Evaluation of network reliability using stochastic user equilibrium

Public transport (PT) agencies are increasingly keen on integrating ride-hailing (RH) services with PT to improve overall mobility. Understanding the traffic flow distribution in the integrated system is vital for the policy decision-making and services design of such a system. We propose a stochastic user equilibrium (SUE) model for multimodal transport systems consisting of private car, PT and RH. The travel costs in the SUE model are investigated using a multimodal graph representation to capture the relationship of different travel modes in the integrated system. We apply the proposed model to a toy case and a real-world case. A RH subsidy strategy is compared with the benchmark to demonstrate travellers’ route and mode shifts in the integrated system. Our findings offer insights on subsidising RH services through the proposed model, and provide valuable knowledge on the planning and design of the integrated system.

As one of the most promising travel modes in the modern urban transportation network, ridesharing is widely favored because of its convenience and lower travel costs. In the literature on ridesharing equilibrium modeling, the deterministic user equilibrium (DUE) and logit-based stochastic user equilibrium (SUE) are often adopted in the role choice or route choice. Although SUE models tackle the inability of DUE models that cannot consider perception errors, the logit-based SUE model assumes the perception variance is fixed for all travel modes or travel routes. In order to deal with the homogenous perception variance issue, this study proposes a weibit-based SUE model to characterize the mode choice and route choice in the stochastic ridesharing user equilibrium (SRUE) problem. In the proposed model, we focus on the travelers' conversion among three modes (i.e., solo driver, ridesharing driver, ridesharing passenger) and explicitly consider the relationship between origin-destination (O–D) supply (i.e., the number of ridesharing drivers) and O–D demand (i.e., the number of ridesharing passengers). Moreover, we consider a non-additive path cost function that consists of travel time, monetary cost, ridesharing compensation, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$a$</tex> nd/or inconvenient cost in the SRUE problem. We customize a solution framework for solving this novel model efficiently. Numerical examples are conducted to illustrate the applicability of the weibit-based SRUE model.

The stochastic user equilibrium (SUE) traffic assignment model integrates the concepts of random assignment and Wardrop equilibrium, and it makes the assignment results more reasonable. The conventional Logit-based SUE model is explicitly built upon path flow variables, which encumbers its large-scale applications and further theoretical analyses. In this paper, a link-based SUE traffic assignment model with link capacity constraints is developed by using the network equilibrium modeling approach. The solution equivalence and uniqueness of the proposed model are rigorously proved. An efficient solution algorithm is also proposed to obtain the equilibrium solution. Numerical results indicate that the proposed link-based SUE model can reflect the real route choice behavior of travelers more reasonable and also facilitate the algorithmic development and further theoretical analyses.

Since regret theory has been introduced to model travellers’ route choices, various random regret minimization (RRM) models have been developed for the choice situation of multiple alternatives and multiple attributes. There are two approaches dealing with multi-objective optimisations: one is to combine different attributes into a single additive one and the other is to consider each attribute separately. The existing RRM models adopt the first approach to measure regret. However, travellers might not always trade off attributes in such a compensatory way. In this paper, under the assumption that travellers might consider attributes separately, we develop two new regret-based stochastic user equilibrium (SUE) models by incorporating the RRM model and the hybrid RUM-RRM model into a non-compensatory multi-objective framework. The majority of the second approaches dealing with multiple objectives generally provide a feasible solution set caused by conflicts among objectives. Different from that, the two new models provide probabilistic choice to each route, based on which a single SUE path flow pattern would be attained. Meanwhile, the compromise effect which is widely seen in consumer behaviour can be explained by the two new models. The equivalent variational inequality problems for the proposed models and a path-based algorithm using the method of successive averages have been given. Numerical examples are further conducted to illustrate the properties of the proposed models and the effectiveness of the algorithm.

A mathematical programming method for sensitivity analysis of the link-capacitated stochastic user equilibrium model is presented in this article. By the sensitivity matrices, the changes in the network flows can be easily obtained, while some links reach the capacity limits. By link-based stochastic user equilibrium model with link capacity constraints, it is possible to formulate an efficient algorithm for the sensitivity analysis. Two numerical examples are provided for demonstrating the correctness and implementability of the method finally. Since the link capacity is one of the constraints of the model, the method presented here can also be used for the basic model with other constraints.

The work zone on the urban road network will affect the surrounding road traffic. To represent the influence area of the work zone, the concept of a subnetwork is proposed in this paper. Delineating a suitable subnetwork quantitatively is a challenging problem. To address this issue, the node synthesized indexes (NSI) are deployed as a variability measure that captures both the change of link flow and origin-destination (OD) demand. The inertia-based stochastic user equilibrium with the elastic demand (ISUEED) model is proposed to accurately provide the data of link flow and OD demand for the network with the work zone. Correspondingly, the data of the network without a work zone can be obtained by the stochastic user equilibrium (SUE) model. According to the value of NSI, the initial range of the subnetwork is determined. Finally, the connectivity and compactness can be guaranteed by the modified L-shell algorithm. To demonstrate the performance of the method, two case studies and sensitivity analyses are conducted based on the Braess network and the local road network in Changchun, China. The proposed method is beneficial to reduce the complexity of the traffic model by substituting the entire network with a subnetwork.

An economic analysis of a multi-modal transportation system with ride-sourcing services and multi-class users

Cordon toll competition in a network of two cities: Formulation and sensitivity to traveller route and demand responses

Path sets size, model specification, or model estimation: Which one matters most in predicting stochastic user equilibrium traffic flow?

To enhance the overall accessibility and operational efficiency of highway networks, this paper proposes an integrated analytical approach based on node importance, network reliability, and critical link identification to identify key transportation corridors within highway networks. Initially, a comprehensive node importance measurement method is developed by integrating static geometric characteristics and dynamic traffic attributes of complex networks. The weights of static indicators are calculated using an improved entropy weight method, while the dynamic importance of nodes is assessed based on the h-index, resulting in a ranked node importance list. Subsequently, from the perspective of network reliability, critical nodes are identified and ranked by simulating node failure scenarios through attack strategies, evaluating their impact on network connectivity and travel time. Further, critical links are identified utilizing the Stochastic User Equilibrium (SUE) model and Ant Colony Optimization (ACO). Finally, a multi-objective key corridor identification method based on feature lines is formulated by comprehensively considering node importance, network reliability, and critical road segments. An empirical analysis is conducted on the highway network across 11 counties/districts of Zhaotong City, Yunnan Province. Three key transportation corridors are ultimately identified:Ludian County-Zhaoyang District-Daguan County-Yanjin County, Ludian County-Zhaoyang District-Daguan County-Yongshan County, Ludian County-Zhaoyang District-Yiliang County.

To ensure the equity of exclusive bus lane (EBL) allocation under multimodal traffic conditions, a bi-level programming model is first constructed. The upper-level model is the minimum total system cost considering the Gini coefficient and the lower-level model constructed a stochastic user equilibrium (SUE) model based on logit loading. Secondly, a heuristic algorithm combining an improved genetic algorithm (GA) and a method of the successive average method (MSA) is designed. Finally, the Nguyen and Dupuis networks are used as examples to verify and analyze the effectiveness, superiority and sensitivity of the model and algorithm. The results show that the method can effectively obtain the optimal solution of the upper-level model as 15,004 RMB, the Gini coefficient is 0.31, and the equity is at a relatively reasonable level. Compared with the different allocation schemes, the proposed scheme has a higher bus sharing rate and lower Gini coefficient. At the same time, when the actual demand is twice the basic demand, the bus share rate is the largest, 65%, and the Gini coefficient is the smallest at 0.3. The bus share rate decreases with the increase in the proportion of high time value travelers, which fully verifies the sensitivity of the model to the type of traveler.

Stochastic ridesharing equilibrium problem with compensation optimization

Based on the random utility theory of passengers' boarding choices, this paper has proposed a Stochastic User Equilibrium Model with elastic demand for different trains. Taking the Stochastic User Equilibrium Model as the lower model, it has constructed a Bi-level Programming Model in which the upper model aims for maximizing the railroad department's income. It has solved the lower model with MSA algorithm to obtain the flow distribution by using Bi-level Programming with Particle Swarm Optimization. The passenger-dedicated line from Xi'an to Lanzhou is taken as an example, where rational off -line range under different moving distances on high-speed line was obtained.

In order to design the traffic network more accurately, the bi-level programming model for the continuous network design problem based on the paired combinatorial Logit stochastic user equilibrium model is proposed in this study. In the model, the paired combinatorial Logit stochastic user equilibrium model which is used to characterize the route choice behaviors of the users is adopted in the lower level model, and the minimum summation of the system total costs and investment amounts is used in the upper objective function. The route-based self-regulated averaging (SRA) algorithm is designed to solve the stochastic user equilibrium model and the genetic algorithm (GA) is designed to get the optimal solution of the upper objective function. The effectiveness of the proposed combining algorithm which contains GA and SRA is verified by using a simple numerical example. The solutions of the bi-level models which use the paired combinatorial Logit stochastic user equilibrium model in the lower level model with different demand levels are compared. Finally, the impact of the dispersion coefficient parameter which influences the decision results of the network design problem is analyzed.

Understanding the route choice behaviour of metro-bikeshare users