The M/M/1 Repairable Queueing System with Two Types of Server Breakdowns and Negative Customers

analyze the affect of server breakdowns and negative customers on queueing systems. Using the quasi-brith-and-death (QBD) process and matrix geometry solution method, the M/M/1 repairable queueing system with two types of server breakdowns and negative customers was studied. In the model, arriving at a negative customer will offset one positive customer, simultaneously, it may reduce the service rate or stop working of the system. The stationary conditions are given, the steady-state probability vectors are obtained, and some steady-state queueing and reliable measures are calculated. The results suggest that the system's mean queue length decreases the increase of the negative customers arrival rate. Finally, the affect of parameter changes on the system performance measures are shown by graphs, which can provide an actual reference for practical applications.