It is expected that the insensitive congestion measures for service times in the  type queueing systems paradoxically behave in the  queueing systems having phase-type completely monotonic  arrivals. In this paper, this expectation is theoretically proved for infinite server and loss systems with phase-type completely monotonic  arrivals. That is, the stationary number of customers in the  becomes stochastically less variable and the blocking probability of the  decreases, as the service time becomes stochastically more variable. It should be noted that it is necessary that the service time has a monotonic failure rate for

infinite server system, loss system, phase-type completely monotonic arrival, sensitivity of service time, paradoxical behavior.