Solving for equilibrium in the basic bathtub model

Richard Arnott and Joshua Buli

Transportation Research Part B: Methodological, 2018, vol. 109, issue C, 150-175

Abstract: The basic (identical individuals) bathtub model has an unfamiliar mathematical structure, with a delay differential equation with an endogenous delay at its core. The early papers on the model circumvented this complication by making approximating assumptions, but without solution of the proper model it is unclear how accurate the results are. More recent work has either considered special cases that can be solved analytically using familiar methods, or has turned to generic computational solution. This paper develops a customized method for computational solution of equilibrium in the basic bathtub model with smooth preferences that exploits the mathematical structure of the problem. An inner loop solves numerically for the entry rate, conditional on the equilibrium utility level, by verifying a trip distance condition. An outer loop uses the computed start time from the inner loop to solve for the population that commutes over the rush hour, then lowers the equilibrium utility level to repeat the inner loop for a new level of utility. One result in that, even though tastes and the congestion technology are smooth, the entry rate and exit rate functions exhibit discontinuities at breakpoints. Another result is that, depending on the form of tastes and the congestion technology, the user cost curve as a function of population and may be backward bending.

Keywords: Traffic congestion; Bathtub model; Computational solution (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0191261517305258
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:transb:v:109:y:2018:i:c:p:150-175

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.trb.2017.12.003

Access Statistics for this article

Transportation Research Part B: Methodological is currently edited by Fred Mannering

More articles in Transportation Research Part B: Methodological from Elsevier
Bibliographic data for series maintained by Catherine Liu ().