Skip to main content
Article thumbnail
Location of Repository

Selfish traffic allocation for server farms

By Artur Czumaj, Piotr Krysta and Berthold Vöcking


We study the price of selfish routing in noncooperative networks like the Internet. In particular, we investigate the price of selfish routing using the price of anarchy (a.k.a. the coordination ratio) and other (e.g., bicriteria) measures in the recently introduced game theoretic parallel links network model of Koutsoupias and Papadimitriou. We generalize this model toward general, monotone families of cost functions and cost functions from queueing theory. A summary of our main results for general, monotone cost functions is as follows: 1. We give an exact characterization of all cost functions having a bounded/unbounded price of anarchy. For example, the price of anarchy for cost functions describing the expected delay in queueing systems is unbounded. 2. We show that an unbounded price of anarchy implies an extremely high performance degradation under bicriteria measures. In fact, the price of selfish routing can be as high as a bandwidth degradation by a factor that is linear in the network size. 3. We separate the game theoretic (integral) allocation model from the (fractional) flow model by demonstrating that even a very small or negligible amount of integrality can lead to a dramatic performance degradation. 4. We unify recent results on selfish routing under different objectives by showing that an unbounded price of anarchy under the min-max objective implies an unbounded price of anarchy under the average cost objective and vice versa. Our special focus lies on cost functions describing the behavior of Web servers that can open only a limited number of Transmission Control Protocol (TCP) connections. In particular, we compare the performance of queueing systems that serve all incoming requests with servers that reject requests in case of overload. Our analysis indicates that all queueing systems without rejection cannot give any reasonable guarantee on the expected delay of requests under selfish routing even when the injected load is far away from the capacity of the system. In contrast, Web server farms that are allowed to reject requests can guarantee a high quality of service for every individual request stream even under relatively high injection rates

Topics: QA76, QA
Publisher: Society for Industrial and Applied Mathematics
Year: 2010
OAI identifier:

Suggested articles


  1. (1993). A .O r d a ,R .R o m ,a n dN .S h i m k i n , Competitive routing in multi-user communication networks, doi
  2. (2003). Approximate equilibria and ball fusion, doi
  3. (1999). Avoiding the Braess paradox in noncooperative networks, doi
  4. (2004). Bounding the inefficiency of equilibria in nonatomic congestion games, doi
  5. (1997). Capacity allocation under noncooperative routing, doi
  6. (1999). Dynamics of IP traffic: A study of the role of variability and the impact of control, doi
  7. (1998). Fundamentals of Queueing Theory, 3rd ed., doi
  8. (2004). Genericity and congestion control in selfish routing, doi
  9. (2002). How bad is selfish routing?, doi
  10. (2002). How unfair is optimal routing?,
  11. (2007). ocking, Selfish load balancing, in Algorithmic Game Theory, doi
  12. (1994). On complexity as bounded rationality, doi
  13. (1996). On the relationship between file sizes, transport protocols, and self-similar network traffic, doi
  14. (2006). On the severity of Braess’s Paradox: Designing networks for selfish users is hard, doi
  15. (1975). Queueing Systems. Volume I: Theory, doi
  16. (1982). r a n k e n ,D .K o n i g ,U .A r n d t ,a n dV .S c h m i d t , Queues and Point Processes,A k a d e m i e -Verlag,
  17. (1995). Randomized Algorithms, doi
  18. (1997). Rate of change and other metrics: A live study of the World Wide Web,
  19. (2007). Routing games, in Algorithmic Game Theory, doi
  20. (1997). Self-similarity in World Wide Web traffic: Evidence and possible causes, doi
  21. (1952). Some theoretic aspects of road traffic research, doi
  22. (2004). Stackelberg scheduling strategies, doi
  23. (2005). T h ep r i c eo fr o u t i n gu n s p l i t t a b l efl o w ,
  24. (1981). The Braess paradox, doi
  25. (1983). The prevalence of Braess’ paradox, doi
  26. (2003). The price of anarchy is independent of the network topology, doi
  27. (2005). The price of anarchy of finite congestion games, doi
  28. (2007). The price of selfish routing, doi
  29. (2007). Tight bounds for the worst-case equilibria, doi
  30. (1997). Virtual path bandwidth allocation in multiuser networks, doi
  31. (1995). Wide area traffic: The failure of Poisson modeling, doi
  32. (1999). Worst-case equilibria, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.