Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation

Abstract

The model of a fully available group of servers with a Poisson flow of primary calls and the possibility of losses before and after occupying a free server is considered. Additionally, a call can leave the system because of the aging of transmitted information. After each loss, there is some probability that a customer repeats the call. Such models are seen in the modeling of various telecommunication systems such as emergency information services, call and contact centers, access nodes, etc., functioning in overloading situations. The stationary behavior of the system is described by the infinite-state Markov process. It is shown that stationary characteristics of the model can be calculated with the help of an auxiliary model of the same class but without call repetitions due to losses occurring before and after the occupation of a free server and the aging of transmitted information. The performance measurements of the auxiliary model are calculated by solving a system of state equations using a recursive algorithm based on the concept of the truncation of the used state space. This approach allows significant savings of computer resources to be made by ignoring highly unlikely states in the process of calculation. The error caused by truncation is estimated. The presented numerical examples illustrate the use of the model for the elimination of the negative effects of emergency information service overload based on the filtering of the input flow of calls.