A Survey on Queuing Inventory Models with Server Vacations and Retrials

This paper presents a comprehensive survey of queueing inventory models that incorporate server vacations and retrials, focusing on their applications, methodologies, and performance metrics. These models address complex real-world systems where service mechanisms are influenced by inventory constraints, server availability, and customer retry behavior. Key features such as vacation policies, retrial queues, and inventory replenishment strategies are examined in detail. The survey highlights the interplay between these components, exploring their impact on system performance, including queue lengths, waiting times, service rates, and inventory costs.