Performance Analysis of a Buffer Under Locking Protocols
This paper formulates and analyzes stochastic models of process communication in computer systems. Messages are entered in a buffer (mailbox) 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 rate parameters λ and μ, respectively. 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 be to wait until it is free, or to leave on another period of absence. We apply the analysis to both the “wait” and “no wait” options.
A study of the fluid-approximation model shows that renewal theory forms the proper basis of the analysis; the important relevant results are briefly reviewed. These results along with renewal-theoretic arguments, especially those exploiting regenerative properties, are then applied to derivations of basic performance measures, e.g., transforms or expectations of busy periods and steady-state buffer levels. In particular, the formulas bring out the dependence of the expectations on the variance of message lengths. Desirable extensions of the models are sketched.
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