We study that the insensitive congestion measures to the form of service time distribution in the infinite server system  and the loss system  having Poisson arrivals paradoxically behave in the associated infinite server system  and the associated loss system  having common completely monotone (CM) arrivals. That is, the stationary number of customers in the  becomes stochastically less variable as well as the blocking probability in the  decreases, as the service time becomes stochastically more variable. The  and the  having constant service times are the most congested in the  and the  having general service times, respectively.

infinite server system, loss system, completely monotone arrival, sensitivity of service time, paradoxical behavior.