{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:27:12Z","timestamp":1787340432453,"version":"build-2736575974"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1137\/070693862","type":"journal-article","created":{"date-parts":[[2010,2,3]],"date-time":"2010-02-03T18:09:38Z","timestamp":1265220578000},"page":"1957-1987","source":"Crossref","is-referenced-by-count":12,"title":["Selfish Traffic Allocation for Server Farms"],"prefix":"10.1137","volume":"39","author":[{"given":"Artur","family":"Czumaj","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Piotr","family":"Krysta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Berthold","family":"V\u00f6cking","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,2,3]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"B. Awerbuch, Y. Azar, and A. Epstein,\n                      The price of routing unsplittable flow\n                      , in 37th , ACM, New York, 2005, pp. 57\u201366.","DOI":"10.1145\/1060590.1060599"},{"key":"R2","unstructured":"M. Beckmann, C. B. McGuire, and C. B. Winston,\n                      Studies in the Economics of Transportation\n                      , Yale University Press, New Haven, CT, 1956."},{"key":"R3","doi-asserted-by":"crossref","unstructured":"G. Christodoulou and E. Koutsoupias,\n                      The price of anarchy of finite congestion games\n                      , in 37th , ACM, New York, 2005, pp. 67\u201373.","DOI":"10.1145\/1060590.1060600"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/90.650143"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"A. Czumaj and B. V\u00f6cking,\n                      Tight bounds for the worst-case equilibria\n                      , ACM Trans. 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Friedman,\n                      Genericity and congestion control in selfish routing\n                      , in 43rd IEEE Conference on Decision and Control, IEEE Control Systems Society, Piscataway, NJ, 2004, pp. 4667\u20134672.","DOI":"10.1109\/CDC.2004.1429524"},{"key":"R11","unstructured":"D. Gross and C. M. Harris,\n                      Fundamentals of Queueing Theory\n                      , 3rd ed., John Wiley and Sons, New York, 1998."},{"key":"R12","unstructured":"L. Kleinrock,\n                      Queueing Systems. Volume\n                      I:\n                      Theory\n                      , John Wiley and Sons, New York, 1975."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1109\/9.557575"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1032374242"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"E. Koutsoupias, M. Mavronicolas, and P. 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Roughgarden,\n                      How unfair is optimal routing?\n                      , in 13th , ACM, New York, SIAM, Philadelphia, 2002, pp. 203\u2013204."},{"key":"R27","doi-asserted-by":"crossref","unstructured":"T. Roughgarden, The price of anarchy is independent of the network topology, 67 (2003), pp. 341\u2013364.","DOI":"10.1016\/S0022-0000(03)00044-8"},{"key":"R28","doi-asserted-by":"crossref","unstructured":"T. Roughgarden,\n                      Routing games\n                      , in Algorithmic Game Theory, N. Nisan, T. Roughgarden, \u00c9. Tardos, and V. V. Vazirani, eds., Cambridge University Press, Cambridge, UK, 2007, pp. 461\u2013486.","DOI":"10.1017\/CBO9780511800481.020"},{"key":"R29","doi-asserted-by":"crossref","unstructured":"T. Roughgarden and \u00c9. Tardos, How bad is selfish routing? 49 (2002), pp. 236\u2013259.","DOI":"10.1145\/506147.506153"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2003.06.004"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.17.3.301"},{"key":"R32","doi-asserted-by":"crossref","unstructured":"B. V\u00f6cking,\n                      Selfish load balancing\n                      , in Algorithmic Game Theory, N. Nisan, T. Roughgarden, \u00c9. Tardos, and V. V. 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