Showing papers in "Transportation Science in 1971"
TL;DR: 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.
Abstract: 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.
378 citations
TL;DR: In this paper, it is shown that if the capacity of the vehicles is sufficiently large to serve all waiting passengers and n is large, then the optimal flow rate of vehicles and the number of passengers served per vehicle, both vary with time approximately as the square root of the arrival rate of passengers.
Abstract: Suppose that a given number n of vehicles (buses, trains, etc.) maybe dispatched at any times from some source to serve passengers along a route. The arrival rate of passengers is some given (nonconstant) smooth function of time, typically having one or more peaks. One wishes to choose the dispatch times tj, j = 1, …, n in such a way as to minimize the total waiting time of all passengers. It is shown that if the capacity of the vehicles is sufficiently large to serve all waiting passengers and n is large, then the optimal flow rate of vehicles (reciprocal of the headways) and the number of passengers served per vehicle, both vary with time approximately as the square root of the arrival rate of passengers. If the vehicles have limited capacity, their dispatch schedule will be distorted so that certain vehicles are dispatched as soon as they are full.
239 citations
TL;DR: In this article, a model for determining airline overbooking policies is presented, which is formulated as a nonhomogeneous Markovian sequential decision process, and solutions that are optimal in several different senses are obtained with the aid of dynamic programming.
Abstract: A model for determining airline overbooking policies is presented. The problem is formulated as a nonhomogeneous Markovian sequential decision process. Solutions that are optimal in several different senses are obtained with the aid of dynamic programming. An example based upon airline data illustrates the character of the policies and the sensitivity of the model with respect to certain parameters.
201 citations
TL;DR: An extended traffic assignment model where the traveling cost on a link becomes a function of the entire flow pattern in the network is introduced and appears particularly suitable for application to networks containing two-way streets.
Abstract: A transportation network is considered. The traffic demands associated with pairs of nodes and the traveling cost functions associated with the links are assumed given. An extended traffic assignment model where the traveling cost on a link becomes a function of the entire flow pattern in the network is introduced. The model appears particularly suitable for application to networks containing two-way streets, in view of its capability of taking into account delays to travelers of one lane caused by traffic on the opposite lane. It is also suitable for application to urban transportation networks, where the travel time on a link depends crucially on the delays occurring at the intersections. This in turn depends on the traffic volumes on the intersecting links. The concepts of system-optimizing and user-optimizing traffic patterns are studied. Moreover, an algorithm for the construction of the above patterns is presented and applied in an example.
184 citations
TL;DR: A method is discussed for estimating the number of vehicles on a section of a roadway from speed and flow measurements at the entrance and exit points of the section, and emphasis is placed on economy in instrumentation and data processing.
Abstract: A method is discussed for estimating the number of vehicles on a section of a roadway from speed and flow measurements at the entrance and exit points of the section. The method consists of obtaining rough estimates of this count at regular intervals, and then filtering random errors of these estimates by means of a sequential correction scheme. Emphasis is placed on economy in instrumentation and data processing.
157 citations
TL;DR: In this article, the authors formulated models of fleet routing and scheduling problems for transportation systems as integer linear programs with 0-1 variables and proposed a solution technique of the Land-and-Doig type.
Abstract: Models of fleet routing and scheduling problems for transportation systems are formulated as integer linear programs with 0-1 variables. Detailed formulations and a solution technique of the Land-and-Doig type are presented and demonstrated on examples. The conclusion is that large scale models can be solved using this technique.
126 citations
TL;DR: In this article, two integer programming methods, Branch-and-Bound (B&B) and Decomposition (DWC), are used to solve vessel scheduling problems, where the branching is performed on one of the essential fractional variables and the bounds are obtained by the decomposition algorithm.
Abstract: In a previous paper, Appelgren (Appelgren, L. 1969. A column generation algorithm for a ship scheduling problem. Trans. Sci. 3 53–68.), a decomposition algorithm for a class of vessel scheduling problems was presented. In some problems, the algorithm gives fractional solutions that cannot be interpreted as feasible schedules. This paper treats two integer programming methods that can be used to resolve these cases. The cutting plane method that was first tested was abandoned because it was not able to solve all the test problems. The second method is a branch-and-bound algorithm, where the branching is performed on one of the “essential” fractional variables and where the bounds are obtained by the decomposition algorithm. All fractional problems that have been found by simulation or in regular use of the algorithm have been solved, mostly with one branching only. There are fundamental difficulties in combining these integer programming methods with the Dantzig-Wolfe decomposition, since the constraints g...
103 citations
TL;DR: In this article, the authors presented a 3D model of traffic flow on a roadway, where the trajectories of vehicles on the same x − t graph can be interpreted as the contours of a three-dimensional surface for which the third dimension is vehicle number n. If the surface is smoothed, the orientation of the tangent plane at any point determines the flow q, density k, and car velocity v.
Abstract: If one numbers vehicles consecutively along a roadway and draws the space-time trajectory of each vehicle on the same x − t graph, then this family of curves can be interpreted as the contours of a three-dimensional surface for which the third dimension is vehicle number n. The intersection of the surface with planes of constant x are the cumulative arrival curves, n vs. t, at the location x. If the surface is smoothed, the orientation of the tangent plane at any point determines the flow q, density k, and car velocity v. All commonly observed properties of traffic flow have simple geometric interpretations in this three-dimensional model.
87 citations
TL;DR: In this article, a general utility maximization model on the level of individual trip-making decisions is developed from basic hypotheses regarding the costs and benefits attributed to travel disaggregated into individual trips.
Abstract: This paper shows how the problem of predicting traveler behavior may be approached in terms of economic utility theory. A general utility maximization model on the level of individual trip-making decisions is developed from basic hypotheses regarding the costs and benefits attributed to travel disaggregated into individual trips. For predictive purposes the form of the utility functions involved must be specified, and several possibilities are explored. The functional forms of the resulting travel demand functions are then derived. In order to pursue an analysis of variations in traveler behavior and in order to perform aggregation over individuals, disturbances in the parameters of the utility functions are considered. The parameters investigated are marginal utilities and the distributions used are normal distributions. In considering binary choices, a trip demand model, a modal split model, and a destination split model are obtained from the same basic methodology. Finally, possible approaches to testi...
73 citations
TL;DR: In this article, a combined traffic distribution-assignment model is formulated as a mathematical program, based on the equilibrium traffic distribution model and a linear programming assignment model, and the behavior of this model using the Dantzig-Wolfe decomposition principle is investigated.
Abstract: The traffic assignment and distribution problems are customarily treated as though they were independant rather than related and interacting. In this paper a combined traffic distribution-assignment model is formulated as a mathematical program, based on the equilibrium traffic distribution model and a linear programming assignment model. The behavior of this model using the Dantzig-Wolfe decomposition principle is investigated and illustrated by means of an example. A number of areas for extension are indicated and an alternative formulation that has certain advantages is also given.
53 citations
TL;DR: In this article, the authors presented a method for determining the optimum location of ambulance stations to minimize the average response time to emergency calls in large medical centers, where the existence of well equipped, well staffed and rapid emergency ambulance service becomes increasingly important.
Abstract: As large medical centers become ever more capable, the existence of well equipped, well staffed, and rapid emergency ambulance service becomes increasingly important This paper presents a method for determining the optimum location of ambulance stations to minimize the average response time to emergency calls A new point-to-point driving time model is introduced, and a computer optimization algorithm used to determine the optimum locations A constraint that the average response time to any point in the service area be less than some specified minimum is also considered The method is applied to Washtenaw County, Michigan
TL;DR: In this article, a branch-and-bound enumerative scheme in conjunction with a decomposed linear program with network sub-problems is presented to solve the Dantzig and Fulkerson tanker scheduling problem.
Abstract: The Dantzig and Fulkerson Tanker Scheduling Problem is concerned with the determination of the minimum size and optimal routing of a fleet of homogeneous tankers needed to meet a prescribed schedule of deliveries. This problem has been formulated as a network flow problem. Later formulations consider an existing nonhomogeneous tanker fleet and relax the fixed shipping schedule. These problems are treated as multicommodity minimal cost flow problems. This paper further extends the problem to consider differing carrying capabilities of the vehicles and formulates a mixed integer linear program that permits partially loaded tankers. A branch-and-bound enumerative scheme in conjunction with a decomposed linear program with network sub-problems is presented.
TL;DR: In this article, a generalized analysis of the effects of on-ramp time varying flow on unidirectional n-lane freeways is presented, which incorporates the speed-density relations for every lane, which are then used to set up separate continuity equations for each lane and are coupled by some reasonable lane-changing hypotheses.
Abstract: This paper presents a generalized analysis of the effects of on-ramp time varying flow on unidirectional n-lane freeways. The analysis incorporates the speed-density relations for every lane, which are then used to set up separate continuity equations for every lane and are coupled by some reasonable lane-changing hypotheses. The paper assumes the same wave velocities (uniform freeway) for the perturbed flow in each lane of a freeway. Using the generalized n-lane analysis, the paper then predicts the relative propagation of density perturbations in time and space in different lanes of a two-lane, three-lane, and four-lane freeway. The corresponding relaxation distances from the on-ramp, where the initial perturbation had started, have been defined and compared for the two-lane, three-lane, and four-lane freeway. The above studies have then incorporated the effects of controlled ramp flow by suitable mathematical expressions that simulate controlled ramp flow.
TL;DR: In this paper, an algorithm is proposed to guide the selection of a fleet of equi-cost vehicles for a public transport route based on the Pareto optimum principle, which reduces the range from which the choice can be made.
Abstract: For the same total cost, a public transport route can be served by few large vehicles or more smaller ones. The problem is posed: which out of all equi-cost fleets to select? An algorithm is proposed to guide such selection. To avoid potentially controversial value judgments, the algorithm is based on systematic reduction of the range from which the choice can be made. Considerable reduction in the range of choice can be achieved making use of the “Pareto optimum” principle alone. Analysis is based on a mathematical model describing the relation between the route fleet and characteristics of service to the passenger.
TL;DR: In this article, a model for merging from an acceleration lane of finite length is presented, where the gap acceptance function is assumed to be a step function and the distribution of headways is negative exponential.
Abstract: A model is presented for merging from an acceleration lane of finite length. It is assumed that a car in the acceleration lane travels at speed v while the traffic on the main road travels at speed V > v. A merging car reaching the end of the lane stops instantaneously. The gap acceptance function is assumed to be a step function and the distribution of headways is negative exponential. An expression for the expected delay is given. The calculations suggest that the expected delay does not depend strongly on the length of the acceleration lane, and that most of the merging occurs near the beginning of the lane. Increasing the length of the lane beyond some necessary length, say 600 ft, results in relatively little further benefit in merging.
TL;DR: In this article, a computer control scheme is developed that concentrates upon providing real-time, traffic-responsive corrective action for a critical intersection, defined as a point in the network at which primary driver routes cross or those where congestion has arisen for other reasons.
Abstract: 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,” 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 sub-optimal scheme attempts to minimize the total delay, measured in vehicle-seconds, not only to all users of the intersection but also of accumulated delay at downstream intersections. Within upper and lower limits on the cycle time, the control of the traffic signal is variable split and variable cycle-length in response to traffic needs. A simulation evaluation of the method is given via several test cases, using as a base case actual traffic data from San Jose, California.
TL;DR: In this article, the variability in the round-trip time of an elevator car is studied and the usefulness of solutions obtained from an optimization procedure in which roundtrip time was assumed constant.
Abstract: The variability in the round-trip time of an elevator car is studied. Using the derived analytical expressions for the variance of round-trip time, we can evaluate the usefulness of solutions obtained from an optimization procedure in which round-trip time was assumed constant. Also, it is shown by numerical examples why passenger-carrying capability can be increased by operating a single bank of cars as two independent banks.
TL;DR: In this paper, the decision process of how to allocate cars to upper floors is formulated as a dynamic programming problem and the solution to the dynamic program for a given arrangement of cars is the banking policy in which the time to fill the building completely (under heavy up-traffic) is minimized.
Abstract: An important design criterion for elevator installations in modern office buildings is the carrying capability during the morning rush-hour. It is common practice to divide the total number of cars into banks, each bank serving a common set of upper floors with an express run to the lowest of these floors. The decision process of how to allocate cars to upper floors is formulated as a dynamic programming problem. Solution to the dynamic program for a given arrangement of cars is the banking policy in which the time to fill the building completely (under heavy up-traffic) is minimized.
TL;DR: In this paper, the authors derived vehicle interaction criteria as a function of flow rate for each lane of a two-lane one-way highway and used a statistical analysis to determine the time headways below which vehicle interaction occurs (at the 1 per cent significance level).
Abstract: Vehicle interaction criteria are derived as a function of flow rate for each lane of a two-lane one-way highway. The data used were obtained from time series measurements at the flow rates of 1,479, 2,311, and 3,505 vehicles per hour. The basic approach is to study the dependency between successive speeds introduced by the interaction process. This study has shown that the phase of traffic flow for which vehicle interaction occurs can be defined in terms of time headway. A statistical analysis is used to determine the time headways below which vehicle interaction occurs (at the 1 per cent significance level); the resulting values vary between 2.5 sec and 4.3 sec depending on lane number and traffic flow rate. Plots of mean absolute relative speeds versus time headway show the effect of vehicle interaction as a function of time headway.
TL;DR: A model for the flow of automobiles in one direction along a two-lane, country road exhibits a sudden change from sparse-traffic conditions, where queuing is rare and delay of the faster cars is minimal, to dense-tra traffic conditions where nearly all cars find themselves trapped in a slow queue, as the passing-delay parameter is increased beyond its transitional value.
Abstract: A model is developed for the flow of automobiles in one direction along a two-lane, country road. The model takes into account the fact that cars differ in speed, that slower cars accumulate queues behind them, and that the rate of escape from such a queue, by passing the lead car, depends on the speed of the lead car, on the nature of the road, and on the density of traffic going in the opposite direction. Equations for the stochastic steady state of the system reduce to an in-integral equation for the mean queue length, as a function of lead-car speed and of a queue-delay parameter. Solutions are obtained, with tables and graphs, for two different assumptions regarding the dependence of passing delay on lead-car speed. In both cases the model exhibits a sudden change from sparse-traffic conditions, where queuing is rare and delay of the faster cars is minimal, to the dense-traffic conditions where nearly all cars find themselves trapped in a slow queue, as the passing-delay parameter is increased beyond...
TL;DR: The mean speed of the steady-state speed distribution is investigated and it is shown that all the parameters in the model, at least for the determination of the mean speed, can be effectively consolidated into a single parameter.
Abstract: In a Boltzmann-like description of traffic developed by Prigogine, et al., the speed distribution has been expressed as an implicit function in terms of its own mean. In order to determine the speed distribution, it is, therefore, necessary to first determine the mean speed of the distribution. In this paper, the mean speed of the steady-state speed distribution is investigated. The mean speed is determined on the basis of the intersection of two functions; one of the functions is given by the desired speed distribution, which is a description of the goals that drivers want to attain in traffic; the other function is given by the concentration-dependent traffic parameters of the model. These parameters give a description of the restrictions that drivers exert on each other in the process of attaining their individual goals. Since the model is basically a description of the interaction between these two conflicting traffic characteristics, the effect on the mean speed due to each characteristic can hence b...
TL;DR: In this paper, an elementary model defining maximum entropy populations for a set of nodes is developed, where nodes are connected by a simple transportation network to a central point where all work places are concentrated.
Abstract: An elementary model defining maximum entropy populations for a set of nodes is developed. These nodes are connected by a simple transportation network to a central point where all work places are concentrated. A congestion cost function is defined for network arcs. Then the model yields an equilibrium solution that identifies nodal populations as an entropic function of the total cost of the journey to work.
TL;DR: This paper shows how to determine the optimal number and routings of containers used to move mail among several cities using a network flow linear program for which efficient solution methods are known.
Abstract: Generalizing work of Samuel and Ullmann, this paper shows how to determine the optimal number and routings of containers used to move mail among several cities. Critical assumptions are (a) periodic demand patterns and linear transportation costs (for full or empty containers, or uncontainerized mail) between each city-pair, and (b) constant fixed cost per container in the system. The optimization problem is transformed into a network flow linear program for which efficient solution methods are known.
TL;DR: In this paper, a method has been developed for determining the mean speed of the speed distribution in the Boltzmann-like traffic theory developed by Prigogine, et al. This method was extended to more general functional forms assumed for the details of the interaction, relaxation, and adjustment processes.
Abstract: A method has recently been developed by the authors for determining the mean speed of the speed distribution in the Boltzmann-like traffic theory developed by Prigogine, et al. This method has now been extended to more general functional forms assumed for the details of the interaction, relaxation, and adjustment processes. The mean speed for the more general case is again expressed in terms of the intersection of two mathematical functions identical to those previously obtained. On the basis of this method a numerical procedure for calculating the mean speed is given. For most reasonably well behaved desired speed distributions this method offers satisfactory rates of convergence and is applicable for both the “individual” and “collective” flow cases.
TL;DR: In this article, the authors apply an earlier non-emographic factor modal split model to business travel from Washington, D.C., to New York and Philadelphia, and use survey data to calibrate the model and predict the future market shares of both hypothetical and contemporary intercity travel modes operating in this section of the Northeast Corridor.
Abstract: Expanding an earlier nondemographic factor modal split model, the author applies a revised model to business travel from Washington, D.C., to New York and Philadelphia. Actual businessman survey data is used to calibrate the model and to predict the future market shares of both hypothetical and contemporary intercity travel modes operating in this section of the Northeast Corridor.
TL;DR: In this paper, the authors quantified the incommensurable and imputed monetary values impacts of the transportation system technologies planned for the Northeast Corridor on: noise, air pollution, aesthetics, safety, and air and highway congestion.
Abstract: Rational decision making in the transportation sector cannot be undertaken without consideration of the important externalities or third party effects. This paper presents the quantification of the incommensurable and imputed monetary values impacts of the transportation system technologies planned for the Northeast Corridor on: noise, air pollution, aesthetics, safety, and air and highway congestion. A final tableau of social benefits summarizes the imputed monetary values of incremental environmental and social impacts of the following modes—high-speed rail, tracked air cushion vehicles, STOL, and VTOL—over the social costs of a 1975 base case composed of auto, bus, conventional air, and the continuation of current demonstration rail projects underway. The magnitudes of environmental and external nonuser benefits are compared with the magnitudes of direct benefit categories represented by net revenues and value of users' time savings.
TL;DR: In this paper, a hyperbolic partial differential equation is set up, and expressions 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 operation had registered a given amount of cumulative units on or before a specified time.
Abstract: 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 (eg, distance) and for the probability that the operation has registered a given number of cumulative performance units on or before a specified time
TL;DR: In this article, the optimal size of the container inventory for a two-gateway system is determined, according to which containers are acquired until the last container produces savings just greater than the costs incurred due to empty trips.
Abstract: The optimal size of the container inventory for a two-gateway system is determined. A rule is found, according to which containers are acquired until the last container produces savings just greater than the costs incurred due to empty trips. The actual size of the optimal inventory depends on container costs, the costs of shipping full and empty containers, the cost of shipping mail uncontainerized, and the probability distribution of the volume in each direction. Numerical results are given for two parcel-post systems.