B.S.T.J. Briefs: A Telephone Traffic Model Based on Randomly Closing Crosspoints, and its Relationships to Other Models

A Telephone Traffic Model Based on Randomly Closing Crosspoints, and Its Relationships to Other Models By V. E. B E N E S (Manuscript received December 23, 1970) In the theory of traffic in telephone connecting networks it is on one hand a virtual necessity, for practical purposes, to compromise the true complexity of the system under study and to introduce drastic simplifying assumptions that allow some calculation to be done, and on the other, it is perfectly feasible to pursue basic theoretical studies without such compromise and simplification. For this reason, a spectrum of several mathematical models for describing traffic in networks has been developed in recent j'ears. These models range from "simple" ones that furnish an incomplete description based on strong stochastic independence assumptions, to "complicated" ones that exactly mirror network structure and routing. Each grade of model has its uses: "simple" ones for easy computation and involved ones for general understanding. An example of a useful "simple" model is the probability linear graph 1 suggested by C. Y. Lee in 1955, an outgrowth of earlier work by L. E. Kittredge and E. C. Molina. At the other end of the scale, an example of a "complicated" model is the Markov process2 proposed by the author in 1963 as an improvement of the "thermodynamic" model. 3 We shall describe here another "simple" model, with a basic starting point similar to that of Lee, and then show how a certain natural restriction of this model yields in many cases precisely the thermodynamic model.