The limit behavior of a semi-Markov process, depending on a small parameter, is important for the analysis and optimization of telecommunication systems. Semi-Markov processes are an extension of Markov processes that allow modeling systems with preservation of some previous states. Such processes are important, for example, for modeling data transmission over wireless channels or communication networks. The limit behavior of a semi-Markov process is determined by a small parameter, which is usually denoted as \(\varepsilon \) (epsilon). Various important characteristics of the system depend on the limit value of \(\varepsilon \) , such as the probability of blocking, data transfer rate, average waiting time, etc. Markov renewal theorems are used as analytical tool for studying the limiting behavior of a semi-Markov process that depends on a small parameter \(\varepsilon >0\) at \(\varepsilon \to 0, t\to \infty , \varepsilon t\to u\) . This theorem makes it possible to study transient phenomena arising in telecommunication systems, such as the asymptotic behavior of additive functionals from ergodic processes, boundary value problems for random walks and processes with independent increments, branched processes close to critical ones, and others. Analyzing the limit behavior of a semi-Markov process with respect to a small parameter is a valuable tool for understanding and optimizing telecommunication systems, ensuring their reliability, and meeting performance requirements.