At first, we prove that, in the  having general renewal arrivals, the entropy of inter-arrival time is smaller than or equal to the entropy of inter-departure time by using the second law of thermodynamics. On the basis of that result, we prove that the inter-departure time in the  having smoothed (SMTH) arrivals, in which the inter-arrival time density is a convolution of a finite number of exponential densities, becomes stochastically more variable, as the service time becomes stochastically more variable, that is, the inter-departure time behaves conventionally to the service time distribution. However, the number of departures and the stationary number of customers may not behave conventionally to the service time distribution, if the coefficient of variation  of the SMTH inter-arrival time Ais smaller than  We prove that the number of departures and the stationary number of customers behave conventionally to the service time distribution, if and only if the coefficient of variation  of Ais greater than or equal to  In case of the  the condition  is necessary and sufficient to ensure the conventional behavior of the stationary number of customers. However, both the inter-departure time and the number of departures may not behave conventionally to the service time distribution in the  even if  

   smoothed arrival, entropy, second law of thermodynamics, departure process, conventional behavior.