Stochastic User Equilibrium Research Articles

Bounding the Inefficiency of the Multiclass, Multicriteria C-Logit Stochastic User Equilibrium in a Transportation Network

We derive the exact inefficiency upper bounds of the multiclass C-Logit stochastic user equilibrium (CL-SUE) in a transportation network. All travelers are classified on the basis of different values of time (VOT) into M classes. The multiclass CL-SUE model gives a more realistic path choice probability in comparison with the logit-based stochastic user equilibrium model by considering the overlapping effects between paths. To find efficiency loss upper bounds of the multiclass CL-SUE, two equivalent variational inequalities for the multiclass CL-SUE model, i.e., time-based variational inequality (VI) and monetary-based VI, are formulated. We give four different methods to define the inefficiency of the multiclass CL-SUE, i.e., to compare multiclass CL-SUE with multiclass system optimum, or to compare multiclass CL-SUE with multiclass C-Logit stochastic system optimum (CL-SSO), under the time-based criterion and the monetary-based criterion, respectively. We further investigate the effects of various parameters which include the degree of path overlapping (the commonality factor), the network complexity, degree of traffic congestion, the VOT of user classes, the network familiarity, and the total demand on the inefficiency bounds.

Sensor Deployment Strategy and Traffic Demand Estimation with Multisource Data

Since traffic origin-destination (OD) demand is a fundamental input parameter of urban road network planning and traffic management, multisource data are adopted to study methods of integrated sensor deployment and traffic demand estimation. A sensor deployment model is built to determine the optimal quantity and locations of sensors based on the principle of maximum link and route flow coverage information. Minimum variance weighted average technology is used to fuse the observed multisource data from the deployed sensors. Then, the bilevel maximum likelihood traffic demand estimation model is presented, where the upper-level model uses the method of maximum likelihood to estimate the traffic demand, and the lower-level model adopts the stochastic user equilibrium (SUE) to derive the route choice proportion. The sequential identification of sensors and iterative algorithms are designed to solve the sensor deployment and maximum likelihood traffic demand estimation models, respectively. Numerical examples demonstrate that the proposed sensor deployment model can be used to determine the optimal scheme of refitting sensors. The values estimated by the multisource data fusion-based traffic demand estimation model are close to the real traffic demands, and the iterative algorithm can achieve an accuracy of 10−3 in 20 s. This research has significantly promoted the effects of applying multisource data to traffic demand estimation problems.

On Stochastic-User-Equilibrium-Based Day-to-Day Dynamics

Researchers have proposed many different concepts and models to study day-to-day dynamics. Some models explicitly model travelers’ perceiving and learning on travel costs, and some other models do not explicitly consider the travel cost perception but instead formulate the dynamics of flows as the functions of flows and measured travel costs (which are determined by flows). This paper investigates the interconnection between these two types of day-to-day models, in particular, those models whose fixed points are a stochastic user equilibrium. Specifically, a widely used day-to-day model that combines exponential-smoothing learning and logit stochastic network loading (called the logit-ESL model in this paper) is proved to be equivalent to a model based purely on flows, which is the logit-based extension of the first-in-first-out dynamic of Jin [Jin W (2007) A dynamical system model of the traffic assignment problem. Transportation Res. Part B Methodological 41(1):32–48]. Via this equivalent form, the logit-ESL model is proved to be globally stable under nonseparable and monotone travel cost functions. Moreover, the model of Cantarella and Cascetta is shown to be equivalent to a second-order dynamic incorporating purely flows and is proved to be globally stable under separable link cost functions [Cantarella GE, Cascetta E (1995) Dynamic processes and equilibrium in transportation networks: Towards a unifying theory. Transportation Sci. 29(4):305–329]. Further, other discrete choice models, such as C-logit, path-size logit, and weibit, are introduced into the logit-ESL model, leading to several new day-to-day models, which are also proved to be globally stable under different conditions.

A Multiclass Cumulative Prospect Theory-Based Stochastic User Equilibrium Model with Path Constraints in Degradable Transport Networks

The limited driving range and the unavailability or insufficiency of battery charging/swapping stations cause the so-called range anxiety issue for traffic assignment involving battery electric vehicle (BEV) users. In addition, expected utility theory-based stochastic user equilibrium (EUT-SUE) model generates the perfectly rational issue when the travellers make route choice decisions. To tackle these two problems, this article improves the cumulative prospect theory-based stochastic user equilibrium (CPT-SUE) model in a degradable transport network through incorporating the constraints of multiple user classes and distance limit. In this degradable network, the travellers experience stochastic travel times due to network link capacity degradations. For this improved CPT-SUE model, the equivalent variational inequality (VI) model and associated method of successive averages (MSA) based solution are provided. The improved CPT-SUE model is tested and compared with the EUT-SUE model with distance limit, with results showing that the improved CPT-SUE model can handle jointly the range anxiety issue and the perfectly rational issue.

Impacts of the least perceived travel cost on the Weibit network equilibrium

ABSTRACT This study investigates the impacts of the least perceived travel cost on the stochastic user equilibrium (SUE) problem. The Weibit SUE models are considered since they have a location parameter that naturally capture the least perceived travel cost. Considering a positive location parameter enhances the behavioral reality by attaching a positive lower-bound to the perceived travel cost distributions. It reduces the perception variances route-specifically and causes route-specific coefficients of variation (CVs). The CVs reduce proportionally slower for shorter routes, thus contributing to resolving the scale insensitivity issue in the Weibit SUE models. In the meantime, the route-specific CVs cause better discrimination between short and long routes in terms of relative variability; more travelers shift to the shortest route between each origin-destination pair. Numerical results confirm the analytical results regarding the effects of the least perceived travel costs and demonstrate the efficiency and robustness of the proposed solution algorithm.

Modeling the effect of sensor failure on the location of counting sensors for origin-destination (OD) estimation

The network sensor location problem (NSLP) for origin–destination (OD) estimation identifies the optimal locations for sensors to estimate the vehicular flow of OD pairs in a road network. Like other measurement apparatuses, these sensors are subject to failure, which can affect the reliability of the OD estimations. In this paper, we propose a novel model that allows us to solve the NSLP for OD demand estimation by identifying the most reliable locations to install sets of sensors with consideration for a nonhomogeneous Poisson process to account for time-dependent sensor failure. The proposed model does not rely on the assumption that true OD demand information is known. We introduce two separate objective functions to minimize the maximum possible information loss (MPIL) associated with OD demand on sensor-equipped links and OD pairs during the lifetimes of the sensors. Both objective functions are formulated to incorporate the possibility of sensor failure into the calculated OD demands. We use stochastic user equilibrium (SUE) to address the stochasticity of traffic route selection. We then employ the weighted sums method (WSM) and an ε-constraint to incorporate the objective functions into an integrated formulation. Two sensor types with different time-dependent failure rates are considered to identify the optimal locations for sets of sensors for OD demand estimation purposes while addressing the available budget constraints. We also address the problem of scheduled/routine maintenance of existing sensors by introducing an additional sensor deployment phase that focuses on maintaining the reliability of information by repairing or replacing failed sensors, installing additional sensors or a combination of both. The numerical results from the proposed model demonstrate how the deployment of more advanced sensors with lower failure rates can effectively improve the reliability of the information obtained from sensors. We also evaluate the use of different weights for the WSM’s objective functions to explore alternative combinations of sensor configurations. The introduction of additional sensors to a network shows that the decision between repairing failed sensors and installing new sensors is highly dependent on the available budget and the failed sensors’ locations.

Traffic Control Scheme for Social Optimum Traffic Assignment with Dynamic Route Pricing for Automated Vehicles

In transportation modeling, after defining a road network and its origin-destination (OD) matrix, the next important question is how to assign traffic among OD-pairs. Nowadays, advanced traveler information systems (ATIS) make it possible to realize the user equilibrium solution. Simultaneously, with the advent of the Cooperative Intelligent Transport Systems (C-ITS), it is possible to solve the traffic assignment problem in a system optimum way. As a potential traffic assignment method in the future transportation system for automated cars, the deterministic system optimum (DSO) is modeled and simulated to investigate the potential changes it may bring to the existing traditional traffic system. In this paper, stochastic user equilibrium (SUE) is used to simulate the conventional traffic assignment method. This work concluded that DSO has considerable advantages in reducing trip duration, time loss, waiting time, and departure delay under the same travel demand. What is more, the SUE traffic assignment has a more dispersed vehicle density distribution. Moreover, DSO traffic assignment helps the maximum vehicle density of each alternative path arrive almost simultaneously. Furthermore, DSO can significantly reduce or avoid the occurrence of excessive congestion.

Monocentric versus polycentric urban structure: Case study in Hong Kong

Activity resource allocation or dispersion (e.g., employment, education), transport network improvement, and property development, affect the urban community in different ways. To illuminate their intricate relations, we study the perspectives of three groups of stakeholders: i) households with heterogeneous members seeking a common residence to optimize their proximity to activity resources; ii) transport planners aiming to relieve traffic congestion; and iii) property developers aiming to maximize their housing profit through the bid-rent process. To assess the impacts of different resource allocation patterns (centralized versus dispersed), a household bid-rent and residential location choice model with heterogeneous compositions is developed, including household members’ activity destination choices and travel choices under stochastic user equilibrium. We apply this model to a new redevelopment region in Kowloon, Hong Kong. The results show that centralized resource allocation increases the producer surplus but reduces the household disposable income. Compared with dispersion in school resource allocation or transport improvement, job reallocation is the most efficient in alleviating traffic congestion as employments are dispersed into multiple centers, and inter-zonal commute trips are converted into intra-zonal trips. We also investigate the outcomes as the urban structure varies from monocentric, dual-core into multiple self-contained communities (i.e. polycentric). The results show that any accessibility gain due to a change in the urban form will be capitalized by developers into higher housing prices in the new central business district (CBD) regions, hence shrinking the consumer surplus and disposable income. Therefore, it is unlikely to find an urban form that will achieve win–win–win situations for all three stakeholder groups in the case study example.

Evaluating the Capacity Coordination in the Urban Multimodal Transport Network

The urban multimodal transport network is composed of multiple layers of networks; thus, coordinating the capacity equilibrium among different sub-transport networks plays a crucial role to keep the entire network running efficiently. To quantify and evaluate the passenger flow distribution in an urban multimodal transport network, this research proposes a method to evaluate the capacity coordination in an urban multimodal transport network on the basis of assignment results calculated by the Stochastic User Equilibrium (SUE) model considering the link and path impedance of different sub-transport networks. It suggests evaluation functions for the indicator level of service (LOS) of the multimodal transport network, Gini coefficient of transport network, and mode share of transport modes, and it shows how the functions were estimated. Then, it reports on results with the evaluation scheme collected in a multimodal example application for roadway network, transit networks (bus transit network and urban rail transit network), and connection network. The evaluation results under different assumed origin–destination (OD) demand show the coordination degree and can be used to recognize shortcomings of the network. Moreover, the OD demand interval of real network with good coordination can be deduced, which can also help transport planners to find the optimal strategy.

Demand-responsive passenger flow control strategies for metro networks considering service fairness and passengers’ behavioural responses

This paper presents a methodology for developing demand-responsive passenger flow control strategies for oversaturated metro networks. A stated preference-off-revealed preference survey was conducted to capture passengers’ behavioural responses to the passenger flow control strategies, and revealed significant behavioural change intentions in terms of departure times and mode choices. Currently, such behavioural responses are often ignored, leading to deviations in estimating the size of a target group and performance of a proposed strategy. To address this issue, in this study, a mathematical programming with equilibrium constraints (MPEC) approach was developed to optimise demand-responsive passenger flow control strategies. The proposed MPEC model highlights the importance of balancing the operational efficiency of a metro system with service fairness perceived by passengers. In particular, a nested logit-based stochastic user equilibrium problem was included to accommodate potential changes in demand patterns driven by candidate passenger flow control strategies. Two empirical cases based on the Guangzhou and Beijing metros were used to demonstrate the effectiveness of the proposed model and solution algorithm. The results show that the inclusion of service fairness considerations does not contradict the pursuit of efficiency. Instead, dual emphases on service fairness and passengers’ behavioural responses help create a win–win situation for both metro operators and passengers. In the Guangzhou and Beijing metros, the highest section load rate decreased from 126.6% to 105.7% and from 122.98% to 106.87%, respectively, under the optimal passenger flow control strategies. The corresponding network load Gini coefficients improved from 0.278 to 0.259 and from 0.269 to 0.248, demonstrating the remarkable performance of this approach in regards to peak cutting and load balancing.

Optimal locations and electricity prices for dynamic wireless charging links of electric vehicles for sustainable transportation

Electric vehicles are one of the effective tools for pollution reduction and sustainable transportation in emerging markets. In this paper, we investigate the optimal locations and electricity prices for dynamic wireless charging links of electric vehicles to minimize total social cost within a given budget while ensuring nonnegative operating profit to alleviate a government’s operational pressure. A logit-based stochastic user equilibrium model is proposed to capture drivers’ routing and recharging behavior, and a linear programming approach is developed to determine a path recharging plan. The problem is rendered as a bi-level formulation and solved using an efficient surrogate model-based algorithm.

A Continuous Transportation Network Design Problem with the Consideration of Road Congestion Charging

This paper proposes a biobjective continuous transportation network design problem concerning road congestion charging with the consideration of speed limit. The efficiency of the traffic network and the reduction of pollution in the network environment are improved by designing a reasonable road capacity enhancement and speed limit strategy. A biobjective bilevel programming model is developed to formulate the proposed network design problem. The first target of the upper problem is the optimization of road charging efficiency, and the other target is the total cost of vehicle emissions; these objectives are required to devise the optimal road capacity enhancement scheme, speed limiting schemes for different time periods, and the road pricing scheme. The lower-level problem involving travellers’ route choice behaviours uses stochastic user equilibrium (SUE) theory. Based on the nondominated sorting genetic algorithm, which is applied to solve the bilevel programming model, a numerical example is developed to illustrate the effectiveness of the proposed model and algorithm. The results show that the implementation of congestion charging measures on the congested road sections would help to alleviate road congestion in the transportation network, effectively save transportation infrastructure investment and limited urban land resources, increase fiscal revenue, and open up new sources of funds for urban infrastructure construction.

A Stochastic User Equilibrium Formulation for the Cumulative Prospect Theory-Based Cross-Nested Logit

The cumulative prospect theory provides a better description for route choice behavior of the travelers in an uncertain road network environment. In this study, we proposed a multiclass cumulative prospect value- (CPV-) based cross-nested logit (CNL) stochastic user equilibrium (SUE) model. For this model, an equivalent variational inequality (VI) model is provided, and the existence and equivalence of the model solutions are also proved. The method of successive averages (MSA), method of successive weighted averages (MSWA), and self-regulated averaging (SRA) method are designed and compared. In addition, the proposed multiclass CPV-based CNL SUE model is also compared with the multiclass utility value- (UV-) based CNL SUE model. The results show that the path flow assigned by the multiclass CPV-based CNL SUE model is more consistent with the actual situation. The impact of different model parameters on the cumulative prospect value (CPV) is investigated.

A stochastic user equilibrium model solving overlapping path and perfectly rational issues

A stochastic user equilibrium model solving overlapping path and perfectly rational issues

Dynamic Traffic Assignment for regional networks with traffic-dependent trip lengths and regional paths

The estimation of trip lengths has been proven to be a key feature for the application of aggregated traffic models based on the Macroscopic Fundamental Diagram. The paths and distances to be traveled by vehicles in regional networks vary over time, due to changes in the traffic conditions. In this paper, we develop a methodological framework to explicitly determine traffic-dependent regional paths and estimate their travel distances. This framework is incorporated into a dynamic traffic assignment module designed to target the Deterministic and Stochastic User Equilibrium in regional networks. We first discuss how regional paths and their characteristic trip lengths are influenced by changes in the regional traffic dynamics. We then test the proposed methodology for estimating traffic-dependent travel distances on small and medium-sized networks, considering a simulation environment. We show that our methodology provides good estimations of the traffic-dependent trip lengths. Our results also shed light on the importance of how time-dependent trip lengths influence the traffic dynamics in the regions.

Coordinated operation of coupled transportation and power distribution systems considering stochastic routing behaviour of electric vehicles and prediction error of travel demand

The popularisation of electric vehicles (EVs) and the development of dynamic wireless charging technology have created an emerging trend of transportation electrification, which strengthens the coupling between electrified transportation network (ETN) and power distribution network (PDN). Meanwhile, the stochastic routing behaviour of EVs and prediction error of traffic demand pose a severe challenge to the coordinated ETN-PDN operation problem. This paper proposes a new hybrid optimisation method using stochastic user equilibrium (SUE)/information gap decision theory (IGDT) to study the impact of the unavoidable uncertainties on the coordinated ETN-PDN operation, which consists of the following two stages. In the first stage, a collaborative optimisation model based on SUE and Dist-Flow equations is established to deal with the stochastic EV routing behaviour. Built upon this model, the second stage continues to consider the traffic demand prediction error and establish a risk decision model using IGDT. The proposed model can provide proper road congestion tolls and local generator production schedules to lead to a minimum expected socio-economic cost. Also, two different coordinated operation strategies, that is, risk-seeker and risk-averse strategies, are provided to deal with the uncertainties. Case studies are carried out to demonstrate the effectiveness of the hybrid SUE/IGDT optimisation method.

Demand forecasting model analysis for Al-kufa road network

For the design of transport facilities and services, as well as for planning, expenditure, and policy development, travel demand modelling studies are important. The goal of this research is to improve and apply projected models for each stage of the Al-Kufa city travel demand forecast process that includes, in addition to the road network database, social, economic, location and land-use features. The study region is separated into four sectors to accomplish the study goal. For data collection, full interview, and home questionnaire, two methods have been used. In September 2019, the data collection began. The six-purpose trip generation models (home base work, educational, religious, social, shopping, other trips) were advanced by stepwise regression method (Multiple Linear Regression, MLR) using software SPSS version 20. The results indicated that the determination coefficient R2 for (Y) (the total number of trips is 0.88 and considered to be a very good correlation. Travel time and cost of each utility mode are the key parameters that have affected the mode option models and the gravity model used in Al-Kufa city for the trip distribution method. The assignment models for the allocation of traffic in the Al-Kufa road network for the base year of the analysis are used by the (Stochastic user equilibrium), the network suffers from high congestion with near and higher v/c links 1.

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 Strategic Markovian Traffic Equilibrium Model for Capacitated Networks

In the realm of traffic assignment over a network involving rigid arc capacities, the aim of the present work is to generalize the model of Marcotte, Nguyen, and Schoeb [Marcotte P, Nguyen S, Schoeb A (2004) A strategic flow model of traffic assignment in static capacitated networks. Oper. Res. 52(2):191–212.] by casting it within a stochastic user equilibrium framework. The strength of the proposed model is to incorporate two sources of stochasticity stemming, respectively, from the users’ imperfect knowledge regarding arc costs (represented by a discrete choice model) and the probability of not accessing saturated arcs. Moreover, the arc-based formulation extends the Markovian traffic equilibrium model of Baillon and Cominetti [Baillon JB, Cominetti R ( 2008 ) Markovian traffic equilibrium. Math. Programming 111(1-2):33–56.] through the explicit consideration of capacities. This paper is restricted to the case of acyclic networks, for which we present solution algorithms and numerical experiments.

A bounded path size route choice model excluding unrealistic routes: formulation and estimation from a large-scale GPS study

This paper develops a new route choice modelling framework that deals with both route correlations and unrealistic routes in a consistent and robust way. To do this, we explore the integration of a correlation-based Path Size Logit model with the Bounded Choice Model (BCM) (Watling et al. 2018. “Stochastic User Equilibrium with a Bounded Choice Model.” Transportation Research Part B: Methodological 114: 254–280). We find, however, that the natural integration of these models leads to behavioural inconsistencies and/or undesirable mathematical properties. Solving these challenges, we derive a mathematically well-defined Bounded Path Size (BPS) model form that utilises a consistent criterion for assigning zero choice probabilities to unrealistic routes while eliminating their path size contributions. A closed-form and fixed-point BPS model are consequently formulated. Subsequently, we consider parameter estimation in a simulation study and on a real-life large-scale network using GPS data, where computational feasibility is demonstrated. Estimation results show the potential of the BPS models to give improved fit relative to non-bounded versions (and BCM).