Recently, queues with setup time (or vacation) are extensively studied because they have applications in various real world systems. In data centers, idle servers are turned off in order to save energy and are turned on again when the workload increases. The off-servers need some setup time to be active so as to serve waiting customers. On the other hand, vacation is a typical feature in service system such as call center where an operator may have secondary job when he is not serving an incoming call. In this talk, we present an analysis of these models with setup time or vacation based on a generating function approach. We prove a conditional decomposition showing that the queue length under the condition that all the servers are busy is decomposed into the sum of two independent random variables which have a clear physical interpretation.