### Abstract

Modeling route choice behavior aims at representing travelers’ knowledge of transportation network characteristics, selecting a function that describes how this knowledge is processed and integrated into a summary psychological or economic construct (usually utility) and making assumptions about the decision rule that travelers apply to predict the effects of a particular transportation policy. Resembling other decision contexts, the commonly used (linear-additive) random utility maximization models have been applied to describe route choice behavior. The unobserved utilities (error terms) in these models has been interpreted to reflect imperfect knowledge of travelers regarding transportation network characteristics, leading to stochastic user equilibrium. For computational advantages, the unobserved utilities are generally assumed to be identically and independently Gumbel distributed. This assumption leads to the so-called Independence from Irrelevant Alternatives (IIA) property, which states that the odds of choosing a particular route are independent from the existence and attributes of the remaining alternatives in the choice set.

One of the classical issues in route choice modeling is the fact that routes partly overlap. The physical overlap leads to correlated (imperfect) traveler knowledge of transportation network characteristics, which implies that the IIA property is violated. To represent the effect of route overlap, transportation researchers have suggested route choice models that include correction terms in the specification of the utility function, such as the C-logit (Cascetta, Nuzzolo, Russo and Vitetta, 1996) and the path size logit model (Ben-Akiva and Bierlaire, 1999), or modified assumptions about the unobserved utilities such as in the cross nested logit model (Prashker and Bekhor, 1998) and the Kernel logit model (Bekhor, Ben-Akiva and Ramming, 2002).

In this study, we propose a regret-rejoice model as opposed to a utility-maximizing model that includes both perception error (imperfect knowledge) and route overlap. The model can be viewed as an extension of the regret minimization models introduced in transportation research a decade ago (e.g. Chorus, Arentze, and Timmermans, 2008; Chorus, 2010). Before, a regret-based route choice model considering the effect of route overlap were proposed by Prato (2014). He suggested a hybrid choice structure, assuming that attributes are processed based on the regret-minimization rule, while the effect of route overlap was captured by a utility-based correction factor such as in the Path-Size logit model. In this study, we extend the hybrid route choice structure to both regret and rejoice. We further provide a detailed discussion of the implications of route overlap in regret and rejoice. In addition, since the hybrid model considers route overlap based on a utility-based correction, in this study, we explore how route overlap affects the comparison of alternative routes, and then propose an alternative model by introducing varying perception error in the correlation structure of the error terms. We compare both models and the classic utility-based route choice model based on simulated and empirical data.

The concept of varying perception (Sheffi, 1985) states that the perception of route differences varies as a function of route size. This issue has been addressed in the (linear-additive) random utility maximization models by relaxing the assumption of identically distributed error terms (e.g. Castillo et al., 2008), and in the random regret minimization models by redefining the regret function as the ratio of objective attribute differences and the size of attribute (Jang, Rasouli and Timmermans, 2017). We explore how the concept of varying perception can be formulated as a function of route overlap. In addition, we assume that drivers cannot perceptually differentiate between small travel time differences. This idea has led to the formulation of user equilibrium models under perception thresholds (e.g. Szeto, Wang and Han, 2015).

To empirically examine the performance of the models and analyze elasticities, GPS data about route choice behavior in Rotterdam, the Netherlands are used. Results show that varying perception error as a function of route overlap significantly affects route choice behavior.

One of the classical issues in route choice modeling is the fact that routes partly overlap. The physical overlap leads to correlated (imperfect) traveler knowledge of transportation network characteristics, which implies that the IIA property is violated. To represent the effect of route overlap, transportation researchers have suggested route choice models that include correction terms in the specification of the utility function, such as the C-logit (Cascetta, Nuzzolo, Russo and Vitetta, 1996) and the path size logit model (Ben-Akiva and Bierlaire, 1999), or modified assumptions about the unobserved utilities such as in the cross nested logit model (Prashker and Bekhor, 1998) and the Kernel logit model (Bekhor, Ben-Akiva and Ramming, 2002).

In this study, we propose a regret-rejoice model as opposed to a utility-maximizing model that includes both perception error (imperfect knowledge) and route overlap. The model can be viewed as an extension of the regret minimization models introduced in transportation research a decade ago (e.g. Chorus, Arentze, and Timmermans, 2008; Chorus, 2010). Before, a regret-based route choice model considering the effect of route overlap were proposed by Prato (2014). He suggested a hybrid choice structure, assuming that attributes are processed based on the regret-minimization rule, while the effect of route overlap was captured by a utility-based correction factor such as in the Path-Size logit model. In this study, we extend the hybrid route choice structure to both regret and rejoice. We further provide a detailed discussion of the implications of route overlap in regret and rejoice. In addition, since the hybrid model considers route overlap based on a utility-based correction, in this study, we explore how route overlap affects the comparison of alternative routes, and then propose an alternative model by introducing varying perception error in the correlation structure of the error terms. We compare both models and the classic utility-based route choice model based on simulated and empirical data.

The concept of varying perception (Sheffi, 1985) states that the perception of route differences varies as a function of route size. This issue has been addressed in the (linear-additive) random utility maximization models by relaxing the assumption of identically distributed error terms (e.g. Castillo et al., 2008), and in the random regret minimization models by redefining the regret function as the ratio of objective attribute differences and the size of attribute (Jang, Rasouli and Timmermans, 2017). We explore how the concept of varying perception can be formulated as a function of route overlap. In addition, we assume that drivers cannot perceptually differentiate between small travel time differences. This idea has led to the formulation of user equilibrium models under perception thresholds (e.g. Szeto, Wang and Han, 2015).

To empirically examine the performance of the models and analyze elasticities, GPS data about route choice behavior in Rotterdam, the Netherlands are used. Results show that varying perception error as a function of route overlap significantly affects route choice behavior.

Original language | English |
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Title of host publication | The 6th International Choice Modelling Conference |

Publication status | Published - Aug 2019 |

Event | 6th International Choice Modelling Conference - Kobe, Japan Duration: 19 Aug 2019 → 21 Aug 2019 |

### Conference

Conference | 6th International Choice Modelling Conference |
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Country | Japan |

City | Kobe |

Period | 19/08/19 → 21/08/19 |

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## Cite this

Jang, S., Rasouli, S., & Timmermans, H. (2019). Representing varying perception error as a function of route overlap in regret-rejoice models of route choice behavior. In

*The 6th International Choice Modelling Conference*