The streams of messages generated at terminals or of data generated by computers are quite often sporadic. In order to enhance the utilization of communication links, a technique such as buffering is commonly adopted. A buffer store is interposed between the set of incoming links and an output link; its general purpose is to receive and store information according to a stochastic process defining the source, and then to output the information according to a different process that defines the sink. In this chapter we shall restrict ourselves to an output process which is simply a smoothing of the input process; i.e. the output of a non-empty buffer is at a constant rate which is normally assumed to be less than the source rate. A central design parameter is the buffer size, which must be sufficiently large to accommodate large backlogs of messages or data units that may occasionally develop because of large, transient demands of the input process. Accordingly, we shall discuss the problem of finding the steady state distribution of the amount of information stored in the buffer.
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