Capturing the interaction between travel time reliability and route choice behavior based on the generalized Bayesian traffic model

Highlights

• The generalized Bayesian traffic model can consider different ways travelers tend to consider travel time reliability in route choice through different formations of perceived knowledge.

• The Bayesian model with an infinitely long memory and mean-variance-based perceived knowledge will converge to the mean-variance UE condition.

• The convergence of route choice dynamics to a UE condition is not affected by adding a bounded weight to the daily perceived knowledge.

• Non-UE-based formulations of perceived knowledge also lead to fixed points for the mean route choice proportion.

Abstract

Travel time reliability plays an important role in travelers’ route choice behaviors. Based on a previously developed generalized Bayesian traffic model, we propose different types of perceived knowledge (i.e., mean-variance-based type, relative gap-based type, and penalty-based type) to model travelers’ daily route choice behavior concerning travel time reliability. We theoretically demonstrate the flexibility of the generalized Bayesian model in capturing various existing UE-based travel behaviors and other non-UE-based travel behaviors (e.g., penalty-based) in stochastic transportation systems. Three major conclusions are obtained. First, the route choice dynamics induced by the Bayesian model with an infinitely long memory and mean-variance-based perceived knowledge will converge to the mean-variance UE condition. Second, the convergence of route choice dynamics to a UE condition is not affected by adding a bounded weight on the daily perceived knowledge. Thirdly, non-UE-based formulations of perceived knowledge also lead to fixed points for the mean route choice proportion. The convergences of the models with different types of perceived knowledge are verified based on numerical studies and the underlying day-to-day route choice dynamics with both recurrent and non-recurrent unreliability are examined.

Introduction

Travel time reliability is sensitive to day-to-day uncertainties in transportation systems. Daily events such as unpredicted vehicle breakdowns, traffic accidents, traffic signal failures, and unexpected sudden travel demand increases will significantly influence the reliability of transportation systems. Recent empirical studies have demonstrated the importance of travel time reliability to people's travel decisions, which in return affects the performance of the system (e.g., Lam and Small, 2001; de Palma and Picard, 2005; Fosgerau and Karlström, 2010; Zhu et al., 2010; Watling et al., 2012; Siu and Lo, 2014; Currie and Muir, 2017), including travel time reliability.

The mechanism of travel decision-making under uncertainty plays an essential role in modeling travel choices with the consideration of travel time reliability and the resulting transportation system dynamics. Conventional choice models are developed based on utility-based theories, in which travelers make their route and departure time choices to maximize their satisfaction or utility. Generally, researchers apply the user equilibrium (UE) condition such that any traveler in the system cannot improve his or her expected utility by unilaterally adjusting the route or departure time. In most existing studies, the utility is formulated as a linear combination of the mean travel time and its variability (e.g., standard deviation (SD)). This formulation is referred to as the “mean-variance” form, which has been widely applied in route choice modeling (Jackson and Jucker, 1982; Abdel-Aty et al., 1995; de Palma and Picard, 2005; Shao et al., 2006; Ordóñez and Stier-Moses, 2010). In studies of the departure time choice with uncertain travel times, the extra costs of being late or being early compared with the preferable schedule are usually part of the disutility to be minimized, leading to a “scheduling” problem (Small, 1982; Arnott et al., 1999; Xiao et al., 2013; Zhu et al., 2019b). Fosgerau and Karlström (2010) proved the equivalence between the “mean-variance” approach and the “scheduling” approach. In the stochastic context, the calculation of expected utility requires the probability distribution of origin-destination (OD) demands and the probability distribution of link or route travel times. The requirement for system information makes utility-based models somehow unrealistic to describe traveler behavior concerning travel time reliability.

The aforementioned modeling approaches focus more on equilibrium conditions rather than day-to-day behavior shifts in stochastic transportation systems. To better represent travelers’ choice dynamics, some studies have introduced perceived knowledge and subjective belief updating processes in day-to-day travel choice modeling (e.g., Horowitz, 1984; Cascetta, 1989; Watling, 1999; Hazelton, 2002; Guo et al., 2015; Ye and Yang, 2017; Ma and Qian, 2017; Zhu et al., 2019a). The majority of these studies still adopt a utility-based modeling approach and a traffic assignment framework, and thus require comprehensive and detailed information about the transportation system. In contrast, Zhu et al. (2019b) proposed a general Bayesian framework to model day-to-day travel choices and transportation system dynamics. Instead of prescribing normative travel behavior (e.g., travel time minimization), this Bayesian framework used a Dirichlet prior-and-posterior updating approach to model travel choices based on observed travel choice data, which is increasingly available in the industry (e.g., companies like Streetlight and AirSage can now provide OD demand and route choice patterns based on passively collected location data on a continuous basis; connected and autonomous vehicles could serve as more promising data sources in the future). This data-driven modeling framework does not require specific assumptions on the probability distributions of OD demand or link capacity, and follows a perceived knowledge-based route choice process. The authors demonstrated the equivalence between the Dirichlet route choice mechanism and statistical UE when travelers have an infinitely long memory and only care about travel time. However, the interaction between travel time reliability and route choice dynamics was not fully investigated in either the generalized Bayesian traffic model or the utility-based day-to-day models.

The Dirichlet choice model in Zhu et al. (2019b) assumes that travel time uncertainty comes mainly from the exogenous stochasticity of the system, and travelers make route choices only based on the average performance but not the reliability of route travel time (Zhu et al., 2019b). In this paper, we extend the generalized Bayesian traffic model by incorporating the impact of travel time reliability into the endogenous route choice process. We formulate the daily perceived knowledge in four types: a baseline type based on statistical averages, a mean-variance-based type, a travel time gap-based type, and a travel time penalty-based type. Different types of perceived knowledge and the underlying convergence behavior of the day-to-day traffic dynamics are discussed. The major contribution of this paper lies in that we analytically demonstrate the flexibility of the generalized Bayesian framework in capturing various travel behavior assumptions that consider travel time reliability. More specifically, we first show that the day-to-day process with mean-variance-based knowledge will converge to the mean-variance UE when travelers’ memory is infinitely long. Second, the convergence of the system remains the same if a bounded weight is added to the daily perceived knowledge. Thirdly, fixed points for mean route choice proportions exist with a wide range of perceived knowledge formulations. We use numerical analyses to verify the theoretical findings and examine the sensitivity of different perceived knowledge types to travel time reliability under both recurrent and non-recurrent scenarios. This paper demonstrates that the data-driven, Bayesian-based traffic model can be extended to consider different types of travel time and travel time reliability preferences, including both those commonly seen in the literature for prescriptive models and the others that require much less information about the system. The flexibility in formulating perceived knowledge and the ability to replicate many existing UE conditions makes the generalized Bayesian traffic model a good alternative in describing travelers’ real-world route choice behaviors. Therefore, the generalized Bayesian model, which is more compatible with emerging transportation data and holds better promise to be empirically calibrated and tested (Zhu et al., 2019b), provides a new approach to understand day-to-day travel behavior and transportation system dynamics in the era of big data.

The remainder of this paper is organized as follows. Section 2 comprehensively reviews the existing literature related to the static travel behavior models considering travel time reliability and stochastic day-to-day traffic models. Section 3 provides an overview of the generalized Bayesian traffic model. Different types of perceived knowledge are proposed in Section 4 and the convergences of corresponding models are theoretically proved. Section 5 shows the results of numerical studies, in which scenarios with both recurrent and non-recurrent sources of unreliability are considered. Conclusions and discussions are presented in Section 6.