An equivalent optimization problem for combined multiclass distribution,assignment and modal split which obviates symmetry restrictions

This paper presents a model for combined multiclass trip distribution, trip assignment and modal split. Although this model is based on an equivalent optimization problem, it avoids the symmetry restrictions heretofore always associated with such approaches to multiclass trip assignment. This is accomplished by expressing Wardrop's first principle as a set of nonlinear constraints in standard mathematical programming form. An algorithm is proposed, each iteration of which requires solving a nonlinear program with linear constraints.     

Bregman's balancing method

In this paper we observe that most of the independently discovered balancing methods, used in transportation planning and in other fields, are in fact special cases of a method of Bregman. Examples include the usual Kruithof or Furness method, the Evans-Kirby three dimensional balancing procedure, the Murchland multiproportional balancing procedure, the Osborne or Grad method for preconditioning matrices, the Jefferson-Scott procedure for gravity models with inequality constraints, and the method considered by Macgill for partially constrained gravity models. The convergence of all of these methods follows from Bregman's general result.     

Traffic control and route-choice; a simple example

The paper considers, in a simple case, the interaction between Webster's Method and drivers' route-choice decisions. In the example considered the overall network capacity is severely reduced by using Webster's Method. This shows that Webster's Method does not, in general, maximize the travel capacity of a road network. The analysis of this simple case suggests a signal-setting policy which does maximize the travel capacity of a general network.     

Further evidence on the temporal stability of disaggregate travel demand models

Current evidence on the transferability of disaggregate travel demand models is inconclusive. Adding to this body of research, the present analysis focuses upon the temporal characteristics of work trip behavior in the San Francisco Bay Area. Using before and after data sets associated with the BART Impact Travel Study, multinomial logit models of work trip modal choice are estimated. The results indicate that the general form and the coefficient estimates of a pre BART model are transferable in time. Moreover, when updated to reflect BART's presence, the model's predictive success and its implied elasticity measures are generally accurate, relative to those implied by reestimating the entire model on post BART data. Finally, as economic theory would predict, elasticity measures of the service related variables were found to increase over time.     

On the convergence of iterative methods for the distribution balancing problem

A general distribution balancing problem, specified by the given outflows and inflows and the factorial form of its solution, is formulated. Solution uniqueness and boundedness is discussed—primarily in graph theoretical terms. An entropy maximisation problem, subject to general linear constraints, is transformed into an unconstrained optimisation problem by application of standard duality theory, and a relevant general convergence theorem for iterative solution methods is given. The optimum solution in a special case is identified with the flow solution. When expressed in flow variables, the dual objective has a unique and bounded optimum solution and is an appropriate unifying concept for measuring the rate of convergence of different solution methods. By regarding the balancing procedure as an iterative optimisation method, a new and simple proof of its convergence is given, together with some asymptotic results, which are also compared with those of Newton's method. It is pointed out that there are two different forms of Newton's method, according to the choice of variables—untransformed or transformed— in the original distribution balancing problem. When Newton's method is applied to the whole system of equations simultaneously, the trajectory of iterates is observed to depend on this variable choice. For the transformed variables it is noticed that the convergence with the balancing procedure is quicker than with Newton's method applied to the outflow- and inflow- equations, alternately. To guarantee global convergence with Newton's method and to increase the rate a supplementary linear search routine is recommended.     

An algorithm for the combined distribution and assignment problem

Much interest has recently been shown in the combination of the distribution and assignment models. In this paper we adopt a generalized Benders' decomposition to solve this combined problem for a system optimized assignment with linear link costs and explicit capacity constraints on link flows. The master problem which is generated is used to show that the combined problem can be viewed as a modified distribution problem, of gravity form, with a minimax instead of a linear objective function. An algorithm for solving the master problem is discussed, and some computational results presented.     

Statistical estimation of the parameters of Daganzo's gap acceptance model

In a recent article in Transportation Research, Daganzo (1981) described a model of gap acceptance that permits the mean of the gap acceptance function to vary among drivers and permits the duration of the shortest acceptable gap for each driver to vary among gaps. The model contains several constant parameters whose values must be estimated statistically from observations of drivers' behavior. The results of numerical experiments reported by Daganzo (1981) suggested that the values of the parameters cannot be estimated by the method of maximum likelihood, which is the most obvious estimation technique, and Daganzo proposed using a sequential estimation method instead. The sequential method appeared to yield reasonable numerical results. In this paper, it is shown that subject to certain reasonable assumptions concerning the true parameter values and the probability distribution of gap durations, the maximum likelihood method does, in fact, yield consistent estimates of the parameters of Daganzo's model, whereas the sequential method does not. Hence, maximum likelihood is the better estimation method for this model.     

A regional railroad network optimization model for coal transportation

A regional railroad network is presented to evaluate the system's response to increased coal traffic. An optimal, multimodal, coal-shipping pattern is developed for the study region to minimize total costs and to efficiently use the existing network. A two-stage, general model allocates resources among demands and then assigns flows to the network according to efficiency criteria. The model is sufficiently general to permit modification for specific needs, assumptions and data. Government agencies and industries can apply the model in resource allocation decisions and transportation policy analysis.     

A microeconomic interpretation for the system optimal traffic assignment problem with nonadditive path cost

Using a Bergson–Samuelson welfare function, we outline a microeconomic interpretation of the effects of the non-linearity in the time/cost relationship for travellers in a congested transport network. It is demonstrated that a marginal cost traffic flow assignment following Wardrop's second principle, although it minimizes the total cost of a transport network, may reduce social welfare compared to the market equilibrium assignment based on Wardrop's first principle. A welfare-maximizing assignment model is presented and used to show that if the travellers' utility functions are linear, the assignment that maximizes social welfare will be the same as the assignment that minimizes total network cost, but if users' utility functions are non-linear (reflecting the traditional non-satiation and diminishing marginal utility axioms), the two assignments will be different. It is further shown that the effects of this non-linearity are such that a welfare-maximizing assignment will meet with less user resistance than a minimum total network cost assignment.     

再生沥青混合料理论最大相对密度确定方法研究

再生沥青混合料内部孔隙较多,掺入的旧料为沥青与集料裹合物,依据规范现有的计算法与试验法难以确定其理论最大相对密度。基于沥青混合料理论最大相对密度计算法和实测法测定原理,通过新拌不同级配类型的沥青混合料,建立理密计算值与实测值关系系数,以再生沥青混合料实测值计算真实值,修正再生沥青混合料理密计算和试验公式。     

A comparative study of aggregate and disaggregate gravity models using Seoul metropolitan subway trip data

Abstract

Existing origin constrained and doubly constrained gravity models have not been compared, theoretically or empirically, in terms of their forecasting power. Due to the newly advanced technology of intelligent transport systems, the expanded data presently available have made various models more comparable in terms of forecasting power. This paper uses archived automatic passenger counting (APC) data for urban rail in the Seoul metropolitan area. The APC data contains information about each trip's origin, destination, ticket type, fare, and distance on a daily basis. The objective of this paper is to compare the goodness-of-fit of aggregate and disaggregate gravity modeling using these data. A Hyman aggregate gravity model is used as the aggregate model without the spatial effect. The disaggregate model adopts a multinomial logit as the destination choice model with the spatial effect. In general, while the formulation of aggregate and disaggregate gravity model models are similar, the calibration and parameter estimation methods of the two models are different. As a result, this empirical study demonstrates that the variation in goodness-of-fit and forecasting power largely depends on the estimation method and selected variables. The forecasting power of the disaggregate modeling approach outperforms that of the aggregate model. This paper further confirms that spatial arrangement plays important roles in gravity modeling.     

A model of traffic dispersion from a congested road

The study of traffic flow dynamics is developed by defining and clarifying traffic divergence, continuity, congestion and dispersion. Velocity potential is introduced as a gravity function generated by the interaction of two or more motorists occupying neighbouring points in space and describes interference to continuous traffic flow. The relationship between the potential function and carrying capacity is developed and dispersion, when considered as a random walk, satisfies a diffusion equation. A model of traffic dispersion along a maximum congested road in space and time is presented as eigenfunctions of the velocity potential. This suggests that traffic can be dispersed by a series of quantum steps. A probability density function is introduced to define the probability of locating a motorist in a congestion zone.     

Measuring the benefits derived from a transportation investment

This paper reviews the problems associated with application of the concept of consumers' surplus to the measurement of benefits derived from a transportation investment. This review is warranted since such measurement is very complicated when alternative modes or different paths are available to the users and benefit measures have been proposed which, on the surface, appear not to agree. In particular, as Mohring (1976), Williams (1976) and Agnello (1977), among others, have discussed, demand curves for interdependent modes will shift in response to a modal specific improvement, i.e. a unimodal investment, thereby complicating the measurement of consumers' surplus. The perspective taken in this paper resolves seeming inconsistencies in the literature regarding the directions of demand shifts and the correct measure to be used in calculating changes in consumer's surplus following an investment. This is accomplished by introducing an aggregate, origin-destination demand curve which is independent of the alternative modes actually available and from which traditional modal demands can be derived. An approach for deriving the modal demands from the aggregate demand and the behavioral assumptions behind the aggregate supply is described; the aggregate demand is used to unequivocably determine the directions of shifts in the modal demand curves due to specific modal investments. The resulting consistency of modal and aggregate demand is shown to lead to an unambiguous measure of total consumers' surplus variation. Extensions to include producers' surplus are also given.     

Traffic assignment in a two-dimensional continuous representation of a traffic network with flow-dependent speeds

The work deals with the assignment of traffic to a two-dimensional continuous representation of a traffic network. An important aspect of the treatment is that the reciprocal of the speed on each road in the network is at all times a linear function of the flow on that road. This speed-flow relationship is generalized to two-dimensional space using travel intensities and taking account of road densities, so that there is direct dependence of speeds upon flows at all points regardless of their location. There is also dependence of flows upon speeds at all points because Wardrop's first assignment principle is adopted. That is, for a given O-D pair, journey times on all routes actually used are identical, and less than journey times on all other possible routes. This results in the identification for each O-D pair of an “assignment zone”, an area within which all trips between that O-D pair are made, and beyond which no such trips are made. For a single O-D pair the assignment zone is identified by ?_m, the maximum angular divergence of a path from the straight line between O and D. Paths are then assumed to be bilinear so that for a single O-D pair the assignment zone is a parallelogram. Journey times, speeds, lateral displacement and other related quantities are obtained as functions of the flow Q between O and D. The work is extended to three O-D pairs located at the extremities of an equilateral triangle and four O-D pairs located at the corners of a square. At low flows these two configurations are trivial extensions of the single O-D pair problem because assignment zones do not overlap. At higher flows account is taken of this tendency to overlapping, so that although they do not overlap they do touch, becoming kite-shaped. Origins and destinations are assumed to be at the periphery of small circles of arbitrary radius. The work is inelegant to the extent that it involves a numerical integration but it is possible that this might eventually be circumvented.     

Analysis of an O(N2) heuristic for the single vehicle many-to-many Euclidean dial-a-ride problem

We develop an O(N²) heuristic to solve the single vehicle many-to-many Euclidean Dial-A-Ride problem. The heuristic is based on the Minimum Spanning Tree of the modes of the problem. The algorithm's worst case performance is four times the length of the optimal Dial-A-Ride tour. An analysis of the algorithm's average performance reveals that in terms of sizes of single-vehicle problems that are likely to be encountered in the real world (up to 100 nodes) and in terms of computational complexity, the O(N²) heuristic performs equally well, or, in many cases, better than heuristics described earlier by Stein for the same problem. The performance of the heuristic exhibits statistical stability over a broad range of problem sizes.     

Optimal scheduling of public transport fleet at network level

This paper deals with the development of a strategic approach for optimizing the operation of public transport system that considers both user's objective and operator's objective. Passengers of public transport are assumed to seek a minimum wait time to conduct the trips, while on the other hand, operators are concerned with the efficient operation such as minimum fleet size. The average minimum wait time is to be achieved by creating an optimal despatching policy for each vehicle from the terminal. As for efficient operation the utilisation of vehicle should be maximised by having a minimum number of vehicles in operation. User's and operator's objectives are optimized within certain operational constraints such as vehicle capacity to maintain acceptable level of service. The i‐model is contructed in a bi‐level programming form in which the user's objective is minimized by dynamic programming and the operator's objective is minimized by various routing strategies. Furthermore, an algorithm and a contrived example are developed to solve and see the performance of the approach.     

A microscopic simulation model for merging control on a dedicated-lane automated highway system

The automated highway systems (AHS) are not designed as stand-alone transportation facilities. Drivers will by necessity drive from their origins to the AHS entrance, and from the AHS exit to their final destinations. Therefore, the AHS will affect other transportation facilities, and should be integrated with all other facilities in the transportation system. Interfaces create much of the congestion for today’s transportation systems. Likewise, AHS interfaces may cause a similar problem, due to either AHS interactions with conventional systems or internal limitations from AHS merging capabilities. If these problems exist, either the AHS or the conventional road network cannot function properly. Consequently, the system as a whole may break down and the AHS could potentially become a detriment to the overall transportation system.Clearly, not enough is known about the automated merging process to determine what conditions would lead to congestion at interface points. The current macroscopic analysis techniques assume parameters that are not applicable to an AHS, and no detailed AHS merging models have been developed and validated. This paper addresses the interface problem between an AHS, and conventional roadway. Specifically, it presents a microscopic simulation model for one scenario of the automated merging maneuver. The results of the model show that for low flows and conventional highway speeds, an one-lane AHS merging section with a dedicated automated entrance ramp has many similar characteristics as a two-lane conventional freeway with or without fixed-time ramp metering. However, when the conventional freeway starts to “break down” near its capacity, the AHS continues to perform with little delay. The model also validates that the minimum ramp length requirements are a function of the merging vehicle’s speed, the mainline vehicles’ speed, and the acceleration and deceleration rates of the merging vehicle.     

Bus garage location planning with dynamic vehicle assignments: A methodology

A simultaneous vehicle scheduling and bus garage location and sizing optimization is described. The methodology's importance lies in its treating garage locations and sizes and vehicle schedules as dynamic. In other bus garage planning methodologies, vehicle schedules are assumed fixed.     

On some traffic equilibrium theory paradoxes

We consider the asymmetric equilibrium problem with fixed demands in a transportation network where the travel cost on each link may depend on the flow on this as well as other links of the network and we study how the travellers' cost is affected by changes in the travel demand or addition of new routes. Assuming that the travel cost functions are strongly monotone, we derive formulas which express, under certain conditions, how a change in travel demand associated with a particular origin-destination (O / D) pair will affect the travelers' cost for any O / D pair. We then use these formulas to show that an increase in the travel demand associated with a particular O / D pair (all other remaining fixed) always results in an increase in the travelers' cost on that O / D pair, however, the travelers' cost on other O / D pairs may decrease. We then derive formulas yielding, under certain conditions, the change in travelers' cost on every O / D pair induced by the addition of a new path. These can be used to determine, whether Braess' paradox occurs in the network. We then show that when a new path is added, the travelers' cost associated with the particular O / D pair joined by this path will decrease (hence Braess' paradox does not occur) if a test matrix is positive semidefinite.