A semi-analytical approach for solving the bottleneck model with general user heterogeneity

Transportation Research Part B: Methodological

Nie

2015

Self Cite

Two new numerical methods, a semi-analytical method and an exact method, are proposed in this paper for solving the step-tolled user equilibrium problem for the bottleneck model with general user heterogeneity. The semi-analytical method transforms the step-tolled user equilibrium problem into a static, asymmetric traffic assignment problem with side constraints, which is formulated and solved as a variational inequality problem (VIP). Existence and uniqueness results are obtained by examining the properties of the VIP. The exact method, on the other hand, locates the equilibrium solution by enumerating all possible combinations of user departure orders. To improve the computational efficiency of the exact method, a simple heuristic is developed to reduce the number of solutions to be enumerated. Examples of up to 1000 classes are tested. The results confirm that ignoring user heterogeneity may lead to sub-optimal design of step tolls. In all experiments, the semi-analytical method is found to be more efficient than the heuristic version of the exact method by an order of magnitude, albeit they consistently produce nearly identical equilibrium solutions.

Section: Formulationmentioning

confidence: 99%

Section: Proposition 2 (Solution Existence) There Exists a Solution Tomentioning

confidence: 99%

Solving the step-tolled bottleneck model with general user heterogeneity

Chen

Transportation Research Part B: Methodological

Nie

2015

Self Cite

“…Travelers choose their departure times to minimize individual travel cost including travel delay cost and schedule delay cost. Based on this model, various issues have been studied, e.g., existence and uniqueness of user equilibrium solution at a single bottleneck (Smith, 1984;Daganzo, 1985;Lindsey, 2004); road pricing, tradable credits, and tradable permits to manage traffic congestion (Arnott et al, 1990;Laih, 1994;Xiao et al, 2012;Tian et al, 2013;Nie and Yin, 2013;Wada and Akamatsu, 2013); stochastic bottleneck capacity and travel demand (Arnott et al, 1999;Lindsey, 2009;Xiao et al, 2015); morning commute with heterogeneous travelers (Arnott et al, 1994;van den Berg and Verhoef, 2011;Liu and Nie, 2011;Liu et al, 2014b;Liu et al, 2015a;Liu et al, 2015c); integrated problem of parking and morning commute (Arnott et al, 1991;Zhang et al, 2008;Qian et al, 2011;Qian et al, 2012;Yang et al, 2013;Liu et al, 2014a;Xiao et al, 2016); capacity drop and/or hypercongestion (Arnott, 2013;Liu et al, 2015b;Liu and Geroliminis, 2016); complementarity formulation or ordinary differential equation formulation (Ramadurai et al, 2010;Wu and Huang, 2015;Wang and Xu, 2016).…”

Section: ! Introductionmentioning

confidence: 99%

Modeling and managing morning commute with both household and individual travels

Transportation Research Part B: Methodological

Zhang

Yang

2017

This study investigates the morning commute problem with both household and individual travels, where the household travel is a shared ride of household (family) members. In particular, it considers the situation when a proportion of commuters have to drive their children to school first and then go to work (household travel). For household travel, departure time choice is a joint decision based on all household membersÕ preferences. Unlike the standard bottleneck model, the rush-hour dynamic traffic pattern with mixed travelers (household travelers and individual travelers) varies with the numbers of individual travelers and households, as well as the schedule difference between school and work. Given the numbers of individual travelers and households, we show that by appropriately coordinating the schedules of work and school, the traffic congestion at the highway bottleneck can be relieved, and hence the total travel cost can be reduced. This is because, departure/arrival of individual and household travels can be separated by schedule coordination. System performance under schedule coordination is quantified in terms of the relative proportions of the two classes of travelers and is compared with the extreme case when the same desired arrival time applies to both schooling and working. Furthermore, the efficiency of work and school schedule coordination in reducing travel cost is bounded. This efficiency is also compared with that at the system optimum where queuing is fully eliminated and schedule delay cost is minimized (achieved by a joint scheme of first-best pricing and schedule coordination).

“…1 Smith (1984) and Daganzo (1985) established the existence and uniqueness of the user equilibrium solution at a single bottleneck. Thanks to its tractability, the bottleneck model has been extended to study various issues, e.g., stochastic bottleneck capacity and travel demand (Lindsey, 2009;Xiao et al, 2014Xiao et al, , 2015; heterogeneous travellers (Arnott et al, 1994;van den Berg and Verhoef, 2011;Liu and Nie, 2011;Liu et al, 2015b;Wang and Xu, 2016); road pricing, tradable credits or parking permits to manage traffic congestion (Arnott et al, 1990;Xiao et al, 2012;Liu et al, 2014b); integrated problem of parking and morning commute (Arnott et al, 1991;Qian et al, 2012;Yang et al, 2013;Liu et al, 2014a); integrated modelling of morning and evening commutes (Zhang et al, 2005(Zhang et al, , 2008; morning commute with car-pooling (Xiao et al, 2016); activity-based modelling (Li et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

A new look at the morning commute with household shared-ride: How does school location play a role?

Zhang

Transportation Research Part E: Logistics and Transportation Re

Wang

et al. 2017

Recent studies examined the households' trip-timing decisions where adults have to drive their children to school. These studies focus on the cases where school is near workplace. However, different school locations can affect travels and activity patterns significantly. This study re-looks at the household shared-ride problem where school is near home. It is found that the resulting dynamic commuting equilibrium has very different properties, which have been examined and discussed accordingly. Three management strategies have been proposed to reduce total travel cost, and efficiencies of these strategies are evaluated and compared.