An M/M/2 retrial queueing system with discouragement, breakdowns and repairs

Abstract

The current work aims to investigate the M/M/2 heterogeneous server retrial queueing system with server breakdown and repair, considering the discouragement of customers. An arriving customer will enter the service facility and check for availability of the servers. On finding either of the servers free, the customer will avail service at the available server. If both servers are busy upon arrival, then the customer will enter into the orbit or leave the system without joining the service facility. The customers awaiting service in the orbit may either retry their request for service or expecting an alarming delay in service may depart from the system without having their demands met. While serving a customer, the server may breakdown at any instant and an immediate repair process begins. Further, the customers interrupted by server breakdown stay in the service facility and resume their service once the server gets repaired. We have used the recursive method to derive the steady state queue size probability distribution. A variety of performance indices are derived from the proposed model.