Convolution Algorithm for Evaluation of Probabilistic Characteristics of Resource Loss Systems with Signals

Resource loss systems (ReLS) with signals, in which arrival of a signal triggers resource reallocation of a customer, are often used in the performance analysis of the contemporary mobile networks, especially those that utilize high-frequency bands. An analytical solution for the stationary distribution of such systems is not obtained yet. Approximate calculation methods utilize the stationary distribution of ReLS without signals at the departure instants. In the paper, we develop an efficient convolution algorithm for evaluation of the probability metrics at the departure instants. In the case study, we demonstrate the effectiveness of the proposed algorithm in terms of execution time. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.