{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T04:08:52Z","timestamp":1748578132837,"version":"3.41.0"},"reference-count":36,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2025,5,29]],"date-time":"2025-05-29T00:00:00Z","timestamp":1748476800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>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\u2019 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.<\/jats:p>","DOI":"10.1371\/journal.pone.0324561","type":"journal-article","created":{"date-parts":[[2025,5,29]],"date-time":"2025-05-29T17:39:31Z","timestamp":1748540371000},"page":"e0324561","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling and managing household travels taking into considering of school 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