Height distributions in data communications buffers with locking protocols

This paper analyzes a stochastic model of data communication. Messages are entered in a buffer by a source, and removed by a sink, at rates that are allowed to differ. The source, following message entry, and the sink, following buffer depletion, leave the buffer for independent exponentially distributed periods of absence, with different rate parameters. Locking protocols are in effect, i.e., message entry and removal can not occur simultaneously. The decision of the source or sink arriving to find the buffer active can follow either the ‘wait’ or ‘no wait’ option, i.e., it can wait until the buffer is free, or it can leave on another period of absence. Earlier performance studies of this model have been limited chiefly to expected values. The focus here is on the deeper questions of distribution functions and time-dependent behavior. Specifically, renewal-theoretic arguments, especially those exploiting regenerative properties, are applied to derivations of transforms of buffer-height and busy-period distributions. These transforms lead to formulas for higher moments, and in certain cases they can be inverted to yield distribution functions explicitly. Examples are worked out to illustrate the results.