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Buffer stores are needed at both sender and receiver whenever a real-time signal is coded into a varying rate sequence of digits and these are transmitted over a channel at a uniform rate. Practical sending stores must be finite in size and therefore are subject to overflow; they thus function in a transient mode. In this paper, deterministic constraints on the operation of sending and receiving stores are established and their sizes are related to bittransmission rate and storage delay. The random behavior of the sending store is modeled as a first-order Markov chain with an absorbing state (overflow). The study is motivated by the case of nonuniformly coded differential PCM television signals. Some simulator measurements are reported on the actual incidence of overflows with such signals when using small-capacity stores (<120-bit storage). The Markov model for these cases is seen to give correct trends, although overall the measurements reveal considerably greater incidences of overflow. It can be expected, however, that the agreement between model and measurement would improve with size of stores.