A decision behavior of a call center and the customers are addressed. For a M/M/N+M call center model, a non-cooperative Stackelberg game model is formulated for maximizing the utility value based on the impact of delay time on the customers’ impatient psychology. The performance value of the queuing system is calculated by the combination of the bisection algorithm and the fixed point algorithm based on queue theory. The impacts of the delay time reliability and the patient change rate on the system performance are analyzed with numerical results. Further, Comparison under different game strategies illustrates the reasonability and effectiveness of the method.