Abstract: When each route FAST TCP connections were assumed Poisson arrival and exponentially distributed document sizes,a Lyapunov function including FAST TCP connection's lingering time was constructed to prove that each route connection lingering time was shortest at the invariant manifolds under the heavy traffic service intensity, and to prove that the invariant manifolds were reached in a finite time. Aiming at the weakness of FAST TCP static mapping protocol parameter method, according to the relation between connection numbers and the protocol parameter in reduced order invariant manifolds, a slow timescale iterative search protocol parameter method based on the expected connection numbers and invariant manifolds was proposed. NS-2 simulation results were presented to verify the effectiveness of this method.

Key words: Preference, Invariant manifolds, Heavy traffic, Service intensity, Fluid model, Lingering time