We study whether or not the more variable inter-arrival time yields the more variable stationary number of customers in the infinitely many servers system and that in the loss system, when the service time distribution is arbitrarily fixed. At first, we prove that, when the service time has a completely monotone (CM) density which is a mixture of exponential densities, then that expectation is true. That is, the stationary number of customers in the  and that in the  behaves conventionally, as the inter-arrival time becomes stochastically more variable. However, when the service time is stochastically less variable than the exponential service time, the stationary number of customers in the  and that in the  do not always behave conventionally. In order to have the conventional behavior, it is necessary that the inter-arrival time has a log-convex density or a log-concave density. Accordingly, we bring the completely monotone density for the log-convex inter-arrival density. On the other hand, for the log-concave inter-arrival time density, we bring the generalized Erlang (GE) density which is a convolution of a finite number of exponential densities. For the former case, we prove that, even if the service time is stochastically less variable than the exponential service time, the stationary number of customers in the  and that in the  behaves conventionally, as the inter-arrival time becomes stochastically more variable. However, for the latter case, if the inter-arrival time A is stochastically less variable than the 2th Erlang random variable  then the stationary number of customers behaves paradoxically under some traffic condition. After all, we have that, if and only if  the stationary number of customers in the  and that in the  behaves conventionally, as the inter-arrival time becomes stochastically more variable.

completely monotone, generalized Erlang, effect of inter-arrival time variation, stochastically more (less) variable, conventional behavior.