Queueing systems with vacation: an overview

Abstract

Vacation models deal with a very important class of real life congestion situations encountered in day-to-day as well as in industrial scenario. A vacation in queueing context is the period when the server is not attending to a particularly targeted queue. The server may be under repair, attending to other queues, or simply forced to stop serving. Queueing systems with vacations have wide applications in the performance evaluation and dimensioning of computer networks, telecommunications, manufacturing systems, etc. The present survey article is devoted to the overview, methodology, some key aspects and ramifications concerning queueing systems with vacation. The related literature is classified based on modelling and methodological concepts. We present the review of the related work starting from the advent of vacation queueing systems up to the recent contributions. We illustrate how the seemingly diverse mix of problems is closely related in structure and can be understood in a common framework. Moreover, some general decomposition results and various techniques used to obtain performance indices for various vacation models in different frameworks are presented.