Single server Markovian queueing system with working vacation, impatient customers and disasters

This paper examines the single server Markovian queueing system that incorporates working vacations, disasters, and impatient customers. The server initiates a Vacation when no customers are present in the system, during which it continues to serve arriving customers at a reduced rate. Disasters occurs while the main server is either busy or on a working vacation; leading to the removal of all customers from the system and causing the server to break down. When the main server is down, it is sent for repairs, and a substitute server provides service at a reduced rate until the main server is restored. When a customer arrives while the server is busy, undergoing repairs, or on Working Vacation, an impatience timer is activated. Additionally, arriving customers activate an impatience timer if the server is busy, under repair, or on a working vacation. If service is not completed before the timer expires, the customer abandons the system. The paper further presents a cost analysis and numerical illustrations to evaluate system performance.