This paper describes probabilistic analysis of NewReno version of TCP protocol AIMD algorithm which plays key role for congestion avoidance in data communication infrastructure. The model is formulated as a piecewise-linear stochastic process which presents the congestion window size and the data loss events are described by the renewal process with absolutely continuous renewal function. Markovian moments sequence embedded in the piecewise-linear process is defined. Its further analysis yields theorems proved on the ergodic properties of the Markovian moments sequence and the piecewise-linear process itself. Characteristic functions of sliding window size distribution for the sequence and the process are obtained as well. Reverse transforms of the characteristic functions yields complete set of AIMD characteristics. Also we expand estimation of the average congestion window size to the case of renewal data loss process.