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 pointwise stationary and modified of fered load approximations used for the nonstationary Erlang loss model or M(t)/M/c/c queue. These approximations reduce the analysis of nons tationary circuit switched networks to solving a small set of simple d ifferential equations and using the methods for computing the steady s tate distributions for the stationary versions of such loss networks. We also discuss how the use of time varying arrival rates literally ad ds a new dimension to the class of telecommunication networks we can m odel. For example, we can model the behavior of alternate routing due to link-failure, which is a feature that the classical stationary vers ion of the model cannot capture. Our nonstationary model can also desc ribe aspects of the dynamic calling traffic behavior arising in cellul ar mobile traffic. For the special case of a two-link, three node netw ork, 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 call ing traffic due to link-failure. The results are achieved by formulati ng some new recursions for evaluating the steady state blocking probab ilities of such networks. We also generalize These techniques to devel op analogous formulas for a linear N-node circuit switched network.