A Model for Telephone Networks and Its Use for Routing Optimization Purposes

The problem studied here concerns the modeling of call blocking in telephone networks. From the usual assumptions such as exponential arrivals and holding time, lost call cleared, the state of the network is described by a finite Markov chain. From the transition probabilities of this process are derived the differential equations associated with the average occupancy of all trunk groups. These traffic equations are simplified by considering independence of blocking for trunk groups in series. The blocking probabilities are estimated using fictitious offered traffic and the Erlang B formula. Such representation takes into account peaky or smooth traffic characteristics. We develop this one-moment model for routing policies such as load sharing and overflow routing. Performances of the model are given in comparison to the solution of the exact Markov chain model or the results of Monte Carlo simulation. Finally, an application to routing optimization and network dimensioning is treated.