A modified offered load approximation for nonstationary circuit switched networks

In this paper, we develop approximation methods to analyze blocking in circuit switched networks with nonstationary call arrival traffic. We formulate generalizations of the point-wise stationary and modified offered load approximations used for the nonstationary Erlang loss model or M(t)/M/c/c queue. These approximations reduce the analysis of nonstationary circuit switched networks to solving a small set of simple differential equations and using the methods for computing the steady state distributions for the stationary versions of such loss networks. We also discuss how the use of time varying arrival rates literally adds a new dimension to the class of telecommunication networks we can model. For example, we can model the behavior of alternate routing due to link-failure, which is a feature that the classical stationary version of the model cannot capture. Our nonstationary model can also describe aspects of the dynamic calling traffic behavior arising in cellular mobile traffic. For the special case of a two-link, three node network, we present numerical results to compare the various approximation methods to calculations of the exact blocking probabilities. We also adapt these calculations to approximate the behavior of rerouting calling traffic due to link-failure. The results are achieved by formulating some new recursions for evaluating the steady state blocking probabilities of such networks. We also generalize these techniques to develop analogous formulas for a linear N-node circuit switched network.