On a link-based day-to-day traffic assignment model

In this paper, we perform a rigorous analysis on a link-based day-to-day traffic assignment model recently proposed in He et al. (2010). Several properties, including the invariance set and the constrained stability, of this dynamical process are established. An extension of the model to the asymmetric case is investigated and the stability result is also established under slightly more restrictive assumptions. Numerical experiments are conducted to demonstrate the findings.     

Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment

The paper proposes a first-order macroscopic stochastic dynamic traffic model, namely the stochastic cell transmission model (SCTM), to model traffic flow density on freeway segments with stochastic demand and supply. The SCTM consists of five operational modes corresponding to different congestion levels of the freeway segment. Each mode is formulated as a discrete time bilinear stochastic system. A set of probabilistic conditions is proposed to characterize the probability of occurrence of each mode. The overall effect of the five modes is estimated by the joint traffic density which is derived from the theory of finite mixture distribution. The SCTM captures not only the mean and standard deviation (SD) of density of the traffic flow, but also the propagation of SD over time and space. The SCTM is tested with a hypothetical freeway corridor simulation and an empirical study. The simulation results are compared against the means and SDs of traffic densities obtained from the Monte Carlo Simulation (MCS) of the modified cell transmission model (MCTM). An approximately two-miles freeway segment of Interstate 210 West (I-210W) in Los Ageles, Southern California, is chosen for the empirical study. Traffic data is obtained from the Performance Measurement System (PeMS). The stochastic parameters of the SCTM are calibrated against the flow-density empirical data of I-210W. Both the SCTM and the MCS of the MCTM are tested. A discussion of the computational efficiency and the accuracy issues of the two methods is provided based on the empirical results. Both the numerical simulation results and the empirical results confirm that the SCTM is capable of accurately estimating the means and SDs of the freeway densities as compared to the MCS.     

A dynamic traffic assignment model for a continuum transportation system

A predictive continuum dynamic user-optimal (PDUO-C) model is formulated in this study to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers within a region with a dense urban road network. The modeled region is arbitrary in shape with a single central business district (CBD) and travelers continuously distributed over the region. Within this region, the road network is represented as a continuum and travelers patronize a two-dimensional continuum transportation system to travel to the CBD. The PDUO-C model is solved by a promising solution algorithm that includes elements of the finite volume method (FVM), the finite element method (FEM), and the explicit total variation diminishing Runge-Kutta (TVD-RK) time-stepping method. A numerical example is given to demonstrate the utility of the proposed model and the effectiveness of the solution algorithm in solving this PDUO-C problem.     

Dynamic user optimal traffic assignment on congested multidestination networks

An equivalent continuous time optimal control problem is formulated to predict the temporal evolution of traffic flow pattern on a congested multiple origin-destination network, corresponding to a dynamic generalization of Wardropian user equilibrium. Optimality conditions are derived using the Pontryagin minimum principle and given economic interpretations, which are generalizations of similar results previously reported for single-destination networks. Analyses of sufficient conditions for optimality and of singular controls are also given. Under the steady-state assumptions, the model is shown to be a proper dynamic extension of Beckmann's mathematical programming problem for a static user equilibrium traffic assignment.     

A dynamic traffic assignment model for the assessment of moving bottlenecks

Moving bottlenecks in highway traffic are defined as a situation in which a slow-moving vehicle, be it a truck hauling heavy equipment or an oversized vehicle, or a long convey, disrupts the continuous flow of the general traffic. The effect of moving bottlenecks on traffic flow is an important factor in the evaluation of network performance. This effect, though, cannot be assessed properly by existing transportation tools, especially when the bottleneck travels relatively long distances in the network.This paper develops a dynamic traffic assignment (DTA) model that can evaluate the effects of moving bottlenecks on network performance in terms of both travel times and traveling paths. The model assumes that the characteristics of the moving bottleneck, such as traveling path, physical dimensions, and desired speed, are predefined and, therefore, suitable for planned conveys.The DTA model is based on a mesoscopic simulation network-loading procedure with unique features that allow assessing the special dynamic characteristics of a moving bottleneck. By permitting traffic density and speed to vary along a link, the simulation can capture the queue caused by the moving bottleneck while preserving the causality principles of traffic dynamics.     

A predictive dynamic traffic assignment model in congested capacity-constrained road networks

In this paper, a predictive dynamic traffic assignment model in congested capacity-constrained road networks is formulated. A traffic simulator is developed to incrementally load the traffic demand onto the network, and updates the traffic conditions dynamically. A time-dependent shortest path algorithm is also given to determine the paths with minimum actual travel time from an origin to all the destinations. The traffic simulator and time-dependent shortest path algorithm are employed in a method of successive averages to solve the dynamic equilibrium solution of the problem. A numerical example is given to illustrate the effectiveness of the proposed method.     

Dynamic stochastic transit assignment with explicit seat allocation model

This paper proposes a stochastic dynamic transit assignment model with an explicit seat allocation process. The model is applicable to a general transit network. A seat allocation model is proposed to estimate the probability of a passenger waiting at a station or on-board to get a seat. The explicit seating model allows a better differentiation of in-vehicle discomfort experienced by sitting and standing passengers. The paper proposes simulation procedures for calculating the sitting probability of each type of passengers. A heuristic solution algorithm for finding an equilibrium solution of the proposed model is developed and tested. The numerical tests show significant influences of the seat allocation model on equilibrium departure time and route choices of passengers. The proposed model is also applied to evaluate the effects of an advanced public transport information system (APTIS) on travellers’ decision-making.     

A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem

A cell-based variant of the Merchant-Nemhauser (M-N) model is proposed for the system optimum (SO) dynamic traffic assignment (DTA) problem. Once linearized and augmented with additional constraints to capture cross-cell interactions, the model becomes a linear program that embeds a relaxed cell transmission model (CTM) to propagate traffic. As a result, we show that CTM-type traffic dynamics can be derived from the original M-N model, when the exit-flow function is properly selected and discretized. The proposed cell-based M-N model has a simple constraint structure and cell network representation because all intersections and cells are treated uniformly. Path marginal costs are defined using a recursive formula that involves a subset of multipliers from the linear program. This definition is then employed to interpret the necessary condition, which is a dynamic extension of the Wardrop’s second principle. An algorithm is presented to solve the flow holding back problem that is known to exist in many discrete SO-DTA models. A numerical experiment is conducted to verify the proposed model and algorithm.     

Some developments in equilibrium traffic assignment

A network optimization problem is formulated which yields a probabilistic equilibrated traffic assignment incorporating congestion effects and which as a special case, reduces to a user optimized equilibrium solution. In the resulting model, path choice is determined by a logit formula in which path costs are functions of the assigned flows. The article also demonstrates the similarity between some fixed demand incremental methods of traffic assignment and the minimization problem associated with computing the user equilibrium assignment.     

Spillback congestion in dynamic traffic assignment: A macroscopic flow model with time-varying bottlenecks

In this paper, we propose a new model for the within-day Dynamic Traffic Assignment (DTA) on road networks where the simulation of queue spillovers is explicitly addressed, and a user equilibrium is expressed as a fixed-point problem in terms of arc flow temporal profiles, i.e., in the infinite dimension space of time’s functions. The model integrates spillback congestion into an existing formulation of the DTA based on continuous-time variables and implicit path enumeration, which is capable of explicitly representing the formation and dispersion of vehicle queues on road links, but allows them to exceed the arc length. The propagation of congestion among adjacent arcs will be achieved through the introduction of time-varying exit and entry capacities that limit the inflow on downstream arcs in such a way that their storage capacities are never exceeded. Determining the temporal profile of these capacity constraints requires solving a system of spatially non-separable macroscopic flow models on the supply side of the DTA based on the theory of kinematic waves, which describe the dynamic of the spillback phenomenon and yield consistent network performances for given arc flows. We also devise a numerical solution algorithm of the proposed continuous-time formulation allowing for “long time intervals” of several minutes, and give an empirical evidence of its convergence. Finally, we carry out a thorough experimentation in order to estimate the relevance of spillback modeling in the context of the DTA, compare the proposed model in terms of effectiveness with the Cell Transmission Model, and assess the efficiency of the proposed algorithm and its applicability to real instances with large networks.     

Junction interactions and monotonicity in traffic assignment

We consider the traffic equilibrium problem when the travel demand is inelastic and stationary in time. Junction interactions, which abound in urban road networks, are permitted. We prove that the set of equilibria (solutions to the assignment problem) is convex when certain monotonicity and continuity conditions are statisfied at each junction.     

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.     

Calibrating a transit assignment model using smart card data in a large-scale multi-modal transit network

This paper describes a practical automated procedure to calibrate and validate a transit assignment model. An optimization method based on particle swarm algorithm is adopted to minimize a defined error term. This error term which is based on the percentage of root mean square error and the mean absolute percent error encompasses deviation of model outputs from observations considering both segment level as well as the mode level and can be applied to a large scale network. This study is based on the frequency-based assignment model using the concept of optimal strategy while any transit assignment model can be used in the proposed methodological framework. Lastly, the model is validated using another weekday data. The proposed methodology uses automatic fare collection (AFC) data to estimate the origin–destination matrix. This study combines data from three sources: the general transit feed specification, AFC, and a strategic transport model from a large-scale multimodal public transport network. The South-East Queensland (SEQ) network in Australia is used as a case study. The AFC system in SEQ has voluminous and high quality data on passenger boardings and alightings across bus, rail and ferry modes. The results indicate that the proposed procedure can successfully develop a multi-modal transit assignment model at a large scale. Higher dispersions are seen for the bus mode, in contrast to rail and ferry modes. Furthermore, a comparison is made between the strategies used by passengers and the generated strategies by the model between each origin and destination to get more insights about the detailed behaviour of the model. Overall, the analysis indicates that the AFC data is a valuable and rich source in calibrating and validating a transit assignment model.

     

Simplical decomposition of the asymmetric traffic assignment problem

This paper presents a convergent simplicial decomposition algorithm for the variational inequality formulation of the asymmetric traffic assignment problem. It alternates between generating minimum path trees based on the cost function evaluated at the current iterate and the approximate solving of a master variational inequality subject to simple convexity constraints. Thus it generalizes the popular Frank-Wolfe method (where the master problem is a line search) to the asymmetric problem. Rules are given for dropping flow patterns which are not needed to express the current iterate as a convex combination of previous patterns. The results of some computational testing are reported.     

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.     

A methodology to estimate travel time using dynamic traffic assignment (DTA) under incident conditions

This paper presents results from a research case study that examined the distribution of travel time of origin–destination (OD) pairs on a transportation network under incident conditions. Using a transportation simulation dynamic traffic assignment (DTA) model, incident on a transportation network is executed under normal conditions, incident conditions without traveler information availability, and incident conditions assuming that users had perfect knowledge of the incident conditions and could select paths to avoid the incident location. The results suggest that incidents have a different impact on different OD pairs. The results confirm that an effective traveler information system has the potential to ease the impacts of incident conditions network wide. Yet it is also important to note that the use of information may detriment some OD pairs while benefiting other OD pairs. The methodology demonstrated in this paper provides insights into the usefulness of embedding a fully calibrated DTA model into the analysis tools of a traffic management and information center.     

On the dual approach to the traffic assignment problem

This paper attempts to explore the possibility of solving the traffic assignment problem with elastic demands by way of its dual problem. It is shown that the dual problem can be formulated as a nonsmooth convex optimization problem of which the objective function values and subgradients are conveniently calculated by solving shortest path problems associated with the transportation network. A subgradient algorithm to solve the dual problem is presented and limited computational experience is reported. The computational results are encouraging enough to demonstrate the effectiveness of the proposed approach.     

An improved Dial's algorithm for logit-based traffic assignment within a directed acyclic network

Abstract

Dial's algorithm is one of the most effective and popular procedures for a logit-type stochastic traffic assignment, as it does not require path enumeration over a network. However, a fundamental problem associated with the algorithm is its simple definition of ‘efficient paths’, which sometimes produces unrealistic flow patterns. In this paper, an improved algorithm based on the route extension coefficient is proposed in order to circumvent this problem, in which ‘efficient paths’ simultaneously consider link travel cost and minimum travel cost. Path enumeration is still not required and a similar computing efficiency with the original algorithm is guaranteed. A limitation of the algorithm is that it can only be applied to a directed acyclic network because a topological sorting algorithm is used to decide the order of the sequential calculation. A numerical example based on the Beijing subway network illustrates the effectiveness of the proposed algorithm. It is found that it is able to exclude most unrealistic paths, but include all reasonable paths when compared with path enumeration and the original Dial's algorithm.     

A note on traffic assignment and signal timings in a signal-controlled road network

This paper discusses the problems of using signal timings in a signal-controlled road network to influence equilibrium flows in such a way that some network performance index, e.g. total travel time, is optimised, given that at equilibrium each driver is using a minimum-time route. By means of a simple example, we show that an intuitively acceptable approach explored in other articles does not work and may, in fact, lead to a decline in network performance rather than an improvement.