# Modeling and managing household travels taking into considering of school bus

## TL;DR

This paper studies how school buses affect household travel patterns during peak hours and proposes a toll model to reduce traffic congestion.

## Contribution

The paper introduces a net utility function and analyzes equilibrium travel patterns influenced by school bus fares and school-work timing.

## Key findings

- Equilibrium travel patterns are influenced by school bus fares and school-work start time differences.
- A first-best time-varying toll model is proposed to manage traffic congestion.
- Net utilities of household commuters are analyzed at equilibrium travel patterns.

## Abstract

This paper examines the household commuting problem in a bi-modal transportation that includes both autos and school buses. Traditional studies of household commuting have assumed that adults first drop off their children at school before driving to work. However, with the increasing use of school buses in metropolitan areas, household commuting patterns have changed. This paper investigates the impact of school buses on household travel behavior during morning peak hours. Simultaneously, this paper also takes into account the positive utilities of household commuters’ activities at home, school and workplace, as well as the negative utilities of travel time and schedule delay. In this paper, based on activity approach, first, a net utility function is developed using these factors. Then, based on the net utility function, the occurrence conditions of all the possible equilibrium travel patterns are analytically solved and the properties of the user equilibrium are researched. Specifically, this paper examines how equilibrium travel patterns are affected by school bus fares and school-work start time difference, and at equilibrium travel patterns, the net utilities of household commuters are also analyzed. Finally, a first-best time-varying toll model is suggested to alleviate traffic congestion caused by household commuting.