The author studies a generalized single-server queueing system with
bulk arrivals and batch service, where the server takes vacations each time the
queue level falls below r(≥1) in accordance with the multiple vacation
discipline. The input to the system is assumed to be a compound Poisson
process modulated by the system and the service is assumed to be state dependent. One of the essential part in the analysis of the system is the employment
of new techniques related to the first excess level processes. A preliminary
analysis of such processes and recent results of the author on modulated processes enabled the author to obtain all major characteristics for the queueing
process explicitly. Various examples and applications are discussed.