This paper investigates a nonlinear queuing system of type M/M/1/n in which the service rate is assumed to depend on the loss probability. The system of Kolmogorov differential equations is obtained in the analytical form for an arbitrary number of states, and numerical experiments are performed by using the classical fourth-order Runge–Kutta method. The analysis of the numerical results is presented too. This result demonstrates that increasing the proportionality coefficient between the loss probability and the service rate reduces the likelihood of losses and accelerates the transient dynamics.