MAP/PH(1), PH(2)/2 Queue with Multiple Vacation, Optional Service, Consultations and Interruptions

Two types of services are explored in this paper: regular server and main server, both of which provide both regular and optional services. Customers arrive using the Markovian Arrival Process (MAP), and service time is allocated based on phase type. The regular server uses the main server as a resource. Customers' service at the primary server is disrupted as a result. When the queue size is empty, the main server can take several vacations. This system has been represented as a QBD Process that investigates steady state with the use of matrix analytic techniques, employing finite-dimensional block matrices. Our model's waiting time distribution has been examined in more detail during the busy times. The system's key parameters are assessed, and a few graphs and numerical representations are constructed.