Abstract: We consider a queueing system in which several service providers offer a service to a common pool of customers, and customers choose which provider to join on the basis of minimising their own expected costs. Under these conditions, customers are said to be routing selfishly. We use the concept of Nash equilibria to analyse the resulting steady-state behaviour of the system and quantify the social cost of selfish routing using the price of anarchy. We examine the impact of selfishness in a range of scenarios motivated by public service provision in healthcare, and examine the socially optimal routing and the extent to which a social planner can improve the system by imposing an appropriate tolling structure. We show that selfish routing can lead to significant inefficiency in such systems and that simple tolling mechanisms can effectively reduce this inefficiency.
@article{knight2013selfish,
title = {Selfish routing in public services},
author = {Knight, Vincent A. and Harper, Paul R.},
journal = {European Journal of Operational Research},
volume = {230},
number = {1},
pages = {122--132},
year = {2013},
doi = {10.1016/j.ejor.2013.04.003},
}