This paper deals with the problem of admission control for geographically distributed web servers in presence of several access routers. The main contribution of this paper is the proposal of a scalable admission control scheme with the purpose to accept as many new sessions as possible within the constraints on response time imposed by service level agreements. The proposed policy autonomously configures and periodically adapts its component level parameters to the time-varying traffic situations. Extensive simulations of our policy show that our algorithm always guarantees the adherence to SLAs under different traffic scenarios. The proposed method shows a stable behavior during overload by smoothing flash crowd effects. It also improves the successful session termination probability and the utilization of system resources when compared to other traditional admission control schemes.