A study on the performance of a queuing system with heterogeneous arrivals and various types of breakdowns under multiple working vacations

The paper analyses the performance of a single server queue with heterogeneous arrivals and various types of breakdowns under multiple working vacations. Customers enter the queue according to a Poisson process with a rate that varies according to the types of customers. In both the regular busy and working during the vacation states, the server offers services with an exponential distribution. During peak times, the system may breakdown due to server unavailability, the system may breakdown at any time. The model considers systems with two types of breakdowns. In this model, batches of customers are served under the General Bulk Service Rule. The steady-state equations, the performance of measures for the systems, and particular cases of the described model are derived. Finally, in the form of tables and graphs, numerical results have been obtained.