms of its free travel time and route location, in practice the metro provided a faster and more reliable service under normal operating conditions. The results of the study confirm and extend earlier work, and some areas for further research are suggested.
Transportation Product, Transportation Function and Cost Functions
Authors: Jara-Diaz Sergio R.
Published: October 2008

Although major advances have been made in the estimation of transportation cost functions in terms of functional specification and microeconomic properties, available studies present inconsistencies with observed industry behavior, and have been criticized as a reliable basis for policy design. In this paper the concept of transportation cost function is restated on the basis of an improved (multi-) output definition. The transportation function is identified as that component of the production function that relates output to characteristics of vehicles, terminals and rights-of-way. Using this framework, cost functions are derived for two simple transportation systems, which illustrates the ambiguity of the aggregate output definition and shows the importance of spatial complementarity in transportation activities. Eventual contradiction between economic wisdom and firms' behavior are shown to be explainable under the multioutput perspective. The implications of output misspecification on the estimation of transportation cost functions are discussed.
Letter to the Editor—A Simplification for a Note on Computational Simplifications in Solving Generalized Transportation Problems
Authors: Wollmer Richard D.
Published: October 2008

Glover and Klingman (Glover, F., D. Klingman. 1973. A note on computational simplifications in solving generalized transportation problems. Trans. Sci. 7 351–361.) give an extremely efficient procedure for updating the basis and dual evaluators in the solution of the generalized transportation problem. This note poses a shorter and simpler proof of the results of Glover and Klingman. Authors' closure by F. Glover (University of Colorado, Boulder) and D. Klingman (University of Texas, Austin, Texas) follows.
Letter to the Editor—A Note on “Review of Modal Split Models”
Authors: Allsop Richard E.
Published: October 2008

Readers may be interested to know of a substantial unpublished paper entitled “Review of Modal Split Models,” which is available on direct request to its author, M. G. Langdon, of Assessment Division, Transport and Road Research Laboratory (TRRL), Crowthorne, Berkshire, RG11 6AU, England, UK.
Editorial
Authors: Gazis Denos C.
Published: October 2008

Editorial of the new editor-in-chief Denos C. Gazis.
A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution
Authors: Daskin Mark S.
Published: October 2008

The maximum covering location model has been used extensively in analyzing locations for public service facilities. The model is extended to account for the chance that when a demand arrives at the system it will not be covered since all facilities capable of covering the demand are engaged serving other demands. An integer programming formulation of the new problem is presented. Several properties of the formulation are proven. A heuristic solution algorithm is presented and computational results with the algorithm are discussed. Directions for future study are also discussed.
Measuring Critical Gap
Authors: Hewitt R. H.
Published: October 2008

A method is derived which estimates the probability distribution of the critical gaps of those drivers entering a main road at a priority junction who have rejected the initial lag offered to them, using observations of the sizes of the gaps refused and that eventually accepted by the driver. An extension of the method estimates the probability distribution of the critical times of all drivers, on the assumption that each driver’s critical lag and critical gap are equal, from observations of the sizes of the initial lags accepted and rejected by the driver, and the sizes of subsequent gaps considered if the initial lag is rejected. Both methods have been tested using data obtained by computer simulation. Estimates of the mean and standard deviation obtained using each method are substantially unbiased and have a fairly small standard error. Estimates of the critical gap and critical time distributions obtained using the methods are subject to considerable errors in individual cells of the distribution, however, unless the data set used is very large. An approximate method is also suggested whereby the original probability distribution of the critical gap of all drivers, including those who accept the initial lag, can be estimated from the same data by assuming a simple form for any difference between the distributions of critical lags and critical gaps.
A Stochastic, Dynamic Network Model for Railroad Car Distribution
Authors: Jordan William C. , Turnquist Mark A.
Published: October 2008

Freight cars represent a substantial portion of total railroad investment, and the low utilization of this major capital resource is certainly a contributing factor in the poor financial health of many railroads. A key element in improving utilization is the process of empty car redistribution. This paper describes a dynamic network optimization model for distribution of empty freight cars. It incorporates information on potential revenues from loads available at various points in the network for each period over a specified planning horizon, the costs of not being able to satisfy these demands, the costs of holding empty cars in anticipation of demands, and the costs of moving empty cars over the system. The information on supplies of, and demands for, cars in future periods, as well as their travel times over the network, is represented stochastically to reflect the uncertainty inherent in forecasts of future conditions.
Optimal Control of Automobiles for Fuel Economy
Authors: Hooker J. N. , Rose A. B. , Roberts G. F.
Published: October 2008

This paper describes an application of dynamic programming to determining optimal driver control of an automobile for fuel economy. The objective function is provided by a simulator that uses vehicle performance maps derived from statistical analysis of road data collected by the authors. One dynamic program controls acceleration as a function of time subject to constraints on speed, acceleration, and distance covered. Another controls acceleration and gearshift subject to constraints on speed, acceleration, and time required to shift gears. Results are presented for acceleration to a given cruising speed, driving over hills while achieving a given average speed, and driving from one stop sign to another.
The Estimation of an Origin-Destination Matrix from Traffic Counts
Authors: Bell M. G. H.
Published: October 2008

In this paper, a model is described that will under certain circumstances yield the most likely origin-destination matrix which is consistent with measurements of link traffic volumes. Given knowledge of the proportionate usage of each link by the traffic between each zone pair, the model parameters scale each element of a prior estimate of the origin-destination matrix up or down so that the measurements of link traffic volumes are reproduced. The fitted values are shown by example to be invariant to the application of uniform scaling to the prior estimates. A Newton model fitting procedure is outlined. In reality, measurements of link traffic volumes are random variables and the proportionate usage of links by the traffic for each zone pair is not known with certainty. An expression is derived for the variances and covariances of the logarithms of the fitted values in terms of the variances and covariances of the measured link volumes, taking the proportionate usage of links as given. The expression permits the calculation of asymmetric confidence intervals for the elements of the fitted origin-destination matrix.
Optimal Path of a Single Service Unit on a Network to a “Nonemergency” Destination
Authors: Berman Oded , Rahnama Mina Rasty
Published: October 2008

This paper focuses on the problem of finding the optimal travel path of a single service unit to nonemergency destinations. Such destinations result from events other than service calls, e.g., repositioning or relocation operations, returning from the scene of the service call to the “home location,” preventive patrol, etc. The analysis is performed on a network model of the urban environment. The time period of interest begins when the service unit starts its travel to a nonemergency destination and ends when the new call for service arrives. The paper contains two models each of which is suitable for a different application. For the two models two different algorithms are presented; one of which is a dynamic programming. These algorithms take into considerations the probabilistic nature of the demand for service. Illustrative examples are also included.
From the Editor
Authors: Gazis Denos C.
Published: October 2008

This issue of the journal is the first of the special issues which I promised in an editorial earlier this year. The issue is devoted to the general area of transportation equilibrium.
Stochastic Network Equilibrium with Multiple Vehicle Types and Asymmetric, Indefinite Link Cost Jacobians
Authors: Daganzo Carlos F.
Published: October 2008

This paper discusses a family of general link cost functions that can be used to model multimodal transportation network equilibrium problems. The family includes as a special case the currently favored family of monotonically increasing functions but does not necessarily have to have a symmetric or semi-definite Jacobian. In this way multimodal networks can be modeled somewhat more realistically. The paper also allows stochastic link costs for some or all the links and modes. It is shown that under mild conditions the equilibrium exists and is unique, but more importantly, that there is a simple, single-equilibrium algorithm that is proven to converge for stochastic networks with the link cost family discussed in the paper. Finally, it is pointed out that many variable demand problems also exhibit unique equilibria, but that there are some which do not. An example which illustrates this fact is given.
A Flexible and Integrated Methodology for Analytical Classification of Daily Travel-Activity Behavior
Authors: Pas Eric I.
Published: October 2008

The importance of incorporating the derived demand nature of urban person movement and the interdependence of the elemental travel episodes (trips) in analyses of urban travel behavior is discussed. A flexible and integrated approach to the analysis of daily urban travel-activity behavior as a complex phenomenon is described. The methodology incorporates systematic identification of classes of similar daily travel-activity patterns and the evaluation and interpretation of these groups. The approach described here comprises three stages; namely, transformation, group formation, and cluster interpretation and evaluation. In the first stage, raw input data describing the daily travel-activity patterns of a sample of individuals is transformed into a set of points in a real Euclidean space, where each point represents a daily travel-activity pattern. In the second stage, a cluster analysis algorithm is employed to identify groups of similar daily travel-activity patterns. In the third stage, the identified groups are interpreted by defining representative patterns for each group. Classifications produced by the methodology can be used to analyze and model relationships between daily travel-activity behavior and potential explanatory variables.
Stochastic Equilibrium Model of Peak Period Traffic Congestion
Authors: de Palma Andre , Ben-Akiva Moshe , Lefevre Claude , Litinas Nicolaos
Published: October 2008

This paper addresses the problem of peak period traffic congestion. It considers the queues and delays at a single point of insufficient capacity. A model is developed to predict the pattern of traffic volumes and travel times during a peak period. It consists of two basic elements: a deterministic queue and a random utility departure time choice. The utility represents the tradeoff that exists whenever congestion occurs at the desired departure time. A trip-maker can then shift his/her trip forward or backward in time to avoid a long delay. The properties of the equilibrium solution of the model are investigated analytically. It is shown that there cannot be more than one congestion period and that the equilibrium solution is unique.
Alternative Variational Inequality Formulations of the Network Equilibrium-Travel Choice Problem
Authors: Fisk C. S. , Boyce D. E.
Published: October 2008

Alternative variational inequality formulations of the network equilibrium-travel choice problem are given, extending previous results to include models with non-invertible travel demand functions. The model is then developed further to allow for the possibility of dispersion in route choice.
Technical Note—An Improved Lower Bound to the Minimum Fleet Size Problem
Authors: Stern Helman I. , Ceder Avishai
Published: October 2008

We give a formal proof that a procedure similar to that used in the VAMPIRES program to find a starting fleet size is a lower bound on the minimum fleet size problem when deadheading trips are allowed. It is shown that this bound is stronger than the “simultaneous operation” bound used previously by the authors in the URDHC program. The URDHC program is an interactive bus scheduling program which inserts deadheading trips into a timetable in an effort to reduce the required fleet size. The “simultaneous operation” lower bound is equal to the maximum number of trips in a given timetable that are in simultaneous operation over the schedule horizon. The improved lower bound is based on the construction of a temporary timetable in which trips are extended to include potential linkages reflected by deadheading time considerations. One example is given to illustrate the construction of the improved bound. This improved lower bound can be usefully employed in the lower bound termination test of the URDHC program or other procedures for the fleet size reduction problem.
Network Design and Transportation Planning: Models and Algorithms
Authors: Magnanti T. L. , Wong R. T.
Published: October 2008

Numerous transportation applications as diverse as capital investment decision-making, vehicle fleet planning, and traffic light signal setting all involve some form of (discrete choice) network design. In this paper, we review some of the uses and limitations of integer programming-based approaches to network design, and describe several discrete and continuous choice models and algorithms. Our objectives are threefold—to provide a unifying view for synthesizing many network design models, to propose a unifying framework for deriving many network design algorithms, and to summarize computational experience in solving design problems. We also show that many of the most celebrated combinatorial problems that arise in transportation planning are specializations and variations of a generic design model. Consequently, the network design concepts described in this paper have great potential application in a wide range of problem settings.
Garage Location for an Urban Mass Transit System
Authors: Ball Michael , Assad Arjang , Bodin Lawrence , Golden Bruce , Spielberg Frank
Published: October 2008

This paper discusses a model for the problem of locating garages in an urban mass transit system and the associated assignment of vehicles to garages for background and peak services of transit lines. The objective of this model is to minimize the sum of fixed site-related costs, variable vehicle costs, and crew relief costs. The model is solved by an iterative procedure involving a location interchange heuristic and a network flow-based algorithm. The implementation of the model is discussed through its various stages, from data preparation to the final policy recommendations.
Modeling the Choice of Work Schedule with Flexible Work Hours
Authors: Moore Anthony J. , Jovanis Paul P. , Koppelman Frank S.
Published: October 2008

Flexible work hours have been promoted as a low cost approach to improve the productivity of the existing transportation system. However, analytical tools are needed to evaluate the impact such policies have on workers' arrival time choices. This paper develops a behaviorally based structure, using utility maximization concepts, to relate travel, family, workplace and individual influences to the workers' choices of arrival times with flextime. The accuracy of this conceptual structure is explored through the development of disaggregate probability distribution models using maximum likelihood estimation techniques. These models investigate several specifications and examine the use of market segmentation to differentiate varying work arrival time behavior by different subsets of the population. Major findings include: older workers and those living at greater distances from the workplace tend to arrive earlier, and households constrained by the presence of a working spouse and young children have less flexibility to alter arrival times with flextime.
The Stability of a Dynamic Model of Traffic Assignment—An Application of a Method of Lyapunov
Authors: Smith Michael J.
Published: October 2008

This paper considers a dynamic model of traffic assignment in which drivers change their route choices to take advantage of cheaper routes. Using a method due to Lyapunov, we show that if the cost-flow function is monotone and there are no explicit capacity restrictions then any solution trajectory of our dynamical system converges to the set of Wardrop equilibria as time passes.
External Zones in Trip Distribution Models: Characterization and Solvability
Authors: Dinkel John J. , Wong Danny
Published: October 2008

The problem of incorporating zones outside the study area in a spacial interaction or trip distribution model is analyzed in this paper. The framework for the analysis is based on the maximum likelihood formulation of the problem, whose equivalence to the entropy maximization model was established in general by Wong (Wong, D. S. 1981. Maximum likelihood, entropy maximization, and the geometric programming approaches to the calibration of trip distribution models. Trans. Res. 15B 329–343.). We shall deal with two cases—when the number of incoming (or outgoing) trips to the study area is restricted, and when it is unrestricted. Based on this approach, we present a unified numerical solution methodology for these classes of problems. The sensitivity of the model with respect to changes in certain restrictive parameters will be examined. As a result, we characterize the solution space for certain values of the parameters under consideration. A numerical example is used to illustrate our presentation.
The Distance Traveled to Visit N Points with a Maximum of C Stops per Vehicle: An Analytic Model and an Application
Authors: Daganzo Carlos F.
Published: October 2008

The purpose of this paper is to develop a simple formula to predict the distance traveled by fleets of vehicles in physical distribution problems involving a depot and its area of influence. Since the transportation cost of operating a break-bulk terminal (or a warehouse) is intimately related to the distance traveled, the availability of such a simple formula should facilitate the study of more complex logistics problems. A simple manual dispatching strategy intended to mimic what dispatchers do, but simple enough to admit analytical modeling is presented. Since the formulas agree rather well with the length of (nearly optimal) computer built tours, the predictions should approximate distances achievable in practice; the formulas seem realistic. The technique is a variant of the classical “cluster-first, route-second” approach to vehicle routing problems. In these approaches, the depot influence area is first partitioned into districts containing clusters of stops; one vehicle route is then constructed to serve each cluster. Our procedure is characterized by the way district shapes are chosen; ignoring shape during the clustering step can increase significantly travel distances. The technique is simple. To exercise it, one needs only a pencil, eraser, and a scale map showing the destinations. Once mastered, the technique takes only a few minutes. This time should increase only linearly with the number of destinations. For repetitive problems, the technique can be enhanced with the help of interactive computer graphics. A newspaper delivery problem for the city of San Francisco is used as an illustration.
Dynamic User Equilibrium Departure Time and Route Choice on Idealized Traffic Arterials
Authors: Mahmassani Hani , Herman Robert
Published: October 2008

An extension of a recent framework for analyzing the time-dependent departure pattern arising in an idealized situation of a pool of commuters going from a single origin to a single destination along a unique route is presented. Congestion along this route is represented using elementary traffic flow theoretic relationships; time-varying patterns of basic traffic variables are derived under user equilibrium conditions, along with the corresponding time-dependent departure pattern of system users. After demonstrating the basic model in the single-route context, an additional dimension of choice is introduced by considering the joint departure time and route choice decisions of users. Results are derived in a simplified two-route context and numerical illustrations provided.
The Existence of a Time-Dependent Equilibrium Distribution of Arrivals at a Single Bottleneck
Authors: Smith Michael J.
Published: October 2008

The paper gives conditions which guarantee the existence of an equilibrium arrival pattern at a single bottleneck. In the model, the times at which a driver wishes to leave the bottleneck depend on the driver. The equilibrium queue length in this model always has a continuous time derivative everywhere. However, the slope of the equilibrium cumulative arrival distribution is discontinuous at the beginning and end of congestion.
The Influence of Stops on Vehicle Fuel Consumption in Urban Traffic
Authors: Herman Robert , Ardekani Siamak
Published: October 2008

A simple linear relation between fuel consumption per unit distance, ϕ and trip time per unit distance T, ϕ = k1 + k2T is established for the fuel data collected in Austin and Dallas, Texas, and Matamoros, Mexico. The qualities of traffic service in these cities are compared through the study of the spread of the data points along the ϕ, T trend, showing that the Matamoros data in general have higher ϕ and T values. The fuel consumption model ϕ = k1 + k2T is improved by the addition of a term proportional to ΔNs(T), the deviation of the number of stops for a given datum point from the average number of stops associated with the trip time interval into which the datum point falls. It is shown in the resulting new model, ϕ = k1 + k2T + k3ΔNs, that since T and ΔNs are virtually uncorrected, the values of k1 and k2 in the simpler model remain unchanged. A discussion of the physical interpretation of the model parameters is presented. In addition, an analysis of data obtained in central London shows that k1 depends almost entirely on vehicle mass. It is also shown that the value of the parameter k3 is approximately given by the product of the warmed-up idle fuel flow and the average stop duration.
Appreciation to Associate Editors and Referees
Authors: Gazis Denos C.
Published: October 2008

I wish to thank the Associate Editors and referees who have given generously of their time during the past two years to review, and often help improve, papers contributed to the Journal. It is the dedicated service of these individuals that has consistently maintained the high standards of scientific excellence of the Journal.
The Round-Trip p-Center and Covering Problem on a Tree
Authors: Kolen Antoon
Published: October 2008

A task performed by a vehicle consists of picking up goods at a given client and delivering it to another client. The round-trip distance is the distance traveled by the vehicle between the departure from and the return to its depot. The round-trip p-center problem is to locate p depots with respect to a finite number of pairs of clients so as to minimize the maximum round-trip cost, which is defined as a nonlinear increasing function of the round-trip distance from the nearest depot. The round-trip covering problem is to find the minimum number of depots such that each round-trip cost is no more than a given constant. For both problems a dual problem is defined and in case the underlying network is a tree a strong duality result is proved. We give algorithms to solve both tree round-trip location problems in polynomial time.
An Algorithm for the p-Center Problem in the Plane
Authors: Vijay James
Published: October 2008

The problem of locating p facilities to service m demand points in a plane, such that each demand point is as close as possible to some facility, is considered. An algorithm based on geometry is given, and some computational results presented. Extensions to the weighted case, the surface of a sphere, and the rectilinear norm are also provided.
A Regression Formulation of the Matrix Estimation Problem
Authors: McNeil Sue , Hendrickson Chris
Published: October 2008

Matrices are widely used in transportation planning to represent the distribution of characteristics or as origin-destination matrices. Developing such matrices by means of surveys is expensive and time consuming, and once the survey data are collected and compiled the matrices are rapidly outdated. Other methods which are commonly used are unable to include all available data or to provide a measure of the uncertainty of the estimates. This paper formulates a quadratic programming method to estimate matrix entry estimates as an equivalent constrained generalized least squares estimation problem. As well as being able to include any available information in the form of constraints, the variance-covariance matrix of the entry estimates may be found and confidence intervals calculated for matrix entry estimates with some added distributional assumptions. The problem of updating the proportions of nationwide automobile trips by purpose and trip length from 1970 to 1977 is included as a simple example to illustrate the method.
Bibliographic Section
Authors: Mannering Fred L. , Spencer Frank A. , Mahmassani Hani S.
Published: October 2008

Urban Transportation Planning: A Decision Oriented Approach, by Michael D. Meyer and Eric J. Miller, McGraw-Hill, New York, 1984—reviewed by Fred L. Mannering.

Air Transportation—A Management Perspective, Alexander T. Wells, Broward Community College, Wadsworth Publishing Co., Belmont, Calif., 1984—reviewed by Frank A. Spencer.

Proceedings of the Ninth International Symposium on Transportation and Traffic Theory, J. Volmuller and R. Hamerslag (editors), VNU Science Press, Utrecht, The Netherlands, 1984, 597 pp—reviewed by Hani S. Mahmassani.
A Stochastic Approach for Estimating the Effectiveness of a Route Guidance System and Its Related Parameters
Authors: Tsuji Hiroyoshi , Takahashi Riichi , Kawashima Hironao , Yamamoto Yoshitsugu
Published: October 2008

Mathematical models are developed for estimating the effectiveness of a route guidance system (RGS) in which the control strategy is to guide vehicles toward the shortest travel time routes. These models are formulated by considering the stochastic nature of travel time. The parameters which characterize the models are defined and a quantitative analysis of the models is given for various values of the parameters. It is shown that the effectiveness of RGS can be estimated by the number of nodes along the route. The results derived from the models are shown to agree with experimental data collected from a route guidance system constructed in Tokyo. Some practical applications of the results are discussed.
Analysis of Vehicle Holding and Cancellation Strategies in Bulk Arrival, Bulk Service Queues
Authors: Powell Warren B.
Published: October 2008

A general class of vehicle dispatching strategies for bulk arrival, bulk service queues is examined which consist of some combination of vehicle holding and cancellation strategies. The moments of the length of the queue at vehicle departure instants and in continuous time are solved for exactly using transform methods. Relationships between the moments of the waiting time and queue length distributions are developed without further use of transforms, resulting in an exact expression for the expected waiting time and an approximation for the variance. A simple approach for calculating the roots of a particular function, needed to find the moments of the queue length distribution, is presented and used to demonstrate that this task can be accomplished very easily. Finally, the model is used to compare alternative vehicle dispatching strategies in terms of costs and levels of service.
Chance Constrained Models for Transport Pricing and Scheduling under Competition
Authors: Charnes A. , Littlechild S. C. , Kirby M. J. L. , Raike W. M.
Published: October 2008

This paper is concerned with the development of a model for planning shipping prices over various routes of a transportation network. It is assumed that over each route a “railroad” (or other transport firm) competes directly with one other shipping firm (e.g., another railroad, a trucker) for the volume of business that is to be shipped over the route. We allow the possibility that the railroad's competition will come from different firms over different routes. The model we consider is a multiroute problem that involves both institutional and physical operating constraints. Each firm's demand depends linearly upon its own and its opponent's price. Since each competing firm sets its price policy independently and before the variable demand is known, some of these constraints cannot be guaranteed to hold with certainty. Thus they are best expressed as chance constraints. The objective of the “railroad” is to maximize its profit subject to the constraints of the model. The solution of the model synthesizes a pricing policy for the “railroad”; we also indicate how variations of the model can be employed in a sensitivity analysis of the suggested policy and discuss the relation between our model and other notions in game theory and chance-constrained games. An example is outlined, and the implications for a welfare-economic pricing policy considered.
A Semi-Poisson Model of Traffic Flow
Authors: Buckley D. J.
Published: October 2008

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. It is concluded that the model or its particularizations predict headways fairly well and could yield some insights into the nature of road traffic.
Delays Caused by Right-Turning Vehicles
Authors: Reid D. H.
Published: October 2008

This paper presents a mathematical model for the behavior of right-turning (left-hand drive is the convention observed) vehicles at an uncontrolled intersection. The model is a development of the one proposed for this situation in a previous paper by the author. It relates to the intersection of a two-lane major road with a minor road at which vehicles on the major road have absolute priority. Completely random traffic is postulated on the major road, and congestion is caused by drivers of vehicles on the major road who wish to turn right and are unable to do so immediately because of oncoming traffic. It is not possible for following vehicles to filter to the left of a delayed vehicle. The delay distribution for vehicles in each lane of the major road is determined for the case of stochastically stationary behavior, and some numerical results for the mean and variance of this distribution are given. The gap acceptance mechanism used in this paper is similar to the one proposed by Gaver. Further references for this paper are discussed in the Introduction to the author's previous paper.
Headstart Strategies for Combating Congestion
Authors: Gaver Donald P.
Published: October 2008

When a traveler, or other user of a congested system, wishes to be reasonably sure of reaching a destination, or finishing a task, on time he must start early enough to compensate for random delays. This paper investigates the headstart decision policy arising if costs are attached both to lateness and to an otherwise undesirable early departure. The model encompasses a case in which the probability distribution of congestion delays is unknown, and must be inferred from previous experience.
Letter to the Editor—“The Effect of the Interstate System on Short-Haul Air Passenger Demand”
Authors: Scheiner James I.
Published: October 2008

Correction of the author's paper, titled as above, in Transportation Science 1, 286–294 (1967).
Book of Interest
Authors: Beckmann Martin J.
Published: October 2008

A review and recommendation of the book The Urban Transportation Problem by J. R. Meyer, J. F. Kain, M. Wohl, Harvard University Press, Cambridge, Massachusetts, 1965, 400 pages, $11.95.
Maximizing Flow Through a Network With Node and Arc Capacities
Authors: Wollmer R. D.
Published: October 2008

In many actual network flow situations, nodes as well as arcs have limited capacities. This paper presents, for such a network, an algorithm for maximizing flow from a source node to a sink node. The algorithm allows us to treat these situations without introducing artificial arcs and nodes, as has been done in the past. Eliminating the artificial arcs and nodes simplifies network analysis since it always results in half as many nodes, as well as less than half as many arcs if the original arcs are undirected. In addition, the following generalization of Ford and Fulkerson’s max-flow, min-cut theorem is presented and proven. Consider two subsets of the nodes, X and Y, whose union is the set of all network nodes and such that the source node is a member of X, and the sink node is a member of Y. Then, forming a cut set separating the source and sink are the nodes in the intersection of X and Y, and the set of all arcs (i, j), such that i is a member of X − Y, and j is a member of Y − X. Letting a cut set's value be the sum of the capacities of all its arcs and nodes, it follows that the maximum flow is equal to the minimum value of all cut sets separating the source and sink.
The Time to Drive Through a No-Passing Zone
Authors: Hodgson Vincent
Published: October 2008

A no-passing zone is a one-line, one-way highway with one entrance and one exit. Interarrival time between successive cars have a known distribution; the distribution of cars’ preferred speeds is also known; interarrival times and preferred speeds are all mutually independent random variables. Each car drives at its preferred speed until obstructed by the car ahead. When obstructed by a slower car, a car closes the distance between the two to zero (cars have zero length) and assumes the speed of the slower car. Thus platoons are formed which behave like individual cars. We find the distribution of the time to drive through the zone and of related random variables. We also find the distribution of the gap in time between platoons leaving the zone and of the number of cars in a platoon. In general, the results are tractable only when arrivals are Poisson or deterministic.
Estimating Minimum Gap Acceptances for Merging Motorists
Authors: McNeil D. R. , Morgan J. H. T.
Published: October 2008

Assume that motorists arrive at a stop sign and wish to merge into traffic on the main road, using the following criterion for making decisions: For each motorist there is a number, X, which is the smallest headway which the motorist will accept before merging into it. For each of these gaps presented to a particular motorist, X is the same, but X varies from motorist to motorist, and has the distribution function FX(x). Assuming the gaps are independent and identically distributed variates, and the merging motorists arrive at times independent of the traffic on the main road, consistent estimates of the moments of X are obtained, using sample values of the accepted and rejected gaps. An estimator of FX(x) is also obtained, without these assumptions. The paper concludes with a numerical analysis using data obtained from an intersection in Sydney.
Books of Interest
Authors: Cleveland Donald E. , Gibson J. E.
Published: October 2008

Review of books: (1) Traffic System Analysis for Engineers and Planners by Martin Wohl and Brian V. Martin, McGraw-Hill Book Company, New York, 1967, 558 pp., $16.50. Library of Congress catalog card no. 67-26355; (2) A Note on the Special Issue on Transportation Proceedings of the Institute of Electrical and Electronics Engineers.
Rapid Transit Interstation Spacings for Minimum Travel Time
Authors: Vuchic Vukan R. , Newell Gordon F.
Published: October 2008

Several factors influencing the optimal interstation spacings for line-haul passenger transportation, for example, rapid transit or commuter railroads, are analyzed with respect to the objective of minimum total passenger travel time. The study concentrates on a case in which the population of an area commutes to one central point. The number and locations of stations at which the commuters board the trains for their travel to the central terminus are to be determined so that the total time of all passengers—from their origins to the destination—is minimal. The model incorporates as parameters: passenger (“population”) distribution along the line, access speed, dynamic characteristics of the train, standing time of the train in stations, and intermodal transfer time at stations. In general, the spacings are functions of the ratio between the number of passengers traveling on the train and those wanting to board or alight. The optimal station locations satisfy a set of simultaneous difference equations. Algorithms for numerical and graphical solutions for several different sets of parameters are presented and demonstrated by examples. For uniform population along the line, spacings increase in an arithmetic progression in the direction of passenger cumulation. In all cases density and distribution of stations have high sensitivity to the access-to-station speed.
Letter to the Editor—The Minimax Transportation Problem
Authors: Goldman Alan J.
Published: October 2008

This note demonstrates a simple solution method for the following single-commodity flow problem: Given a set of origins each with a known supply, and a set of destinations each with a known demand, find the minimum possible capacity for a vehicle which is to perform all the origin-to-destination transfers one at a time.
Zonal Route Design for Transit Corridors
Authors: Furth Peter G.
Published: October 2008

In “zonal express service,” a transit corridor is divided into zones. Each inbound zonal express route picks up passengers in its zone only, then runs express to the CBD; outbound routes do the opposite. In “zonal local service,” on the other hand, an inbound vehicle will stop between its service zone and the CBD to allow passengers to alight, but not to board. Outbound vehicles do the opposite; they will pick up passengers anywhere along the route, but will allow them to alight in the route’s service zone only. Zonal express service design, i.e., the choice of zone boundaries and of service frequencies, has been studied by Turnquist for linear corridors using dynamic programming. These results are extended to zonal design for bidirectional local service, including light direction dead-heading, and to branching as well as linear corridors. Application to a Boston area corridor shows considerable potential for reducing operator cost.
Approximate, Closed Form Moment Formulas for Bulk Arrival, Bulk Service Queues
Authors: Powell Warren B.
Published: October 2008

Traditional analysis of bulk queues has relied on classical transform methods, which requires the determination of the complex zeroes of a given function, or iterative numerical techniques. In this research, transform results are used to help find approximate closed form expressions for the mean and variance of the length of the queue at departure instants. The moments of the length of the queue in continuous time and of the waiting time distribution are derived in closed form as a function of the new formulas. An approximate method for fitting a distribution for the length of the queue is provided and used to calculate the probability a customer will leave on a given outbound vehicle. Finally, approximate queueing and delay formulas are developed for bulk queues operating under a vehicle cancellation policy.
Bibliographic Section
Authors: Boyce David E.
Published: October 2008

Transportation Research: The State of the Art and Research Opportunities, D. E. Boyce, guest editor, Transportation Research, 19A, 349–542 (1985)—reviewed by David E. Boyce.
Euclidean Distance Location-Allocation Problems with Uniform Demands over Convex Polygons
Authors: Cavalier Tom M. , Sherali Hanif D.
Published: October 2008

In this paper we consider location-allocation problems in which the region to be served is a convex polygon having a uniform demand distribution. Both single and multifacility formulations are considered. For the single facility problem, an algorithm which uses an efficient implementation of the Weiszfeld technique is developed and is shown to converge to a global optimal solution. This analysis is extended to the nonconvex multifacility case. However, although global optimality of the fixed point that the algorithm converges to is not guaranteed, a method suggested for finding a good starting solution increases the likelihood of finding an optimal solution. Extensions of the above problems to include discrete demand points and computational experience are also provided.
A Sequential Shipper-Carrier Network Model for Predicting Freight Flows
Authors: Friesz Terry L. , Gottfried Joel A. , Morlok Edward K.
Published: October 2008

A sequential shipper-carrier predictive freight network model is presented. This model is applied to three detailed network data bases. The predicted arc loadings are compared to published railway arc density codes and goodness-of-fit measures are reported for the origin-destination flows of 15 commodities. A discussion of some sources of error in the model and recommendations for further research to lessen that error are given.
Bibliographic Section
Authors: Wolfe Robert A.
Published: October 2008

Transportation Investment and Pricing Principles, Martin Wohl and Chris Hendrickson, John Wiley & Sons, New York, 1984—reviewed by Robert A. Wolfe.
Individual Decisions and Collective Effects in a Simulated Traffic System
Authors: Mahmassani Hani S. , Chang Gang-Len , Herman Robert
Published: October 2008

The interdependence of the time-dependent behavior of traffic flows and tripmakers' departure time decisions is central to the analysis of congestion phenomena. The study of the day-to-day dynamics of this interaction in the field is hampered by the inability to obtain adequate data. This paper presents an experimental approach involving real commuters, whereby a traffic simulation model is used to predict congestion patterns under given departure distributions resulting from the actual decisions of the individual participants. These decisions are updated daily, in response to information on prior system performance predicted by the simulation model. The results of this experiment are described in this paper, with emphasis on the system's evolution and dynamic properties, particularly convergence. In addition, concentration and congestion patterns as well as the associated travel time variability are addressed. Initial insights into the processes underlying user behavior in this system are also presented.