Abstract :
This article investigates two variations of the Working Vacation framework, incorporating dual server breakdowns and a retrial queue with interruptions during working vacations, all managed under a Classical Retrial Policy. The steady-state probability distribution of the customer count in a single-server Markovian queue is computed using a matrix geometric approach specifically during working vacation periods. Breakdowns may occur in both the working vacation and busy states of the server. Customer arrivals are contingent on the server's state, following the First-Come-First-Serve discipline, and the server can provide alternative service to customers. The study specifically focuses on an M/M/1 retrial queue with working vacation interruptions. In cases where a customer arrives and the server is occupied, they enter an orbit of infinite size. Customers within the orbit attempt service sequentially when the server becomes available, adhering to the classical retrial policy with a retrial rate represented by 𝑛𝛼, where 𝑛 denotes the orbit size. Furthermore, if customers are present in the system at the conclusion of service during a working vacation period, the vacation is interrupted. The article also includes a sensitivity analysis to evaluate how different parameters impact the system's performance. The conclusion provides numerical examples and a discussion on cost optimization.