Random linear network coding (RLNC) is used more and more in transmission protocols these days, including caterpillar random linear network coding (CRLNC). It achieves high throughput and low packet delay at the same time, as acknowledgments are not used. Up to now, however, results have always been taken from simulations or experiments. There is no analytical solution for the achievable throughput and packet delay because of the complex transmission pattern. This paper presents an analytical solution using a Markov-Chain for a single hop system with CRLNC. From the calculations of the state variables of the Markov-Chain, the influence of network coding on the transmission can be read directly. Thus, it can be seen at which error probabilities of the channel it is worthwhile to use network coding and by how much it increases the throughput. The results of the packet delay show that a buffer size of four is already sufficient to recover lost packets. This saves resources in the network. By comparing small and large window sizes, a critical boundary between the code rate and the error probability was discovered, at which it is worthwhile to use a large window size at e < 1 − e and a small window size at e ≥ 1 − c.