Transient moments of the window size in TCP

The window size in TCP can be modeled as a piecewise deterministic Markov process that increases linearly in time and experiences downward jumps at Pois-son times. We present a transient analysis of this window size process. Our main result is the Laplace transform of the transient moments. Explicit formu-lae for the integer and fractional moments are derived, as well as an explicit characterization of the speed of convergence to steady-state. Central to our approach is the infinitesimal generator and Dynkin’s martingale