Excursions of the workload process in G/GI/1 queues

In this paper we study the excursions of the workload process of G/GI/1 queues above a given level. Instead of invoking classical semi-regenerative arguments, we adopt a martingale formulation via the use of the predictable characteristics associated with the semi-martingales of the excursion process. We calculate the stationary distribution of the excursion process as well as analyse the duration of excursions and associated properties.