TY - JOUR

T1 - Nash equilibria for combined flow control and routing in networks

T2 - Asymptotic behavior for a large number of users

AU - Altman, Eitan

AU - Başar, Tamer

AU - Srikant, R.

N1 - Funding Information:
Manuscript received June 10, 2001; revised January 12, 2002. Recommended by Associate Editor L. Dai. This work was supported in part by the National Science Foundation under Grants ANI-9813710, NCR 97-01525, CCR 00-85917 ITR, and INT-9804950, in part by the Air Force Office of Scientific Research under MURI Grant AF DC 5-36128, an EPRI/ARO Grant, and in part by DARPA under Grant F30602–00–2–0542.

PY - 2002/6

Y1 - 2002/6

N2 - We consider a noncooperative game framework for combined routing and flow control in a network of parallel links, where the number of users (players) is arbitrarily large. The utility function of each user is related to the power criterion, and is taken as the ratio of some positive power of the total throughput of that user to the average delay seen by the user. The utility function is nonconcave in the flow rates of the user, for which we introduce a scaling to make it well defined as the number of users, N, becomes arbitrarily large. In spite of the lack of concavity, we obtain explicit expressions for the flow rates of the users and their associated routing decisions, which are in O(1/N) Nash equilibrium. This O (1/N) equilibrium solution, which is symmetric across different users and could be multiple in some cases, exhibits a delay-equalizing feature among the links which carry positive flow. The paper also provides the complete optimal solution to the single-user ease, and includes several numerical examples to illustrate different features of the solutions in the single- as well as N-user cases, as N becomes arbitrarily large.

AB - We consider a noncooperative game framework for combined routing and flow control in a network of parallel links, where the number of users (players) is arbitrarily large. The utility function of each user is related to the power criterion, and is taken as the ratio of some positive power of the total throughput of that user to the average delay seen by the user. The utility function is nonconcave in the flow rates of the user, for which we introduce a scaling to make it well defined as the number of users, N, becomes arbitrarily large. In spite of the lack of concavity, we obtain explicit expressions for the flow rates of the users and their associated routing decisions, which are in O(1/N) Nash equilibrium. This O (1/N) equilibrium solution, which is symmetric across different users and could be multiple in some cases, exhibits a delay-equalizing feature among the links which carry positive flow. The paper also provides the complete optimal solution to the single-user ease, and includes several numerical examples to illustrate different features of the solutions in the single- as well as N-user cases, as N becomes arbitrarily large.

KW - Asymptotic Nash equilibria

KW - Flow control

KW - Networks

KW - Noncooperative equilibria

KW - Nonzero-sum games

KW - Routing

UR - http://www.scopus.com/inward/record.url?scp=0036600717&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036600717&partnerID=8YFLogxK

U2 - 10.1109/TAC.2002.1008358

DO - 10.1109/TAC.2002.1008358

M3 - Article

AN - SCOPUS:0036600717

SN - 0018-9286

VL - 47

SP - 917

EP - 930

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 6

ER -