L\'evy-driven Fluid Queue with Server Breakdowns and Vacations

Abstract

In this paper, we consider a L\'evy-driven fluid queueing system where the server may subject to breakdowns and repairs. In addition, the server will leave for a vacation each time when he finds an empty system. We cast the queueing process as a L\'evy process modified to have random jumps at two classes of stopping times. By using the Kella-Whitt martingale method, we obtain the limiting distribution of the virtual waiting time process. Moreover, we investigate the busy period, the correlation structure and the stochastic decomposition properties. These results may be generalized to L\'evy processes with multi-class jump inputs or L\'evy-driven queues with multiple input classes.