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On Boundedly Rational User Equilibrium in Transportation Systems
Abstract
A boundedly rational user equilibrium (BRUE) is achieved in a transportation system when all users are satisfied with their current travel choices. The theoretical and behavioral background for such a state is given in this paper. The properties of a BRUE in an idealized commuting system with a single bottleneck are investigated, and conditions for the existence of a BRUE are given. More general situations with multiple bottlenecks are also addressed. In general, BRUE flows are not unique, raising methodological and practical issues in flow prediction.
... BRUE (also referred to as length constrained user equilibrium), first introduced in the seminal work by Simon [54] and adapted to transportation systems by Mahmassani and Chang [42], is a relaxation of UE in that it assumes that users are willing to take an acceptable route rather than an optimal one, where acceptable is defined based on the length of the shortest route for a given -pair and a threshold value or aspiration/indifference level that reflects users' behavior. Under BRUE, no user can improve her/his travel time by switching routes by more than a prespecified threshold value [39]. ...
... Under BRUE, no user can improve her/his travel time by switching routes by more than a prespecified threshold value [39]. Following the work of Mahmassani and Chang [42], various studies [22,39,43,58,74] explored and extended BRUE. ...
... Mahmassani and Chang [42] investigate the existence, uniqueness, and where applicable the stability of BRUE in an idealized transportation system. Chen et al. [22] propose a modeling framework for bounded rational interactive decision making, where users follow probabilistic choices using the logit model of discrete choice theory. ...
Demographic changes, urbanization and increasing vehicle ownership at unprecedented rates put a lot of strain on cities particularly on urban mobility and transportation and overwhelm transportation network infrastructures and current transportation systems, which are not built to cope with such a fast increasing demand. Traffic congestion is considered as the most difficult challenge to tackle for sustainable urban mobility and is aggravated by the increased freight activity due to e-commerce and on-demand delivery and the explosive growth in transportation network companies and ride-hailing services. There is a need to implement a combination of policies to ensure that increased urban traffic congestion does not lower the quality of life and threaten global climate and human health and to prevent further economic losses. This study aims to contribute to the United Nations (UN) climate action and sustainable development goals in tackling recurring traffic congestion problem in urban areas to achieve a sustainable urban mobility in that it offers a solution methodology for traffic assignment problem. We introduce an exact generalized solution methodology based on reformulation of existing traffic assignment problems as a second order cone programming (SOCP) problem and propose column generation (CG) and cutting plane (CP) algorithms to solve the problem effectively for large scale road network instances. We conduct numerical experiments to test the performance of the proposed algorithms on realistic road networks.
... In view of this, several traffic assignment models have been proposed to model travelers' fine-grained route-choice behaviors by incorporating travel time perception errors, psychological and behavioral mechanisms. State-of-the-art models include stochastic user equilibrium model (Daganzo and Sheffi, 1977;Sheffi and Powell 1982), random utility maximization model (Bowman and Ben-Akiva, 2001;Habib 2011), reliability-based model (Lam et al., 2008;Chen et al., 2011), regret minimization model (Chorus, 2012), rational choice theory model (Mahmassani and Chang, 1987;Han et al., 2015;Lou et al., 2010;Di and Liu, 2016;González Ramírez et al., 2021), prospect theory model (Ben-Elia and Shiftan, 2010;Gao et al., 2010;Xu et al., 2011;Kahneman and Tversky, 1979) and stochastic network equilibrium with routing inertia (Xie et al. 2014). These state-of-the-art traffic assignment models' explorations revealed the heterogeneity of individuals' decision making and the complexities of route choice behaviors. ...
User equilibrium (UE) has long been regarded as the cornerstone of transport planning studies. Despite its fundamental importance, our understanding of the actual UE state of road networks has remained surprisingly incomplete. Using big datasets of taxi trajectories, this study investigates the UE states of road networks in two Chinese mega-cities, i.e., Wuhan and Shenzhen. Effective indicators, namely relative gaps, are introduced to quantify how actual traffic states deviate from theoretical UE states. Advanced machine learning techniques, including XGBoost and SHAP values, are employed to analyze nonlinear relationships between network disequilibrium states and seven influencing factors extracted from trajectory data. The results in these two study areas reveal consistent and significant gaps between actual traffic states and the theoretical UE states at various times of the day during both weekdays and weekends. The XGBoost analysis shows that differences in travel distances, travel speeds, and signalized intersection numbers among alternative routes are the primary causes of road network disequilibrium. The results of this study could present several important methodological and policy implications for using the UE models in transport applications.
... In view of this, several traffic assignment models have been proposed to model travelers' fine-grained route-choice behaviors by incorporating travel time perception errors, psychological and behavioral mechanisms. State-of-the-art models include stochastic user equilibrium model (Daganzo and Sheffi, 1977;Sheffi and Powell 1982), random utility maximization model (Bowman and Ben-Akiva, 2001;Habib 2011), reliability-based model (Lam et al., 2008;Chen et al., 2011), regret minimization model (Chorus, 2012), rational choice theory model (Mahmassani and Chang, 1987;Han et al., 2015;Lou et al., 2010;Di and Liu, 2016;González Ramírez et al., 2021) Gao et al., 2010;Xu et al., 2011;Kahneman and Tversky, 1979) and stochastic network equilibrium with routing inertia (Xie et al. 2014). Despite their sophistication, how well these models capture the actual traffic state remains unclear. ...
User equilibrium (UE) has long been regarded as the cornerstone of transport planning studies. Despite its fundamental importance, our understanding of the actual UE state of road networks has remained surprisingly incomplete. Using big datasets of taxi trajectories, this study investigates the UE states of road networks in Wuhan. Effective indicators, namely relative gaps, are introduced to quantify how actual traffic states deviate from theoretical UE states. Advanced machine learning techniques, including XGBoost and SHAP values, are employed to analyze nonlinear relationships between network disequilibrium states and seven influencing factors extracted from trajectory data. The results reveal significant gaps between actual traffic states and the theoretical UE states at various times of the day during both weekdays and weekends. The XGBoost analysis shows that differences in travel distances, travel speeds, and signalized intersection numbers among alternative routes are the primary causes of road network disequilibrium. The results of this study could have several important methodological and policy implications for using the UE models in transport applications.
... Exploring this dynamic evolutionary process not only facilitates the prediction of individual travel choices but also enhances the comprehension of traffic congestion dynamics within the transportation system [22], enabling to leverage advanced travel information systems more effectively. Liu et al. [23] considered the impact of benefit changes in travel behavior and modes on flow redistribution. ...
It is important to understand the mechanism of travel location choices, since the dynamic individual behavior would lead to the evolution of the network. The existing location choice researches usually based on the static and perfect information, and analyzed each step of the travel independently. This research considers the interaction between individuals on a series of trips in the travel chain by incorporating the spatial-temporal bounded rationality estimation. The Indifference Zone and information sharing in the travel process are defined to explore the spatial and temporal sides. A within-day location choice model is developed based on the spatial benefit and temporal cost. The proposed spatial-temporal bounded rationality LSTM model is verified in five cities networks in China, and it shows the 8.65% and 20.30% improvement, respectively, compared to the spatial bounded rationality LSTM models and perfect rationality LSTM models. In addition, the improvement becomes more pronounced when more alternative locations (the largest city improve 31.65%), more serious network congestion (improve 27.45%), more obvious location composition path (improve 13.85%), and more stable within-day travel weight (improve 22.88%). The proposed dynamic decision model with bounded rationality would provide insights for travel chain prediction in the complex urban network.
... The disadvantage is that the travel cost inputs for choice set generation are inconsistent over iterations (Watling et al., 2018). The bounded rational models give a space of flow solutions, assuming that travelers are indifferent to path cost differences within an indifference band (Mahmassani and Chang, 1987;Lou et al., 2010;Di et al., 2013;Di and Liu, 2016). However, this method does not give a point solution or a probability distribution of the solution space. ...
Modeling Mobility-on-Demand (MoD) services is important from a regulatory perspective, and requires 11methods to capture the equilibrium of MoD systems. While there exists a large body of literature on MoD services focusing on service design under equilibrium modeling for given demand and operational policies, such policies might not be readily known to the regulatory agencies. Capturing the steady state of the operation-dependent fleet distribution and user equilibrium by fitting only to empirical observations is a challenge. With these motivations, we model the equilibrium of fleet-demand dynamics in MoD systems with the concept of congestible capacities, which is the phenomenon in MoD systems where capacities are affected by flows. An operation-agnostic logit-based stochastic user equilibrium (SUE) formulation is proposed with a Flow-Capacity Interaction (FC) matrix to describe the steady state empirical relationship between flows and capacities as opposed to having to assume operator-specific operating policies. The proof for equivalence of the formulation to SUE is given. A solution algorithm that finds a bounded path set is proposed, with a custom Frank-Wolfe algorithm to solve the non-linear SUE formulation. Since the FC matrix cannot be directly observed, an inverse optimization problem is introduced to estimate it with observed flow and capacity data. Two numerical examples are provided with sensitivity tests. An empirical example with yellow taxi data of downtown Manhattan, NY is provided to demonstrate effectiveness of estimating the FC matrix from real data, and for determining the equilibrium that captures the underlying flow-capacity dynamics.
In this paper, we propose a novel cost function to be embedded in a distributed algorithm for cooperative rerouting of connected and automated vehicles (CAVs) in urban networks. The computation is performed by intersection units managing the portion of the network for which they are in charge by sending updated routes to follow to the CAVs there. Moreover, the intersection units communicate among each other to be updated on the situation of the (in general nonhomogeneous) links of the network. The proposed approach allows the decomposition of the problem into subproblems, which are resolved distributively with little information exchange. The problems are constructed to obtain a fair compromise between user equilibrium and system optimum, taking advantage of the strengths and coping with the limitations of both. We 1) show the results obtained by running simulations with CAVs on the Sioux Falls network compared with a baseline scenario; 2) analyze the results obtained with different penetration rates of CAVs; and 3) provide a sensitivity analysis to investigate how parameters in our approach affect the results of the experiments.
In this chapter, we present an infinite-dimensional variational inequality (VI) formulation of the continuous-time simultaneous route-and-departure-time (SRDT) dynamic user equilibrium.
Travelers always perform some preference during the decision-making process. The preference will affect the decision results and can be improved by continuously learning. In order to understand the influence of individual preference on travel behavior choice , two individual preferences, including indifference preference and compulsive preference are considered in the paper. Two updating mechanisms of compulsive preference are proposed to obtain the choosing probability of all alternatives. Reinforcement learning models are established integrating the gain stimulating and loss stimulating considering expected utility. Nguyen Dupuis network is adopted for numerical simulation to study the updating process. Simulation results denote that the equilibrium state is much more efficient when preference learning mechanism is considered comparing with the traditional stochastic user equilibrium model, and can decrease the total travel time greatly, which can be applied for urban traffic management. Personalized traffic guidance is the effective solution to traffic congestion in the future
This paper presents an experimental approach involving real commuters, whereby a traffic simulation model is used to predict congestion patterns under given departure distributions resulting from the actual decisions of the individual participants. These decisions are updated daily, in response to information on prior system performance predicted by the simulation model. The results of this experiment are described in this paper, with emphasis on the system's evolution and dynamic properties, particularly convergence. In addition, concentration and congestion patterns as well as the associated travel time variability are addressed. Initial insights into the processes underlying user behavior in this system are also presented.
An extension of a recent framework for analyzing the time-dependent departure pattern arising in an idealized situation of a pool of commuters going from a single origin to a single destination along a unique route is presented. Congestion along this route is represented using elementary traffic flow theoretic relationships; time-varying patterns of basic traffic variables are derived under user equilibrium conditions, along with the corresponding time-dependent departure pattern of system users. After demonstrating the basic model in the single-route context, an additional dimension of choice is introduced by considering the joint departure time and route choice decisions of users. Results are derived in a simplified two-route context and numerical illustrations provided.
We develop a simple approach for modeling schedule delay in a deterministic setting based on user equilibrium concepts and deterministic queuing theory. Several cases of peak period commuting or travel to scheduled events (such as sporting events) are analyzed as illustrations. The results demonstrate the importance of schedule delay for departure time decisions. The analysis framework can be used to improve the transportation planning and evaluation process, and we have identified several related research issues which could provide further insights into departure time decisions and the performance of transportation systems
In this paper we show that rational choice in a stationary environment can lead to erratic behaviour when preferences depend on experience. We mean by erratic behaviour choice sequences that do not converge to a long-run stationary value or to any periodic pattern. Early investigations of the effects of experience on choice goes back to Pareto (see also Benhabib (1979)); some Keynesian theories of the consumption function incorporate the effects of experience and habit formation on current levels of consumption (Duesenberry (1949), Modigliani (1949) and Brown (1952)); a general model of experience dependent choice was described in Day (1970) and investigated in Day and Kennedy (1971) while the specific issue of the existence of stable representable long-run consumer demand when tastes vary endogenously has been treated by Gorman (1967), Pollak (1970, 1976), Weizsaicker (1971), McCarthy (1974) and Hammond (1976). Pollak gave conditions for the representability of long-run choice when the equations of preference dependence are linear and utility additive. Hammond, in a generalization of these findings, provides conditions for stable, representable long run choice when preferences are acyclic, a condition which in essence assures convergence to a long-run choice.
Motorists going through a bottleneck during the morning rush hour have to time their departure times to ensure they arrive to work at a reasonable time. Traffic and congestion levels at the bottleneck depend on the motorists' work schedule and the disutility of unpunctuality. This paper shows that, under certain conditions, there is only one equilibrium order of arrivals; an order under which motorists do not have an incentive to continually move for position in the queue.
A model is proposed which expresses consumer satisfaction as a function of expectation and expectancy disconfirmation. Satisfaction, in turn, is believed to influence attitude change and purchase intention. Results from a two-stage field study support the scheme for consumers and nonconsumers of a flu inoculation.
A simplified cognitive model is proposed to assess the dynamic aspect of consumer satisfaction/dissatisfaction in consecutive purchase behavior. Satisfaction is found to have a significant role in mediating intentions and actual behavior for five product classes that were analyzed in the context of a three-stage longitudinal field study. The asymmetric effect found demonstrates that repurchase of a given brand is affected by lagged intention whereas switching behavior is more sensitive to dissatisfaction with brand consumption. An attempt to predict repurchase behavior on the basis of the investigated cognitive variables yielded weak results. However, repurchase predictions were improved when the model was extended to a multipurchase setting in which prior experience with the brand was taken into account.
Introduction, 99. — I. Some general features of rational choice, 100.— II. The essential simplifications, 103. — III. Existence
and uniqueness of solutions, 111. — IV. Further comments on dynamics, 113. — V. Conclusion, 114. — Appendix, 115.
The paper gives conditions which guarantee the existence of an equilibrium arrival pattern at a single bottleneck. In the model, the times at which a driver wishes to leave the bottleneck depend on the driver. The equilibrium queue length in this model always has a continuous time derivative everywhere. However, the slope of the equilibrium cumulative arrival distribution is discontinuous at the beginning and end of congestion. The authors suppose that each car driver has only one reasonable route for his journey to work and that all routes pass through a single bottleneck. The only choice open to drivers, in our model, is that of their time of departure for work.
This paper contains a quantitative evaluation of probabilistic traffic assignment models and proposes an alternate formulation. The paper also discusses the weaknesses of existing stochastic-network-loading techniques (with special attention paid to Dial's multipath method) and compares them to the suggested approach. The discussion is supported by several numerical examples on small contrived networks. The paper concludes with the discussion of two techniques that can be used to approximate the link flows resulting from the proposed model in large networks.