Tests of assignment accuracy: An interurban case study

This paper is concerned with methods of testing the accuracy of traffic assignments. It focuses on the fact that whereas assignment models are usually based on a behavioural hypothesis about drivers' route choice (e.g. cost or time minimisation) the test of the accuracy of the assignment is the extent to which observed link loadings are reproduced. This inconsistency opens up the doubt that an apparently “accurate” assignment on this basis may be a result of compensating errors. It is difficult to apply the same test to accuracy of route choices as is applied to accuracy of link loadings (e.g. chi square, correlation coefficient) and hence a new measure is devised here which can be applied both to comparisons between observed and predicted route choices and comparisons between observed and predicted loadings. It is, moreover, possible to devise a test of significance for this measure so that one can test whether a predicted assignment is significantly different from what one, might have observed on the basis of chance observation. A case study is carried out to test the proposed method. Traffic flows between 72 origins and destinations on either side of the Pennine Mountains in Britain are assigned to a network using different assignment techniques with varied parameters. In all, one hundred and ninety assignments are carried out and the degree of correspondence between observed and predicted route choices and link loadings is measured. The results tend to confirm that the link loadings criterion is not a very stable criterion and that the route choice correspondence criteria seems to behave in a sensible way. A simulation exercise is carried out which produces the probability distribution of the “route-fit” index for different assumed sample levels. The paper concludes by suggesting avenues for further research.     

A chance-constrained based stochastic dynamic traffic assignment model: Analysis, formulation and solution algorithms

This paper is concerned with the system optimum-dynamic traffic assignment (SO-DTA) problem when the time-dependent demands are random variables with known probability distributions. The model is a stochastic extension of a deterministic linear programming formulation for SO-DTA introduced by Ziliaskopoulos (Ziliaskopoulos, A.K., 2000. A linear programming model for the single destination system optimum dynamic traffic assignment problem, Transportation Science, 34, 1–12). The proposed formulation is chance-constrained based and we demonstrate that it provides a robust SO solution with a user specified level of reliability. The model provides numerous insights and can be a useful tool in producing robust control and management strategies that account for uncertainty in applications where SO-DTA is relevant (e.g. evacuation modeling, computing alternate routes around freeway incidents and establishing lower bounds on network performance).     

Accessibility, entropy and the distribution and assignment of traffic revisited

An optimizing model which minimizes average generalised trip cost subject to constraints on the entropy was given in a previous paper. In this note the model is placed in a planning context.     

Rail freight traffic assignment

This paper describes an algorithm for routing freight over a rail network whose tracks are controlled by several carriers in a manner that follows current industrial practices. In particular, the freight is routed to minimize the number of interline transfers and to maximize the revenue division for the originating carrier. The algorithm is based upon generalizing a shortest path algorithm to allow vector valued link impedances.     

Accessibility,entropy and the distribution and assignment of traffic—A comment

In an article in this journal Erlander (1977) has suggested an alternative way of interpreting the entropy maximizing approach when used to derive the gravity model formulation for trip distribution. Erlander views the optimization model as a planning model and for this purpose examines two alternative formulations, which are referred to as the efficiency and accessibility problems. In this comment we point out the similarities and dissimilarities between these formulations and the derivation of the trip distribution model on the basis of conventional neoclassical utility theory. We also question the meaningfulness of interpreting the entropy maximizing framework as a planning model.     

Transit assignment under crowded conditions

This paper presents a transit assignment algorithm for crowded networks. Both congestion in vehicles and queuing at stations are explicitly taken into account in predicting passenger flows for a fixed pattern of origin-destination trip demands. The overflow effects due to insufficient capacity of transit lines are considered to be concentrated at transit stations, while the in-vehicle congestion effects (or discomforts) are considered to be dependent on in-vehicle passenger volume. Overflow delay at a transit station is dependent on the number of excess passengers required to wait for the next transit car. We use a logit model to determine the split between passengers that chose to wait for the next transit car and passengers that chose to board on the alternative transit lines. The proposed algorithm predicts how passenger will choose their optimal routes under both queuing and crowded conditions.     

Multimodal,multiclass stochastic dynamic traffic assignment for evaluating information provision strategies

A multimodal, multiclass stochastic dynamic traffic assignment model was developed to evaluate pre‐trip and enroute travel information provision strategies. Three different information strategies were examined: user optimum [UO], system optimum [SO] and mixed optimum [MO]. These information provision strategies were analyzed based on the levels of traffic congestion and market penetration rate for the information equipment. Only two modes, bus and car, were used for evaluating and calculating the modal split ratio. Several scenarios were analyzed using day‐to‐day and within day dynamic models. From the results analyzed, it was found that when a traffic manager provides information for drivers using the UO strategy and drivers follow the provided information absolutely, the total travel time may increases over the case with no information. Such worsening occurs when drivers switch their routes and face traffic congestion on the alternative route. This phenomenon is the 'Braess Paradox'.     

Traffic assignment considering air quality

This paper presents a methodology of assigning traffic in a network with the consideration of air quality. Traffic assignment is formulated as an optimization problem considering travel cost and on-road emissions. It introduces a cell-based approach to model emission concentrations so that either the average or maximum emissions in a network can be considered in the optimization process. The emissions in a cell are modeled taking into consideration the influence of the emission sources from all cells in the network. A case study demonstrates that minimizing travel cost and reducing air pollutants may not be always achieved simultaneously. The traffic assignment procedure can effectively reduce emission concentrations at those locations with the worst air quality conditions, with only a marginal increase in travel time and average emission concentration in the network.     

The dynamics of traffic assignment and traffic control: A theoretical study

The paper considers traffic assignment, with traffic controls, in an increasingly dynamic way. First, a natural way of introducing the responsive policy, P_o, into steady state traffic assignment is presented. Then it is shown that natural stability results follow within a dynamical version of this static equilibrium model (still with a constant demand). We are able to obtain similar stability results when queues are explicitly allowed for, provided demand is constant. Finally we allow demand to vary with time; we consider the dynamic assignment problem with signal-settings now fixed. Here we assume that vehicles are very short and that deterministic queueing theory applies, and show that the time-dependent queueing delay at the bottleneck at the end of a link is a monotone function of the time-dependent input profile to the bottleneck. We have been unable to obtain results when dynamic demand and responsive signal control are combined.     

Potential-based dynamic pedestrian flow assignment

This study proposes a potential-based dynamic pedestrian flow assignment model to optimize the evacuation time needed for all pedestrians to leave an indoor or outdoor area with internal obstacles and multiple exits, e.g., railway station, air terminal, plaza, and park. In the model, the dynamic loading of pedestrian flows on a two-dimensional space is formulated by a cell transmission model, the movement of crowds is driven by space potential, and the optimization of evacuation time is solved by a proportional swapping process. In this way, the proposed model can be applied to not only efficiently optimize the evacuation process of a crowd with large scale but also recognize local congestion dynamics during crowd evacuation. Finally, a set of numerical examples are presented to show the proposed model’s effectiveness for optimizing crowd evacuation process and its application to design a class of variable guide sign systems.     

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.     

An assignment model with modified Logit,which obviates enumeration and overlapping problems

One of the main components of stochastic assignment models is the route choice model solved with implicit or explicit path enumeration algorithms. Such models are used both for congested networks within equilibrium or dynamic models and for non-congested networks within static or pseudo-dynamic network loading models. This paper proposes a C-Logit model specification within a Dial algorithm structure for the implicit assignment of network flows. The model and its solution algorithm, called D-C-Logit, combine several positive features found in the literature for choice set generation and choices from a given choice set: generation of a set of alternatives with a selective approach; calculation of the path choice probability in a closed form; simulation of the overlapping effect among alternative paths; computation of just one tree for each origin avoiding explicit path enumeration.This paper has two main objectives: the proposition of a Dial-like algorithm to solve a C-Logit assignment model and application of the algorithm to different networks in order to demonstrate certain properties.     

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 frequency-based maritime container assignment model

This paper transfers the classic frequency-based transit assignment method of Spiess and Florian to containers demonstrating its promise as the basis for a global maritime container assignment model. In this model, containers are carried by shipping lines operating strings (or port rotations) with given service frequencies. An origin–destination matrix of full containers is assigned to these strings to minimize sailing time plus container dwell time at the origin port and any intermediate transhipment ports. This necessitated two significant model extensions. The first involves the repositioning of empty containers so that a net outflow of full containers from any port is balanced by a net inflow of empty containers, and vice versa. As with full containers, empty containers are repositioned to minimize the sum of sailing and dwell time, with a facility to discount the dwell time of empty containers in recognition of the absence of inventory. The second involves the inclusion of an upper limit to the maximum number of container moves per unit time at any port. The dual variable for this constraint provides a shadow price, or surcharge, for loading or unloading a container at a congested port. Insight into the interpretation of the dual variables is given by proposition and proof. Model behaviour is illustrated by a simple numerical example. The paper concludes by considering the next steps toward realising a container assignment model that can, amongst other things, support the assessment of supply chain vulnerability to maritime disruptions.     

Frequency-based transit assignment considering seat capacities

This paper proposes a frequency-based assignment model that considers travellers probability of finding a seat in their perception of route cost and hence also their route choice. The model introduces a “fail-to-sit” probability at boarding points with travel costs based on the likelihood of travelling seated or standing. Priority rules are considered; in particular it is assumed that standing on-board passengers will occupy any available seats of alighting passengers before newly boarding passengers can fill any remaining seats. At the boarding point passengers are assumed to mingle, meaning that FIFO is not observed, as is the case for many crowded bus and metro stops, particularly in European countries. The route choice considers the common lines problem and an user equilibrium solution is sought through a Markov type network loading process and the method of successive averages. The model is first illustrated with a small example network before being applied to the inner zone of London’s underground network. The effect of different values passengers might attach to finding a seat are illustrated. Applications of the model for transit planning as well as for information provision at the journey planner stage are discussed.