The Downs-Thomson paradox: multiplicity and stability of
user equilibria
Heti Afimeimounga, Wiremu Solomon and Ilze Ziedins
Department of Statistics
The University of Auckland
Private Bag 92019
Auckland
Abstract
Consider a network where two routes are available for users
wishing to travel from a source to a destination. On one
route(which could be viewed as private transport) service
slows down as traffic increases. On the other (which could
be viewed as public transport) the service frequency
increases with demand. The Downs-Thomson paradox occurs
when improvements in service (e.g. by widening the road)
lead to an overall {\em worsening} in performance as user
equilibria adjust so that the mean travel time is the same on
both routes. We investigate this paradox, modelling the
private transport route as an $M|M|1$ queue, and the public
transport as a bulk-service infinite server queue.