This paper presents an analysis of the blocking phenomenon in circuit-switched routing policies with alternate routing and trunk reservation. From the usual assumptions on the offered traffic (Poisson) and the service time (exponential distribution), a classical Markov chain model is derived. Some approximate formulas are given to compute the blocking probabilities for first- and second-choice traffic. The accuracy of the proposed estimates is evaluated by direct comparison with already known results in simple cases and with the exact solution of the state equations.

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.

The paper provides a simple method for point-to-point blocking estimation in telephone networks. A one-moment model is developed which incorporates the definition of fictitious offered traffic that enables one to take into account the deviation of smooth and peaked traffics from the Poisson. Numerical results illustrate the accuracy of the method.

The paper presents an estimate of time congestion for overflow process. The approximation is derived from the Markovian formulation under classical assumptions (Poissonian traffic offered to the first choice route and exponential service time). Numerical experiments show the accuracy and the limitations of the proposed estimate.