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The communication system considered here interpolates data in the pauses in speech. Speech is gated on and off by comparing its own envelope to a threshold. At the same time a source is generating data at a fixed rate. The data are stored in a buffer, awaiting transmission during one of the gaps in speech. This paper presents a theoretical analysis of a model in which successive speech durations are assumed to be independent exponentially distributed random variables. The successive durations of silence are modeled by independent random variables that are obtained by forming the mixture distribution of two independent exponentially distributed random variables. On the basis of this model for alternating speech and silences, and an infinite buffer that is assumed to take on a continuum of states, we solve for the stationary probability density of nonzero states of the peak buffer occupancy. This enables us to determine buffer allocation as well as average delay using typical speech parameters.