User Equilibrium Assignment Model Research Articles

Timetable synchronization optimization in a subway–bus network

The subway and bus together contribute to the structure of public transport network in a metropolis. However, integrated service of public transport is not satisfied due to the lower timetable synchronization between these two modes at transfer stations. In this paper, a double-layer public transport network composed of subway/bus lines and stations is first created. Then, two stages are included in the timetable optimization process. In the first stage, a user equilibrium assignment model and a capacity restriction iterative algorithm are employed to obtain the passenger distribution in the subway–bus public transport transfer network. Based on this distribution, with the consideration of the synchronization and section service level, a mixed-integer linear programming (MILP) model is applied to optimize the timetables of the subway and bus networks in the second stage. Computational results using real Automatic Fare Collection System (AFC) data from the public transport system in Beijing are reported, and these results show that the suggested model is efficient in improving passenger service levels.

Exploring the robustness of public transportation system on augmented network: A case from Nanjing China

A highly robust urban public transportation network is the foundation for the stable and sustainable development of a city. Managers may benefit from a reasonable investigation into the robustness of the public transportation system to recognize and deliver improved public transportation services. This paper developed a robustness analysis framework for public transportation systems on augmented network (AN). Specifically, an AN was first built to treat the public transit network from a multi-layer perspective. The AN carefully considers the boarding, alighting, riding and transfer behaviors, and develops cost functions under the congestion effect, thus sufficiently simulating the real passengers’ behaviors. Then, the user equilibrium (UE) assignment model, a model widely used for passenger flow forecasting, is applied to guide the robustness analysis under cascading failures. Finally, a real large-scale bus–rail hybrid network in Nanjing is used as a case study. The results show that the initial station capacities are significant to the impact of the cascading failure, from which we conclude that a larger initial capacity of stations can prevent the cascading failures. By investigating the relationship between passenger flow and cascade size, the comparative results further explain the mechanisms of cascading failures. Thanks to the AN and UE, three types of travel times can be compared to reflect the quality of public passenger trips, which should provide traffic managers with pertinent advice for improving service.

Transit Frequency Optimization in Bi-modal Networks Using Differential Evolution Algorithm

This study proposes a bi-level optimization model for the transit frequency setting problem in bi-modal networks. The objective of the upper-level problem is to obtain a solution set of bus line frequencies that provide the minimum total travel cost of the car and bus users. Differential Evolution (DE) algorithm is employed in the upper-level model to determine the optimal headways for a given route structure. The lower-level model is a congested multi-modal user equilibrium assignment model, which considers the interactions of car and bus flows, for determining joint mode/route preferences of the network users, which considers the interactions of car and bus flows. The developed model is tested on Mandl's benchmark network to evaluate its performance and applicability. The comparative experiments demonstrate that the proposed model leads to reductions in transportation costs. Also, the results of numerous optimization runs show that DE performs well in finding similar frequency sets in independent optimizations.

An electric vehicle charging station access equilibrium model with M/D/C queueing

Despite the dependency of electric vehicle (EV) fleets on charging station availability, charging infrastructure remains limited in many cities. Three contributions are made. First, we propose an EV-to-charging station user equilibrium (UE) assignment model with a M/D/C queue approximation as a nondifferentiable nonlinear program. Second, to address the non-differentiability of the queue delay function, we propose an original solution algorithm based on the derivative-free Method of Successive Averages. Computational tests with a toy network show that the model converges to a UE. A working code in Python is provided free on Github with detailed test cases. Third, the model is applied to the large-scale case study of New York City Department of Citywide Administrative Services (NYC DCAS) fleet and EV charging station configuration as of July 8, 2020, which includes unique, real data for 563 Level 2 chargers and 4 Direct Current Fast Chargers (DCFCs) and 1484 EVs distributed over 512 Traffic Analysis Zones. The arrival rates of the assignment model are calibrated in the base scenario to fit an observed average utilization ratio of 7.6% in NYC. The model is then applied to compare charging station investment policies of DCFCs to Level 2 charging stations based on two alternative criteria. Results suggest a policy based on selecting locations with high utilization ratio instead of with high queue delay.

Urban Road Network Maintenance Scheduling Using Ant Colony Optimization

In this study, an optimization model for road maintenance scheduling is proposed. The proposed model determines a maintenance schedule for a given set of links in an urban road network, that minimizes the total travel time during the maintenance period under a set of assumptions and a particular crew number constraint. It is assumed that all lanes of a road to be repaired are closed to traffic during the maintenance. Ant Colony Optimization (ACO), a suitable algorithm for discrete transportation problems, is employed in the proposed model. The model generates a set of roads to be closed for each maintenance day. The total travel time during the whole maintenance period is calculated using the deterministic user equilibrium assignment model. The proposed model is applied to a test network, and more efficient schedules in terms of total travel time are obtained compared to randomly generated schedules.

A Bi-Level Model for Green Freight Transportation Pricing Strategy Considering Enterprise Profit and Carbon Emissions

Due to the impact of COVID-19, enterprises need effective pricing strategies to improve profits and viability. In order to fill research gaps in the literature relating to market competition among different freight modes and to adjust the freight transportation structure by optimizing transportation prices, we propose a multi-objective bi-level programming pricing model that considers market competition and the carbon emissions of the freight system in China. First, an objective function in upper-level planning was used to improve logistics enterprise profits and reduce the total carbon emissions of the freight system. Then, a generalized cost function for the freight transportation mode was designed to quantify the market competition among different transportation modes, and a user equilibrium assignment model was established to obtain the results of cargo flow assignment in lower-level planning. To solve the model, a sensitivity analysis algorithm was designed, and a logistics network example was used to verify the effectiveness of the model. The experimental results show that reasonable freight price adjustment can effectively increase enterprise profits and reduce the total carbon emissions of the freight system. In this paper, we provide a new method for freight pricing research, considering the market competition of multiple transportation modes, and provide a new idea for adjusting the transportation structure through freight price optimization, which will play a positive role in promoting the development of green freight.

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.

A Bi-Level Multi-Objective Optimization Model for Micro-Circulation Road Networks in the Open Block Area Considering Traffic Pollution and Intersection Delays

It is important for urban traffic micro-circulation to improve the density of urban branch road networks by opening roads inside blocks. To reasonably optimize the micro-circulation road network in the open block area, a bi-level multi-objective programming model that considers traffic pollution and intersection delays was developed. In this paper, the goals of minimizing traffic pollution and total travel cost are added to the upper-level programming model and the user equilibrium assignment model with the consideration of intersection delay was presented as the lower-level programming model. A modified genetic algorithm (GA) embedded with the Frank-Wolfe algorithm was designed to solve the established model. The traffic conditions of arterial roads and micro-circulation branch roads before and after optimizing the micro-circulation block road network were compared and analyzed by a numerical example. The results demonstrated that the bi-level programming model can effectively determine the traffic direction of branch roads and the forbidden situation of intersections in the micro-circulation network. Compared with the closed block, the average saturation of the main trunk road decreased from 0.97 to 0.83 with a decline ratio of 14.43% after optimizing the micro-circulation network in the open block area; the average saturation of the secondary trunk road decreased from 0.86 to 0.77, with a decline ratio of 10.47%. The travel time cost decreased by approximately 6.55%, and the traffic pollution decreased by approximately 3.40%, which verified the optimization effect of the model and the algorithm.

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.

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.

Hybrid machine learning and optimisation method to solve a tri‐level road network protection problem

In this study, the authors employ machine learning to develop a new solution method for solving a tri-level network protection problem. In the upper-level, the planner aims to minimise the impact of the interdictor's attempt to disrupt a road network through protection activities. At the middle-level, however, the interdictor seeks to maximise the network's cost function, that is total travel time while the user equilibrium assignment models the road users behaviour at the lower-level. The proposed solution algorithm combines implicit enumeration with machine learning for faster performance. In so doing, four machine learning methods are evaluated among which the artificial neural network model shows the best performance and thereby to be exploited. Principal component analysis is also employed as part of the data pre-processing to perform dimensionality reduction. The proposed solution algorithm exhibits a reasonable level of tractability when employed to solve large problems in which a real-world network is under investigation. Although it cannot guarantee global optimality, it is argued that this is an essential compromise for the application of the network optimisation problems on extensive real-world networks and the large solution space that they generate.

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

Vulnerability Assessment for Cascading Failure in the Highway Traffic System

Vulnerability assessment is of great significance to highway traffic system. As the widespread cascading failure may cause serious damage, factor identification is necessary to improve the security level of highway system. In this paper, the Dematel method is applied to identify the vulnerability priorities of important factors, and a new assessment method for highway system vulnerability is presented by considering system cascading failure. The traffic allocation and reallocation are then optimized under user equilibrium assignment model in different scenarios. Finally, the methodology is applied to the Heilongjiang highway network and the results shows that vulnerable sections in highway networks can be determined efficiently in our proposed process.

Traffic Signal Optimisation in Disrupted Networks with Re-Routing

Abstract This paper describes a modified bi-level framework to simulate disruptive events in urban road networks with different levels of disruption severity and duration. This framework combines the Cross Entropy method to optimise traffic signals and the quasi-dynamic user equilibrium assignment model embedded in SATURN software package. This enables simulation of short-term closures with less computational effort and running time than fully dynamic models. We have applied this model to the Cambridge (UK) network and demonstrated how the degradation at one node affects the optimal signal settings at that node and nearby nodes. The computational results show that for different disruption severities, as traffic starts to divert to other routes, the optimal traffic signal settings changes, to minimise the travel time.

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.

Two Methods to Calibrate the Total Travel Demand and Variability for a Regional Traffic Network

AbstractThis article proposes a novel methodology that uses the bi‐level programming formulation to calibrate the expected total demand and the corresponding demand variability of traffic networks. In the bi‐level formulation the upper‐level is either a new maximum likelihood estimation method or a least squares method and the lower‐level is the strategic user equilibrium assignment model (StrUE) which accounts for the day‐to‐day demand volatility. The maximum likelihood method proposed in this article has the ability to utilize information from day‐to‐day observed link flows to provide a unique estimation of the total demand distribution, whereas the least squares method is capable of capturing link flow variations. The lower‐level StrUE model can take the total demand distribution as input, and output a set of link flow distributions which can then be compared to the link‐level observations. The mathematical proof demonstrates the convexity of the model, and the sensitivity to the prediction error is analytically derived. Numerical analysis is conducted to illustrate the efficiency and sensitivity of the proposed model. Some possible future research is discussed in the conclusion.

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).

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.

Continuous Transportation Network Design Problem Based on Bi-level Programming Model

A bi-level programming model was widely used to describe the continuous transportation network design problem. The objective function in upper-level model was to make the sum of total impedance and total investment budget minimal in a traffic network. The lower-level model was a user equilibrium assignment model with fixed demand. In order to make the results more realistic, this paper proposed an improved model with stochastic transportation network design, and presented genetic algorithm and Frank-Wolfe (FW) algorithm to find optimal solution. Then a specific network example was given to prove the effectiveness of the model. The results show that an optimal value of existing links capacities for the formulation can be obtained and it can minimize the sum of total impedance and investment budget, which can provide a reasonable reference for the decision-makers.