An M/M/1 Queueing System with Balking and Impatient Customers under Differentiated Working Vacations

Abstract: This paper examines an investigation an M/M/1 Queueing System with Balking and ImpatientCustomers under Differentiated Working Vacations. The Poisson Process is used to determine thearrival, and the services are distributed exponentially. FCFS was used to serve the customer. There aretwo different kinds of vacations: the first kind begins after a busy duration, and the second kind startswhen there are no customers waiting for the server to get back from vacation. The two vacations areexponentially distributed and independent. During the first kind and the second kind of vacations, services are exponentially distributed. Additionally, the impatience of the waiting consumer during thevacation period is taken into consideration. Balking customer is one who decides not to enter the queueafter observing its length. Considering the Stochastic Processes (𝑆 (𝑡), 𝑁 (𝑡) ): 𝑡 ≥ 0. This was solvedusing the matrix geometric method. Some parameters are used in the calculation of performancemetrics. Additionally, certain graphical and numerical tables are produced.