Before revision: We consider two types of problems associated with a bufferless server with service preemption (push-out). One type is motivated by "adversarial" coupon collection with applications to modeling the surveillance of a set of servers by a botnet planning a DDoS attack on them collectively. The servers dynamically change according to a moving-target defense. Another type of problem has to do with a sequence of messages handled by the (transmission) server wherein each message obsoletes all previous ones .
After revision: A queueing system handling a sequence of message arrivals is considered where each message obsoletes all previous ones .