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We consider a stochastic fluid queue served by a constant rate server anddriven by a process which is the local time of a certain Markov process. Such astochastic system can be used as a model in a priority service system,especially when the time scales involved are fast. The input (local time) inour model is always singular with respect to the Lebesgue measure which in manyapplications is ``close'' to reality. We first discuss how to rigorouslyconstruct the (necessarily) unique stationary version of the system under somenatural stability conditions. We then consider the distribution of performancesteady-state characteristics, namely, the buffer content, the idle period andthe busy period. These derivations are much based on the fact that the inverseof the local time of a Markov process is a L\'evy process (a subordinator)hence making the theory of L\'evy processes applicable. Another importantingredient in our approach is the Palm calculus coming from the point processpoint of view.

Analysis of stochastic fluid queues driven by local time processes