Network Improvement for Equilibrium Routing
In routing games, agents pick routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average delay have received substantial attention, including network tolls, Stackelberg routing, and edge removal.
A related approach with arguably greater practical relevance is that of making investments in improvements to the edges of the network, so that, for a given investment budget, the average delay at equilibrium in the improved network is minimized. This problem has received considerable attention in the literature on transportation research. We study a model for this problem introduced in transportation research literature, and present both hardness results and algorithms that obtain tight performance guarantees.
In general graphs, we show that a simple algorithm obtains a 4/3-approximation for affine delay functions and an O(p/logp)-approximation for polynomial delay functions of degree p. For affine delays, we show that it is NP-hard to improve upon the 4/3 approximation.
Motivated by the practical relevance of the problem, we consider restricted topologies to obtain better bounds. In series-parallel graphs, we show that the problem is still NP-hard. However, we show that there is an FPTAS in this case.
Finally, for graphs consisting of parallel paths, we show that an optimal allocation can be obtained in polynomial time.
KeywordsTransportation Research Average Delay Network Design Problem Total Delay Equilibrium Constraint
Unable to display preview. Download preview PDF.
- 3.Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the economics of transportation. Yale University Press (1956)Google Scholar
- 4.Bhaskar, U., Ligett, K., Schulman, L.J.: The network improvement problem for equilibrium routing. CoRR abs/1307.3794 (2013)Google Scholar
- 5.Boyd, S., Vandenberghe, L.: Convex optimization. Cambridge University Press (2004)Google Scholar
- 8.Fleischer, L., Jain, K., Mahdian, M.: Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games. In: FOCS, pp. 277–285 (2004)Google Scholar
- 11.Gairing, M., Harks, T., Klimm, M.: Complexity and approximation of the continuous network design problem. CoRR abs/1307.4258 (2013)Google Scholar
- 12.Harker, P.T., Friesz, T.L.: Bounding the solution of the continuous equilibrium network design problem. In: Proceedings of the Ninth International Symposium on Transportation and Traffic Theory, pp. 233–252 (1984)Google Scholar
- 13.Karakostas, G., Kolliopoulos, S.G.: Edge pricing of multicommodity networks for heterogeneous selfish users. In: FOCS, pp. 268–276 (2004)Google Scholar
- 19.Papadimitriou, C.H.: Algorithms, games, and the internet. In: STOC, pp. 749–753 (2001)Google Scholar
- 22.Roughgarden, T.: Selfish Routing and the Price of Anarchy. The MIT Press (2005)Google Scholar
- 26.Wardrop, J.G.: Some theoretical aspects of road traffic research. In: Proc. Institute of Civil Engineers, Pt. II, vol. 1, pp. 325–378 (1952)Google Scholar