Diffusion local time storage

In this paper we study a storage process or a liquid queue in which the input process is the local time of a positively recurrent stationary diffusion in stationary state and the potential output takes place with a constant deterministic rate. For this storage process we find its stationary distribution and compute the joint distribution of the starting and ending times of the busy and idle periods. This work completes and extends to a more general setting the results of Mannersalo et al. [Queueing Systems 46 (2004) 557].