A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations

Abstract

Motivated by modelling the data transmission in computer communication networks, we study a Lévy-driven stochastic fluid queueing system where the server may subject to breakdowns and repairs. In addition, the server will leave for a vacation each time when the system is empty. We cast the workload process as a Lévy process modified to have random jumps at two classes of stopping times. By using the properties of Lévy processes and Kella–Whitt martingale method, we derive the limiting distribution of the workload process. Moreover, we investigate the busy period and the correlation structure. Finally, we prove that the stochastic decomposition properties also hold for fluid queues with Lévy input.