We introduce a model of the Relentless Congestion Control proposed by Matt Mathis. Relentless Congestion Control (RCC) is a modification of the AIMD (Additive Increase Multiplicative Decrease) congestion control which consists in decreasing the TCP congestion window by the number of lost segments instead of halving it. Despite some on-going discussions at the ICCRG IRTF-group, this congestion control has, to the best of our knowledge, never been modeled. In this paper, we provide an analytical model of this novel congestion control and propose an implementation of RCC for the commonly-used network simulator ns-2. We also improve RCC with the addition of a loss retransmission detection scheme (based on SACK+) to prevent RTO caused by a loss of a retransmission and called this new version RCC+. The proposed models describe both the original RCC algorithm and RCC+ improvement and would allow to better assess the impact of this new congestion control scheme over the network traffic.