A literature review on retrial queueing system with Bernoulli vacation

The retrial phenomenon occurs inherently in a wide range of queueing systems. The majority of retrial queueing models do not account for vacation. However, in practice, retrial queueing systems undergo vacations for maintenance or other reasons. In this study, we provide an in-depth analysis of the many possible retrial queueing systems when Bernoulli vacations are in effect. Moreover, this study outlines the key principles and reviews the relevant literature. The framework of a retrial queue with Bernoulli vacation has numerous applications in computer networking systems, manufacturing and production mechanisms, inventory systems, including network service, mail service and file transfer service, etc. Several retrial queueing systems have been investigated, notably M/M/1, M/M/C, M/G/1, M[X]/G/1, and Geo/G/1. Many other important situations, such as server interruption, feedback, G-queue, impatient customers, priority customers, etc., have been explored in relation to retrial queues with Bernoulli vacation and the results of these investigations are also highlighted. The foremost objective of this study is to help researchers, administrators and technical workers who want to use queuing theory to simulate congestion and need to know where to find details on the right models. Finally, some open problems and potential future lines of survey are also covered.