The tandem queueing system is a basic structure of queueing networks. However, it is hard to accurately calculate the mean waiting time of the general tandem queueing system except for the tandem queues with the Markov property or constant service times. To characterize the dependence among stations in the tandem queues, this paper proposes the concept of performance ratio to study the mean waiting time. By analyzing the numerical properties of performance ratio, the fitting function of the performance ratio is achieved with which the mean waiting time of the downward station in the tandem queue is approximated. As a result, numerical experiments show that the approximation method based on the performance ratio performs well.