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.     

Path-constrained traffic assignment: A trip chain analysis under range anxiety

This paper proposes and analyzes a distance-constrained traffic assignment problem with trip chains embedded in equilibrium network flows. The purpose of studying this problem is to develop an appropriate modeling tool for characterizing traffic flow patterns in emerging transportation networks that serve a massive adoption of plug-in electric vehicles. This need arises from the facts that electric vehicles suffer from the “range anxiety” issue caused by the unavailability or insufficiency of public electricity-charging infrastructures and the far-below-expectation battery capacity. It is suggested that if range anxiety makes any impact on travel behaviors, it more likely occurs on the trip chain level rather than the trip level, where a trip chain here is defined as a series of trips between two possible charging opportunities (Tamor et al., 2013). The focus of this paper is thus given to the development of the modeling and solution methods for the proposed traffic assignment problem. In this modeling paradigm, given that trip chains are the basic modeling unit for individual decision making, any traveler’s combined travel route and activity location choices under the distance limit results in a distance-constrained, node-sequenced shortest path problem. A cascading labeling algorithm is developed for this shortest path problem and embedded into a linear approximation framework for equilibrium network solutions. The numerical result derived from an illustrative example clearly shows the mechanism and magnitude of the distance limit and trip chain settings in reshaping network flows from the simple case characterized merely by user equilibrium.     

Trip assignment to radial major roads

The problem of flow-dependent trip assignment is considered for a city with a small number of radial major roads. CBD-based work trips are assigned to these radial major roads on the basis that each commuter seeks to minimise his individual travel time. A system of differential equations is derived for the spatial pattern of trip assignment in a model city with a continuous distribution of home locations and a ring-radial road network. This system is then solved for the special case of a uniform distribution of home locations.     

Link choice proportions from trip distribution and assignment models: An overview and comparison

A number of estimation procedures have been suggested for the situation where a prior estimate of an origin-destination matrix is to be updated on the basis of recently-acquired traffic counts. These procedures assume that both the link flows and the proportionate usage of each link made by each origin-destination flow (referred to collectively as the link choice proportions) are known. This paper examines the possibility and methods for estimating the link choice proportions. Three methods are presented: (1) using ad hoc iteration between trip distribution and traffic assignment; (2) combining trip distribution and assignment in one step; (3) solving a new optimization problem in which the path flows are directly considered as variables and its optimal solution is governed by a logit type formula. The algorithms, covergencies and computational efficiencies of these methods are investigated. Results of testing the three methods on example networks are discussed.     

Traffic assignment by trip type using volume restraint and link restraint for application in small urban areas

This research involved the development of a new traffic assignment model consisting of a set of procedures for an urbanized area with a population of 172,000. Historical, social, and economic data were used as input to conventional trip generation and trip distribution models to produce a trip table for network assignment. This fixed table was divided into three trip types: external-external trips, external-internal trips, and internal-internal trips. The methodology used to develop the new traffic assignment model assigned each of the trip types by varying the diversion of trips from the minimum path. External-external trips were assigned on a minimum path routing and external-internal trips were assigned with a slight diversion from the minimum path. Internal-internal trips were assigned with more diversion than external-internal trips and adjusted by utilizing iterative volume restraint and incremental link restraint. A statistical analysis indicated that assigning trips by trip types using trip diversion and volume and link restraint produces a significant improvement in the accuracy of the assigned traffic volumes.     

Reserve capacity model based on variable demand for land-use development control

In this paper, the concept of reserve capacity has been extended to zone level to measure the land-use development potentiality of each trip generation zone. Bi-level programing models are proposed to determine the signal setting of individual intersections for maximizing possible increase in total travel demand and the corresponding reserve capacity for each zone. The change of the origin–destination pattern with the variation of upper level decision variables is presented through the combined distribution/assignment model under user equilibrium conditions. Both singly constrained and doubly constrained combined models are considered for different trip purposes and data information. Furthermore, we have introduced the continuous network design problem by increasing road capacity and examined its effect on the land-use development potentiality of trip generation zone. A numerical example is presented to illustrate the application of the models and how a genetic algorithm is applied to solve the problem.     

Maximum car ownership under constraints of road capacity and parking space

This paper presents a model for determining the maximum number of cars by zones in view of the capacity of the road network and the number of parking spaces available. In other words, the proposed model is to examine whether existing road network and parking supply is capable of accommodating future zonal car ownership growth (or the reserve capacity in each zone); i.e. the potential maximum zonal car ownership growth that generates the road traffic within the network capacity and parking space constraints. In the proposed model, the vehicular trip production and attraction are dependent on the car ownership, available parking spaces and the accessibility measures by traffic zones. The model is formulated as a bi-level programming problem. The lower-level problem is an equilibrium trip distribution/assignment problem, while the upper-level problem is to maximize the sum of zonal car ownership by considering travellers’ route and destination choice behaviour and satisfying the network capacity and parking space constraints. A sensitivity analysis based heuristic algorithm is developed to solve the proposed bi-level car ownership problem and is illustrated with a numerical example.     

The Dublin transportation study

This article deals with the Transportation Study currently nearing completion in Dublin. A feature of this Study was the use of simplified data collection and modelling techniques. Beginning with a brief outline of the background to the transportation problem in Dublin, the article goes on to outline the objectives of the Study and the methods by which these objectives were fulfilled. These methods involved the taking of detailed inventories of Dublin's travel patterns, of its land uses, population and employment, and of its road and public transport systems. Mathematical models were then developed and modified until they could simulate the existing travel patterns to an acceptable degree of accuracy. These models covered the Study's trip generation, modal split, trip distribution and trip assignment stages, and the forms taken by the models are dealt with in the article. The article ends with a summary of the main recommendations of the Dublin Transportation Study.     

Equity based land‐use and transportation problem

Due to additional trip production by land use development, the O‐D travel costs between some O‐D pairs may also change intuitively. This leads to positive and negative impacts on network users traveling between different O‐D pairs. Therefore the equity issue about the benefit distribution gained from the land‐use development problem is raised. This paper proposes an Equity based Land‐Use Transportation Problem (ELUTP) which is intended to examine the benefit distribution among the network users and the resulting equity associated with land‐use development problem in terms of the change of equilibrium O‐D travel cost. In the resulting bi‐level programming model, the upper level sub‐problem maximizes traffic production incorporating equity constraints, while the lower level sub‐problem is a combined trip distribution/assignment user equilibrium problem. Genetic algorithm based method is applied to test the models using an example network.     

Simplified transport models based on traffic counts

Having accepted the need for the development of simpler and less cumbersome transport demand models, the paper concentrates on one possible line for simplification: estimation of trip matrices from link volume counts. Traffic counts are particularly attractive as a data basis for modelling because of their availability, low cost and nondisruptive character. It is first established that in normal conditions it may be possible to find more than one trip matrix which, when loaded onto a network, reproduces the observed link volumes. The paper then identifies three approaches to reduce this underspecification problem and produce a unique trip matrix consistent with the counts. The first approach consists of assuming that trip-making behaviour can be explained by a gravity model whose parameters can be calibrated from the traffic counts. Several forms of this gravity model have been put forward and they are discussed in Section 3. The second approach uses mathematical programming techniques associated to equilibrium assignment problems to estimate a trip matrix in congested areas. This method can also be supplemented by a special distribution model developed for small areas. The third approach relies on entropy and information theory considerations to estimate the most likely trip matrix consistent with the observed flows. A particular feature of this group is that they can include prior, perhaps outdated, information about the matrix.These three approaches are then compared and their likely areas for application identified. Problems for further research are discussed and finally an assessment is made of the possible role of these models vis-a-vis recent developments in transport planning.     

Dynamic network equilibrium for daily activity-trip chains of heterogeneous travelers: application to large-scale networks

Applications of dynamic network equilibrium models have, mostly, considered the unit of traffic demand either as one-way trip, or as multiple independent trips. However, individuals’ travel patterns typically follow a sequence of trips chained together. In this study we aim at developing a general simulation-based dynamic network equilibrium algorithm for assignment of activity-trip chain demand. The trip chain of each individual trip maker is defined by the departure time at origin, sequence of activity destination locations, including the location of their intermediate destinations and their final destination, and activity duration at each of the intermediate destinations. Spatial and temporal dependency of subsequent trips on each other necessitate time and memory consuming calculations and storage of node-to-node time-dependent least generalized cost path trees, which is not practical for very large metropolitan area networks. We first propose a reformulation of the trip-based demand gap function formulation for the variational inequality formulation of the Bi-criterion Dynamic User Equilibrium (BDUE) problem. Next, we propose a solution algorithm for solving the BDUE problem with daily chain of activity-trips. Implementation of the algorithm for very large networks circumvents the need to store memory-intensive node-to-node time-dependent shortest path trees by implementing a destination-based time-dependent least generalized cost path finding algorithm, while maintaining the spatial and temporal dependency of subsequent trips. Numerical results for a real-world large scale network suggest that recognizing the dependency of multiple trips of a chain, and maintaining the departure time consistency of subsequent trips provide sharper drops in gap values, hence, the convergence could be achieved faster (compared to when trips are considered independent of each other).     

Minimal-revenue congestion pricing Part II: An efficient algorithm for the general case

The second of a two-part series, this paper derives an efficient solution to the minimal-revenue tolls problem. As introduced in Part I, this problem can be defined as follows: Assuming each trip uses only a path whose generalized cost is smallest, find a set of arc tolls that simultaneously minimizes both average travel time and out-of-pocket cost. As a point of departure, this paper first re-solves the single-origin problem of Part I, modeling it as a linear program. Then with a change of variable, it transforms the LP's dual into a simple longest-path problem on an acyclic network. The multiple-origin problem – where one toll for each arc applies to all origins – solves analogously. In this case, however, the dual becomes an elementary linear multi-commodity max-cost flow problem with an easy bundling constraint and infinite arc capacities. After a minor reformulation that simplifies the model's input to better accommodate output from common traffic assignment software, a solution algorithm is exemplified with a numerical example.     

Estimation of origin-destination matrices from link traffic counts on congested networks

Conventional methods for estimating origin-destination (O-D) trip matrices from link traffic counts assume that route choice proportions are given constants. In a network with realistic congestion levels, this assumption does not hold. This paper shows how existing methods such as the generalized least squares technique can be integrated with an equilibrium traffic assignment in the form of a convex bilevel optimization problem. The presence of measurement errors and time variations in the observed link flows are explicitly considered. The feasibility of the model is always guaranteed without a requirement for estimating consistent link flows from counts. A solution algorithm is provided and numerical simulation experiments are implemented in investigating the model's properties. Some related problems concerning O-D matrix estimation are also discussed.     

Dynamic operations and pricing of electric unmanned aerial vehicle systems and power networks

The emergence of electric unmanned aerial vehicle (E-UAV) technologies, albeit somewhat futuristic, is anticipated to pose similar challenges to the system operation as those of electric vehicles (EVs). Notably, the charging of EVs en-route at charging stations has been recognized as a significant type of flexible load for power systems, which often imposes non-negligible impacts on the power system operator’s decisions on electricity prices. Meanwhile, the charging cost based on charging time and price is part of the trip cost for the users, which can affect the spatio-temporal assignment of E-UAV traffic to charging stations. This paper aims at investigating joint operations of coupled power and electric aviation transportation systems that are associated with en-route charging of E-UAVs in a centrally controlled and yet dynamic setting, i.e., with time-varying travel demand and power system base load. Dynamic E-UAV charging assignment is used as a tool to smooth the power system load. A joint pricing scheme is proposed and a cost minimization problem is formulated to achieve system optimality for such coupled systems. Numerical experiments are performed to test the proposed pricing scheme and demonstrate the benefits of the framework for joint operations.     

An integrated, dynamic approach to travel demand forecasting

This paper presents a unified approach for improving travel demand models through the application and extension of supernetwork models of multi-dimensional travel choices. Proposed quite some time ago, supernetwork models solved to stochastic user equilibrium can provide a simultaneous solution to trip generation, distribution, mode choice, and assignment that is consistent with disaggregate models and predicts their aggregate effects. The extension to incorporate the time dimension through the use of dynamic equilibrium assignment methods is proposed as an enhancement that is necessary in order to produce realistic models. A variety of theoretical and practical problems are identified whose solution underlies implementation of this approach. Recommended future research includes improved algorithms for stochastic and dynamic equilibrium assignment, new methods for calibrating assignment models, and the use of Geographic Information Systems (GIS) technology for data and model management.     

The impact of ignoring intrazonal trips in assignment models: a stochastic approach

Transportation - In transportation modeling, intrazonal trips are frequently omitted during trip assignment. These trips are not assigned to the network because their origin and destination are in...     

A branch-and-price approach for solving the train unit scheduling problem

We propose a branch-and-price approach for solving the integer multicommodity flow model for the network-level train unit scheduling problem (TUSP). Given a train operator’s fixed timetable and a fleet of train units of different types, the TUSP aims at determining an assignment plan such that each train trip in the timetable is appropriately covered by a single or coupled train units. The TUSP is challenging due to its complex nature. Our branch-and-price approach includes a branching system with multiple branching rules for satisfying real-world requirements that are difficult to realize by linear constraints, such as unit type coupling compatibility relations and locations banned for coupling/decoupling. The approach also benefits from an adaptive node selection method, a column inheritance strategy and a feature of estimated upper bounds with node reservation functions. The branch-and-price solver designed for TUSP is capable of handling instances of up to about 500 train trips. Computational experiments were conducted based on real-world problem instances from First ScotRail. The results are satisfied by rail practitioners and are generally competitive or better than the manual ones.     

A unified framework for estimating or updating origin/destination matrices from traffic counts

This paper presents an in-depth study of the methodology for estimating or updating origin-to-destination trip matrices from traffic counts. Following an analysis of the statistical foundation of the estimation and updating problems, various basic approaches are reviewed using a generic traffic assignment map. Computational issues related to specific assignment maps and estimation models for both road and transit networks are then discussed. Finally, additional insight into the relative performance of several estimators is provided by a set of test problems with varying input data.     

A comparative analysis of traditional four-step and activity-based travel demand modeling: a case study of Tampa,Florida

Activity-based travel demand modeling (ABTDM) has often been viewed as an advanced approach, due to its higher fidelity and better policy sensitivity. However, a review of the literature indicates that no study has been undertaken to investigate quantitatively the differences and accuracy between an ABTDM approach and a traditional four-step travel demand model. In this paper we provide a comparative analysis against each step – trip generation, trip distribution, mode split, and network assignment – between an ABTDM developed using travel diary data from the Tampa Bay Region in Florida and the Tampa Bay Regional Planning Model (TBRPM), an existing traditional four-step model for the same area. Results show salient differences between the TBRPM and the ABTDM, in terms of modeling performance and accuracy, in each of the four steps. For example, trip production rates calculated from the travel diary data are found to be either double or a quarter less than those used in the TBRPM. On the other hand, trip attraction rates computed from activity-based travel simulations are found to be either more than double or one tenth less than those used in the TBRPM. The trip distribution curves from the two models are similar, but both average and peak trip lengths of the two are significantly different. Mode split analyses show that the TBRPM may underestimate driving trips and fail to capture any usage of alternative modes, such as taxi and nonmotorized (e.g., walking and bicycling) modes. In addition, the ABTDMs are found to be less capable of reproducing observed traffic counts when compared to the TBRPM, most likely due to not considering external and through trips. The comparative results presented can help transportation engineers and planners better understand the strengths and weaknesses of the two types of model and this should assist decision-makers in choosing a better modeling tool for their planning initiatives.     

Comparison of results of two models of transportation demand in Hong Kong: CDAM and a version of microTRIPS

CDAM is a new computer program for solving the combined trip distribution and assignment model for multiple user classes, which enables transport planners to estimate consistent Origin-Destination (O-D) matrices and equilibrium traffic flows simultaneously if the trip production and attraction of each user class at zone centroids are available. This paper reports an application of CDAM to the central Kowloon study area in Hong Kong. The coefficients of the model related to the components of generalized costs are calibrated on 1986 travel data. A comparison of results of CDAM and a version of MicroTRIPS models of transportation demand in Hong Kong are presented. Finally, some conclusions are drawn and the advantage of the CDAM are discussed.