Multiphase fluctuation analysis in a queue with an enhanced maintenance continuous time parameter process

Abstract

We continue our study of a single-vacation queue with enhanced maintenance work. During his vacation time, the server performs secondary jobs which are randomly generated in batches. The stay at the maintenance facility is restricted by a time $T$ (which can be random). As soon as the stay there expires, the server does not leave abruptly, but completes the unfinished batch of units and only then returns to the system. We obtain the limiting probability distribution of the continuous time parameter queueing process and some important performance measures.