We study a perishable inventory system controlled by a (T, S) periodic review order up to level policy. Items have a general lifetime distribution and the lead time is assumed to be constant. The demands arrive according to a Poisson process with rate λ. The customer is impatient. If he is not served, he will leave the queuing systems. Using the approximate solution of the steady-state proba-bilities, we are able to obtain the cost components' analytical expression. Next, we compare the analytical results of our model with the simulation results. Fi-nally, we perform a sensitivity analysis to evaluate the effect of the lifetime var-iation and cost parameters on the optimal cost and stock level S. Our model is an extension of an exponential distribution case. With the general lifetime distribu-tion, we are able to have total flexibility for setting the lifetime variability. This approximation is closer to reality, especially in random environment conditions. Obtained results, from the analytical approximation model, are close to those of the optimal policy with an average accuracy of 7%.