Performance study of the M/M(a,b)/1/MWV queuing system with types of breakdowns

This paper analyses the M/M(a,b)/1/MWV queuing model with various types of breakdowns. During peak times, the system has breakdown due to server unavailability. The model considers system with two types of breakdowns. The system may breakdown in two different ways during busy and working vacation stages. Customer arrives to the system with parameter λ_v which follows Poisson distribution and server provides service in regular busy period with parameter µ_rb and under the multiple working vacations it provides service with parameter µ_wv with exponential distribution. In this model batches of customers are served under General Bulk Service Rule. The system may breakdown at any time. The breakdown that occurs during working vacation is denoted as β_v1 and the breakdown during busy state is denoted as β_v2. The steady-state equation, the performance of measures for the system and particular cases of described model are derived. Finally, a real life example demonstrated the validity of the model in a proper way.