In this article, the optimal model is determined for the family of models ${E_r/M/1, rin N}$ with interarrival times with Erlang distribution and service times with exponential distribution. The method of choosing the optimal model is that first, a cost function is introduced, and then a new index is introduced according to the cost function and the stationary probability of the system called $SER$. A model with a larger $SER$ index is optimal. Numerical analysis is also used to describe the method of determining optimal model.