Looking for Name of Common Server Pattern

I have been having some trouble identifying whether or not there is a name for the following common pattern:

A thing which has at minimum the following lifecycle:

• comes online
• accepts requests for an indefinite period of time
• receives a signal to stop accepting new requests, but finish processing any currently processing requests
• goes offline

I mean this as opposed to something with a terminal lifecycle, something like:

• comes online
• does some work on one request
• goes offline

The most concrete example of this pattern in my mind is a web server which is subject to a load balancer, but am having trouble finding some general literature on the subject.