Stochastic User Equilibrium Assignment Research Articles

Cascading failure-based reliability assessment for post-seismic performance of highway bridge network

This paper proposes a novel reliability assessment framework for post-seismic performance of highway bridge network that considers cascading failures caused by traffic flow redistribution. Firstly, the fragility curve of bridge is obtained by probabilistic seismic demand model. Then, we propose the impact factor of path choice probability to characterize the cascading failure of the network. The stochastic user equilibrium assignment of highway bridge network traffic flow is calculated based on the impact factor of path choice probability. To evaluate the network's efficiency and identify the congestion-prone links, the Monte Carlo simulation method is introduced to calculate the probability density curves of different influencing parameters. Finally, the framework proposed in this paper is utilized to analyze the congestion-prone links of the transportation network of some areas of Mianyang City and verify its applicability.

Incremental equilibrium assignment and applications to traffic network model

AbstractTo find a traffic assignment algorithm that is less complex than the current algorithms in terms of both methodology and implementation, the route‐based incremental equilibrium assignment (IEA) method is proposed. The IEA method iteratively performs incremental assignment and new origin‐destination (O‐D) demand extraction, where the new O‐D demand is obtained by aggregating the traffic flows from the routes whose travel times are greater than the shortest travel time. By extending the IEA method, the incremental stochastic user equilibrium and reliability‐based user equilibrium assignments are proposed to solve the stochastic user equilibrium (SUE) and reliability‐based user equilibrium (RUE) models, respectively. The traffic flow assignment and new O‐D demand extraction are carried out in terms of the route choice probability and the ratio of route flow to O‐D demand in the incremental stochastic user equilibrium assignment method; the redundant traffic flows from the non‐equilibrium routes are extracted. Unlike the IEA method, incremental reliability‐based user equilibrium assignment needs to derive both the mean and variance of the route travel time. The results from numerical experiments demonstrate the essential ideas and convergence performance of the proposed IEA algorithm and illustrate that IEA can be effectively extended to solve the SUE and RUE models.

Path Choice Models in Stochastic Assignment: Implementation and Comparative Analysis

In assignment models, a key role is played by the path choice simulation that evaluates the path chosen by users in relation to the perceived paths and relative costs. This study deals with the effects of the implementation of some most adopted path choice models (Logit, Weibit, Probit, and Gammit) within a Stochastic User Equilibrium assignment procedure. Some considerations on parameters needed to make results comparable and the method used to estimate them are also suggested some extensions based on Weibit model are proposed. Results obtained both on a test network and on a real one are reported.

Multi-class stochastic user equilibrium assignment model with ridesharing: Formulation and policy implications

Abstract This paper proposes a logit-based multi-class ridesharing user equilibrium assignment framework that can incorporate different policy measures such as car restrictions, cordon tolling, and subsidization. The framework is formulated as a mixed complementarity problem (MCP). Numerical studies are conducted to illustrate model properties and compare the effects of these measures under different circumstances. The results show that the effectiveness of different policy measures can be greatly influenced by the performance of the transit mode compared with that of the driving mode and the users’ preference for traveling by car. The “cordon toll” policy can be better than the “car restriction” policy in terms of the improvement in social surplus when the performance of the competing transit system is poor. Subsidizing ridesharing (transit fares) using the toll income is the most effective when the performance of the competing transit system is poor (good). It is also found that the implementation of the cordon toll policy cannot effectively promote ridesharing when the performance of the transit system is good.

OPTIMIZING FARES AND TRANSFER DISCOUNTS FOR A BUS-SUBWAY CORRIDOR

This paper aims to optimize fares and transfer discounts for public transit service along a bus-subway corridor with the consideration of effects of uncertainty in travel times and difference in stop spacing between bus and subway services on passenger behavior. The former factor is captured by the reserved time in travel cost and the latter one produces some passenger Origin–Destination (O–D) pairs along the corridor that can not be served by one mode only. This problem is formulated as a bi-level program, of which the upper level maximizes the social welfare and the lower-level capturing traveler choice behavior is a variable-demand Stochastic User Equilibrium (SUE) assignment model. A Genetic Algorithm (GA) is applied to solve the bi-level program while the Method of Successive Averages (MSA) is adopted to solve the lower-level model. A series of numerical experiments are carried out to illustrate the performance of the model and solution method. Numerical results indicate that the implementation of transfer discounts may be of great benefit to the social welfare and that the uncertainty in travel time and the difference in stop spacing play an important role in determining optimal fares and transfer discounts for the service along a bus-subway corridor.

A Simultaneous Solution for Reserve Capacity Maximization and Delay Minimization Problems in Signalized Road Networks

In this study, we present a bilevel programming model in which upper level is defined as a biobjective problem and the lower level is considered as a stochastic user equilibrium assignment problem. It is clear that the biobjective problem has two objectives: the first maximizes the reserve capacity whereas the second minimizes performance index of a road network. We use a weighted-sum method to determine the Pareto optimal solutions of the biobjective problem by applying normalization approach for making the objective functions dimensionless. Following, a differential evolution based heuristic solution algorithm is introduced to overcome the problem presented by use of biobjective bilevel programming model. The first numerical test is conducted on two-junction network in order to represent the effect of the weighting on the solution of combined reserve capacity maximization and delay minimization problem. Allsop & Charlesworth’s network, which is a widely preferred road network in the literature, is selected for the second numerical application in order to present the applicability of the proposed model on a medium-sized signalized road network. Results support authorities who should usually make a choice between two conflicting issues, namely, reserve capacity maximization and delay minimization.

Stochastic Route Choice Equilibrium Assignment for Travelers with Heterogeneous Regret Aversions

Most route choice models assume that people are completely rational. Recently, regret theory has attracted researchers’ attentions because of its power to depict real travel behavior. This paper proposes a multiclass stochastic user equilibrium assignment model by using regret theory. All users are differentiated by their own regret aversion. The route travel disutility for users of each class is defined as a linear combination of the travel time and anticipated regret. The proposed model is formulated as a variational inequality problem and solved by using the self-regulated averaging method. The numerical results show that users’ regret aversion indeed influences their route choice behavior and that users with high regret aversion are more inclined to change route choice when the traffic congestion degree varies.

Toll Choice and Stochastic User Equilibrium: Ticking All the Boxes

Stochastic user equilibrium is a behaviorally realistic framework for strategic demand modeling and forecasting in cities/regions where there are multiple tolled facilities, especially when it comes to patronage forecasting for existing or planned tolled facilities. However, there is currently no algorithm available in the literature or in commercial software that provides a comprehensive approach for stochastic user equilibrium assignment that addresses the generation of route choice sets for tolled roads, path overlap, and high levels of convergence. This paper presents a novel choice set generation algorithm combined with the path-size logit model and the bi-conjugate Frank-Wolfe equilibrium assignment in a comprehensive algorithm for forecasting tolled road patronage, along with the results of its application to a real-life model in Brisbane, Australia.

An Alternative Stochastic User Equilibrium Formulation Based on Regret Theory

Traffic assignment is the last stage of the classical transportation planning process in which, the travel demand of each O–D pair is allocated to the network links, and links’ flows are estimated. To solve such a problem, some assumptions should be made about travellers’ decision-making behavior. One of the most popular approaches in this regard is the deterministic assignment that assumes all drivers are fully informed about the condition of the network and they always select the best (usually the shortest) route. These assumptions do not thoroughly match to the reality. To deal with this problem, the concept of stochastic user equilibrium has been introduced. The conventional stochastic user equilibrium assignments models are typically based on random utility theory. In this paper an alternative approach for stochastic user equilibrium assignment called random regret theory has been used in which a random regret-minimization (RRM) model is developed. RRM considers the regret of an option just with respect to outperformed options and furthermore does not lead to a closed-form stochastic user equilibrium (SUE) model, though based on that a formulation of SUE is proposed in a variational inequality form. In this study the definition of regret is modified and based on that a closed form SUE model is developed. This model is examined by two network examples.

A Stochastic User Equilibrium Assignment Model under Stochastic Demand and Supply Following Lognormal Distributions

A Stochastic User Equilibrium Assignment Model under Stochastic Demand and Supply Following Lognormal Distributions

Passenger flow control with multi-station coordination in subway networks: algorithm development and real-world case study

ABSTRACTThis paper addresses the problem of passenger flow control in a multi-line subway network during peak hours. A new multi-station coordinated passenger flow control model is proposed to simultaneously adjust the number of inbound and transfer passengers entering multiple stations or lines. The implementation of passenger flow control governs the redundant passengers to queue at given facilities, which is similar to ramp metering that regulates the number of vehicles entering a highway segment. The proposed model is a bi-level programming, whose upper level aims to optimize the system performance with different passenger flow control strategies, while the lower level is a logit-based stochastic user equilibrium assignment problem under a given strategy, considering passenger flow evolution, dynamic path cost, and route choice. An algorithm, integrating the method of successive averages with genetic algorithm, is developed to solve the model. A real-world case study is conducted to examine the validity.

Optimizing a desirable fare structure for a bus-subway corridor.

This paper aims to optimize a desirable fare structure for the public transit service along a bus-subway corridor with the consideration of those factors related to equity in trip, including travel distance and comfort level. The travel distance factor is represented by the distance-based fare strategy, which is an existing differential strategy. The comfort level one is considered in the area-based fare strategy which is a new differential strategy defined in this paper. Both factors are referred to by the combined fare strategy which is composed of distance-based and area-based fare strategies. The flat fare strategy is applied to determine a reference level of social welfare and obtain the general passenger flow along transit lines, which is used to divide areas or zones along the corridor. This problem is formulated as a bi-level program, of which the upper level maximizes the social welfare and the lower level capturing traveler choice behavior is a variable-demand stochastic user equilibrium assignment model. A genetic algorithm is applied to solve the bi-level program while the method of successive averages is adopted to solve the lower-level model. A series of numerical experiments are carried out to illustrate the performance of the models and solution methods. Numerical results indicate that all three differential fare strategies play a better role in enhancing the social welfare than the flat fare strategy and that the fare structure under the combined fare strategy generates the highest social welfare and the largest resulting passenger demand, which implies that the more equity factors a differential fare strategy involves the more desirable fare structure the strategy has.

TRAFFIC ASSIGNMENT MODEL OF AL-AMARAH CITY

The initiation of this study was made with the objective of loading or assigning the flow of traffic in the base and target year (expressed as a matrix identifying the number of trips generated and distributed in the previous study from each Traffic analysis zone (TAZ) to every other within the study area) on a road network of Al-Amarah City. The traffic assignment process is usually implemented in two steps. The first step is constructing the network dataset of road network of Al-Amarah city for obtaining the optimal route between each node to all other nodes depending on two criteria; distance and time for evaluation the accessibility of all nodes in the road network. The second step uses stochastic user equilibrium and system optimum assignment models to assign the traffic distributed between all possible origins and destinations to the road network itself. The analysis is done using TransCAD software ver. 4.5 and Network Analysis/Arc GIS 10.3 for Al-Amarah City. Results showed that in the base year, The results of the stochastic user equilibrium assignment model there is no link in Al-Amarah network has v/c ratio between the range (0.81-1.00) and over which represent level of service equal to or more than D. The overall evaluation of Al-Amarah road network is level of service (LOS) equal to B and there is an improvement in the work of Al-Amarah road network by using the system optimum model. In the target year, the results of two assignment models are proximally similar. The black color (v/c >1.0) is appeared clearly in the assignment result map especially on the two main bridges in the city (Al-Yugoslavi Bridge and Al-Jumhuriah Bridge). When the red color (LOS E) is appeared in the links in near the centers of sectors (1,2, and 4). The most links ranges between (LOS D and LOS C) with v/c ratio Range (0.70-0.90).

Stochastic user equilibrium traffic assignment with equilibrated parking search routes

In this paper we define and formulate the concept of parking search routes (PSR) where a driver visits a sequence of parking locations until the first vacant parking spot is found and in doing so may account for (expected) parking probabilities. From there we define and formulate the stochastic user equilibrium (SUE) traffic assignment in which no driver, by unilaterally changing its PSR, can lower its perceived expected generalized costs. Recognizing the interdependency between PSR flows, travel times and parking probabilities, we propose a queuing model in order to compute endogenous parking probabilities accounting for these factors as well as maximum admissible search times. To solve the SUE assignment with equilibrated PSR we propose a solution algorithm, including a method for PSR choice set generation. The model is implemented and applied both to a number of experimental cases to verify its properties and to a real-life setting to illustrate its usefulness in parking-related studies.

Bounding the inefficiency of the C-logit stochastic user equilibrium assignment

Compared with standard logit-based stochastic user equilibrium assignment model, the C-logit model describes route choice behavior in a more realistic way by considering the overlapping effect between routes. This paper investigates the inefficiency upper bounds of this model against the deterministic system optimum and the C-logit stochastic system optimum in terms of the total network travel time. It is found that the commonality factor of overlapping routes significantly affects the inefficiency bound, besides link congestion degree, total demand and the number of feasible routes. If the commonality factor is not considered, the efficiency loss resulting from selfishly stochastic travel behavior will be to large extent underestimated.

A Two-Stage Algorithm for Origin-Destination Matrices Estimation Considering Dynamic Dispersion Parameter for Route Choice.

This paper proposes a two-stage algorithm to simultaneously estimate origin-destination (OD) matrix, link choice proportion, and dispersion parameter using partial traffic counts in a congested network. A non-linear optimization model is developed which incorporates a dynamic dispersion parameter, followed by a two-stage algorithm in which Generalized Least Squares (GLS) estimation and a Stochastic User Equilibrium (SUE) assignment model are iteratively applied until the convergence is reached. To evaluate the performance of the algorithm, the proposed approach is implemented in a hypothetical network using input data with high error, and tested under a range of variation coefficients. The root mean squared error (RMSE) of the estimated OD demand and link flows are used to evaluate the model estimation results. The results indicate that the estimated dispersion parameter theta is insensitive to the choice of variation coefficients. The proposed approach is shown to outperform two established OD estimation methods and produce parameter estimates that are close to the ground truth. In addition, the proposed approach is applied to an empirical network in Seattle, WA to validate the robustness and practicality of this methodology. In summary, this study proposes and evaluates an innovative computational approach to accurately estimate OD matrices using link-level traffic flow data, and provides useful insight for optimal parameter selection in modeling travelers’ route choice behavior.

A stochastic user equilibrium assignment problem in discrete network design problem

A stochastic user equilibrium assignment problem in discrete network design problem

A stochastic user equilibrium assignment problem in discrete network design problem

We formulate the transportation discrete network design problem (DNDP) as a mixed-integer bi-level mathematical problem, based on the concept reserve capacity. The upper level goal programme maximises the reserve capacity by designing the direction of street and increasing the street capacity through lane addition. The lower level problem is stochastic user equilibrium traffic assignment problem within a probit-based path choice decision framework which generates user equilibrium flow patterns. Because of non-convexity nature of the model, meta-heuristic methods used to solve the problem and we used Monte Carlo simulation approach to compute path choice probabilities and stochastic user equilibrium solved by method of successive averages. A hybrid genetic algorithm with simulated annealing and an evolutionary simulated annealing algorithm are proposed. Numerical examples are presented to verify the proposed model and algorithm.

Combined Gravity Model Trip Distribution and Paired Combinatorial Logit Stochastic User Equilibrium Problem

The equivalent mathematical formulation of the combined doubly-constrained gravity-based trip distribution and paired-combinatorial-logit stochastic user equilibrium assignment problem (CDA-PCL-SUE) is proposed. Its first order conditions are shown to be equal to the gravity equations and PCL formula. The proposed solution method is a path-based partial linearization algorithm to approximately solve the restricted CDA-PCL-SUE. The proposed algorithm is a three-phase iterative process. Phase 1 is an entropy maximization problem on O-D flow space that can be solved by Bregman’s balancing algorithm. Phase 2 is a PCL SUE problem that can be solved by PCL formula. Phase 3 is line search. CDA-PCL-SUE is solved on a small network and a real network, the city of Winnipeg network. The proposed algorithms with the six line search methods, namely, golden section (GS), bisection (BS), Armijo’s rule (AR), method of successive averages (MSA), self-regulated averaging (SRA) scheme, and quadratic interpolation (QI) scheme, are compared in terms of various convergence characteristics: root mean square error, step size, KKT-based mean square error and objective function. In terms of computational efficiency, under different path set sizes, dispersion parameters, impedance parameters and demand levels, the following line search methods are ordered from best to worst: SRA, GS, AR, QI, BS and MSA. The performances of Armijo’s rule and QI have greater variances. The performance of QI is worse with the increase of the path set size. Given all other factors being the same, the increase of dispersion parameter, path set size or demand level yields the increase of CPU time, whereas the change of impedance parameter does not influence CPU time. In addition, CDA-PCL-SUE is compared with its multinomial-logit counterpart (CDA-MNL-SUE).

Travel Distance on Each Grade Road of Urban City Based on Reliability

In order to reflect influence of travel time reliability on route choosing, considering traffic accidents’ influence under random state, we analyzed travel distance distribution regularity of each grade road, through traffic assignment. Travel time reliability model was produced and modified, considering the randomness of accidents, delay time, and capacity. The maximum preponderant travel range of each grade road was defined, and stochastic user equilibrium assignment was adopted to get travel turnover and distance, based on the corrected model. And then regulation of distance distribution was analyzed. Conclusion shows that reasonable travel distance of local way, distribution way, and primary way is 1 km, 2.28 km, and 3.54 km, respectively.