Numerical Analysis of Full-Available Group of Servers with Dependence of Call Repetition on the Type of Call Blocking

Sergey Stepanov, Mikhail Stepanov, Fedor Kroshin
A mathematical model of a fully accessible communication system has been constructed and investigated, taking into account the repetition of a call after the preliminary service stage and due to the busy service devices. The model also assumes that the user's stay in the call repetition state is limited by a random variable that has an exponential distribution, which determines the aging time of the transmitted information. It is shown that the exact values of the stationary characteristics of the constructed model can be calculated by an efficient recursive algorithm developed for the model where the user repeats the call only because the service devices are busy. The constructed model and methods of its analysis can be used for evaluation of the positive effect that the use of the preliminary service like chatbot creates when planning the required number of call center operators. Numerical examples are given to illustrate the practical use of the results obtained.