Blocking probability analysis of circuit-switched networks with long-lived and short-lived connections

We consider a circuit-switched network with nonhierarchical alternate routing and trunk reservation involving two types of connections that are modeled as long-lived and short-lived calls. The long-lived calls can be reserved well in advance, and the short-lived calls are provided on demand. Therefore, we assume that the long-lived calls have strict priority over the short-lived ones. We develop approximations for the estimation of the blocking probability based on the quasi-stationary approach in two ways. One uses the Erlang fixed-point approximation (EFPA), and the other uses the overflow priority classification approximation (OPCA). We compare the results of the approximations with simulation results and discuss the accuracy of the approximations under different system parameters, such as ratio of offered load, number of links per trunk, maximum allowable number of deflections, and trunk reservation. We also discuss the robustness of the quasi-stationary approximation to the ratio of the mean holding times of the long-lived and short-lived calls as well as that of EFPA and OPCA to the shape of the holding time distribution. Finally, we demonstrate that OPCA can be applied to a large network such as the Coronet.