Abstract: In practice production, when failures occurrs to the important equipment, it needs to be repaired in time, and some equipment will leave the system because of impatience. Therefore, model with multi-priority and abandonment should be established in the queuing system. The system state revolution matrix is deduced by the Markov process method and block matrix method. Because For the state transfer rate matrix is block tridiagonal matrix, the steady-state probability and steady-state transfer frequency of each state are obtained by block matrix analysis. The system indexes such as the transfer frequency between key states and the total waiting time are calculated, and the relations between profit and the parameters in the model are deduced. Finally, an example is given to further explain effectiveness of the model. The queuing system modeling method establishes a complete system index by introducing the steady state transfer frequency, which provides a theoretical basis for optimization of system configuration.

Key words: Frequency characteristics, Penetration status, Weld pool oscillation, Weld pool penetration control, Markov process, partitioned matrix, queuing theory, state transfer frequency, state transfer rate matrix