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.