The paper proposes a Markovian approach to the performance evaluation of the ESSE (early slow start exit) modification of the TCP congestion control mechanism. ESSE takes advantage of estimating the optimal pipesize at the sender side to properly select initial slow start threshold. Previous simulative experiments have shown that ESSE allows one to speed-up TCP connections and significantly reduces the packet drop rate at the bottleneck. This work takes a step further in understanding the ESSE behavior by developing a model of TCP source to evaluate the influence of different settings of slow start threshold on a TCP performance. As confirmed by comparison with simulations, the model provides, significantly faster than simulations, accurate estimates of typical performance indicators such as the average completion time and average drop rate of short-lived TCP connections.