This paper stochastically models a single-node telecommunications system both with and without the use of intelligent multiplexing. Intelligent multiplexers take advantage of the idle periods or silences that occur during the course of speech transmissions to merge (or multiplex) packetized talkspurts from more than one source onto a single channel. This allows for a more efficient use of available bandwidth, thereby reducing the amount of bandwidth required to carry a particular traffic load. Digitizing speech into packets of equal size also allows for compression, further reducing bandwidth needs. By comparing the models for systems both with and without multiplexing, we are able to determine the reduction in bandwidth which may be expected for a particular grade of service (measured by blocking probabilities). A bivariate continuous time Markov chain model for a multiplexer is presented. An approximation is introduced to calculate limiting blocking probabilities much more quickly and for larger systems than is possible by solving a set of linear equations for the bivariate model. The accuracy of the approximation is explored through comparison with the bivariate model; the approximation provides a somewhat conservative estimate of blocking, but is close enough to be used as a tool for the range of relevant values. The approximation is then used to compare blocking probabilities for three different levels of speech activity. Results are shown in tabular form.... Telecommunications, Model, Stochastic telecommunications model

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