Docker deploys web services, how to update uninterrupted services?

  docker, question

With docker+jenkins+git+fabric, we have made a set of small projects for automatic deployment. There are web services already running in docker in the company. How can we update the project code with uninterrupted service?

Before hanging a nginx as a proxy, each update nginx configuration is reversed to a different port, and then all traffic is cut off and the old docker is killed.