# Nonadaptive selfish routing with online demands

Harks, Tobias and Végh, László A. (2007) Nonadaptive selfish routing with online demands. In: Fourth Workshop on Combinatorial and Algorithmic Aspects of Networking (CAAN), 14th August 2007, Dalhousie University, Halifax, Canada.

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## Abstract

In this paper, we study the efficiency of selfish routing problems in which traffic demands are revealed online. We go beyond the common Nash equilibrium concept in which possibly all players reroute their flow and form a new equilibrium upon arrival of a new demand. In our model, demands arrive in $n$ sequential games. In each game the new demands form a Nash equlibrium, and their routings remain unchanged afterwards. We study the problem both with nonatomic and atomic player types and with polynomial latency functions on the edges. We give upper and lower bounds on the competitive ratio of the online routing in terms of the maximum degree of the latency functions, the number of games and in the atomic setting the number of players. In particular, for nonatomic players and linear latency functions it is shown that the competitive ratio is at most $4n\over n+2$. Finally, we present improved upper bounds for the special case of two nodes connected by parallel arcs.

Item Type: Conference or Workshop Item (Paper) http://www.mathstat.dal.ca/~caan2007/ © 2007 The Authors Q Science > QA Mathematics > QA75 Electronic computers. Computer science Departments > Management http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx Published item via DOI 11 Oct 2012 12:35 http://eprints.lse.ac.uk/45897/