Link-Nested Logit Model of Route Choice: Overcoming Route Overlapping Problem

1998 ◽  
Vol 1645 (1) ◽  
pp. 133-142 ◽  
Author(s):  
Peter Vovsha ◽  
Shlomo Bekhor
Keyword(s):  
Logit Model ◽  
Route Choice ◽  
User Equilibrium ◽  
Discrete Choice Models ◽  
Nested Logit ◽  
Stochastic User Equilibrium ◽  
Nested Logit Model ◽  
Network Loading ◽  
Proposed Model ◽  
Route Overlapping

A new link-nested logit model of route choice is presented. The model is derived as a particular case of the generalized-extreme-value class of discrete choice models. The model has a flexible correlation structure that allows for overcoming the route overlapping problem. The corresponding stochastic user equilibrium is formulated in two equivalent mathematical programming forms: as a particular case of the general Sheffi formulation and as a generalization of the logit-based Fisk formulation. A stochastic network loading procedure is proposed that obviates route enumeration. The proposed model is then compared with alternative assignment models by using numerical examples.

Investigation of Stochastic Network Loading Procedures

1998 ◽  
Vol 1645 (1) ◽  
pp. 94-102 ◽  
Author(s):  
J. N. Prashker ◽  
S. Bekhor
Keyword(s):  
Logit Model ◽  
Route Choice ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Nested Logit ◽  
Stochastic Network ◽  
Nested Logit Model ◽  
Network Loading ◽  
Stochastic Loading ◽  
The Cross

The network loading process of stochastic traffic assignment is investigated. A central issue in the assignment problem is the behavioral assumption governing route choice, which concerns the definition of available routes and the choice model. These two problems are addressed and reviewed. Although the multinomial logit model can be implemented efficiently in stochastic network loading algorithms, the model suffers from theoretical drawbacks, some of them arising from the independence of irrelevant alternatives property. As a result, the stochastic loading on routes that share common links is overloaded at the overlapping parts of the routes. Other logit-family models recently have been proposed to overcome some of the theoretical problems while maintaining the convenient analytical structure. Three such models are investigated: the C-logit model, which was specifically defined for route choice; and two general discrete-choice models, the cross-nested logit model and the paired combinatorial logit model. The two latter models are adapted to route choice, and simple network examples are presented to illustrate the performance of the models with respect to the overlapping problem. The results indicate that all three models perform better than does the multinomial logit model. The cross-nested logit model has an advantage over the two other generalized models because it enables performing stochastic loading without route enumeration. The integration of this model with the stochastic equilibrium problem is discussed, and a specific algorithm using the cross-nest logit model is presented for the stochastic loading phase.

Pricing Competition Under Specific Discrete Choice Models

2020 ◽  
Vol 37 (02) ◽  
pp. 2050008
Author(s):  
Farhad Etebari
Keyword(s):  
Discrete Choice ◽  
Logit Model ◽  
Choice Model ◽  
Public Information ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Discrete Choice Models ◽  
Nested Logit ◽  
Nested Logit Model ◽  
Substitution Pattern

Recent developments of information technology have increased market’s competitive pressure and products’ prices turned to be paramount factor for customers’ choices. These challenges influence traditional revenue management models and force them to shift from quantity-based to price-based techniques and incorporate individuals’ decisions within optimization models during pricing process. Multinomial logit model is the simplest and most popular discrete choice model, which suffers from an independence of irrelevant alternatives limitation. Empirical results demonstrate inadequacy of this model for capturing choice probability in the itinerary share models. The nested logit model, which appeared a few years after the multinomial logit, incorporates more realistic substitution pattern by relaxing this limitation. In this paper, a model of game theory is developed for two firms which customers choose according to the nested logit model. It is assumed that the real-time inventory levels of all firms are public information and the existence of Nash equilibrium is demonstrated. The firms adapt their prices by market conditions in this competition. The numerical experiments indicate decreasing firm’s price level simultaneously with increasing correlation among alternatives’ utilities error terms in the nests.

Solving the Overlapping Problem in Route Choice with Paired Combinatorial Logit Model

2003 ◽  
Vol 1857 (1) ◽  
pp. 65-73 ◽  
Author(s):  
Anthony Chen ◽  
Panatda Kasikitwiwat ◽  
Zhaowang Ji
Keyword(s):  
Mathematical Programming ◽  
Logit Model ◽  
Choice Model ◽  
Route Choice ◽  
Similarity Index ◽  
User Equilibrium ◽  
Transportation Systems ◽  
Programming Formulation ◽  
Stochastic User Equilibrium ◽  
Mathematical Programming Formulation

Recently, there has been renewed interest in improving the logit-based route choice model because of the importance of the route choice model in intelligent transportation systems applications, particularly the applications of advanced traveler information systems. The paired combinatorial logit (PCL) model and its equivalent mathematical programming formulation for the route choice problem have been studied. An algorithm based on the partial linearization method is presented for solving the PCL stochastic user equilibrium problem. Detailed examples are provided to explain how this hierarchical logit model resolves the overlapping problem through the similarity index while still accounting for both congestion and stochastic effects in the mathematical programming formulation.

Application of Cross-Nested Logit Model to Mode Choice in Tel Aviv, Israel, Metropolitan Area

1997 ◽  
Vol 1607 (1) ◽  
pp. 6-15 ◽  
Author(s):  
Peter Vovsha
Keyword(s):  
Logit Model ◽  
Mode Choice ◽  
Choice Models ◽  
Urban Transport ◽  
Transport Systems ◽  
Light Rail ◽  
Nested Logit ◽  
Nested Logit Model ◽  
Proposed Model ◽  
The Cross

Currently, modal split modeling is done mainly by means of disaggregated mode choice models. The almost absolute dominance of multinomial and nested logit models over other mode choice models among applied transportation modelers is attributable to their theoretical soundness, to their simple and understandable analytical structure, and to the calibration procedures that have been developed. Typical urban transport systems, however, are characterized by a variety of modes including private (automobile), public transit (bus, suburban rail, light rail, and subway), and various combinations of these. Analysis reveals that the nested logit model based on the assumption of groupwise similarities among modes is not a suitable modeling tool in such situations. A cross-nested model that is derived from the generalized extreme value class and that can be thought of as a generalization of the nested logit model is proposed. The model takes into account the cross similarities between different pure and combined modes. The cross-nested structure allows for the introduction of the differentiated measurement of pairwise similarities among modes as opposed to the inflexible groupwise similarities permitted by the nested logit model. The proposed model is described, and it is compared with alternative modeling constructs.

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

2021 ◽  
Author(s):  
Hongbo Ye
Keyword(s):  
Equivalent Form ◽  
Travel Cost ◽  
User Equilibrium ◽  
Discrete Choice Models ◽  
Cost Functions ◽  
Stochastic User Equilibrium ◽  
Travel Costs ◽  
Network Loading ◽  
Link Cost ◽  
Globally Stable

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.

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