Enforcing 1 unique websocket connection per client?

I have a webpage that establishes a websocket connection with the server. I have to make sure that a user of the site can only establish a single connection, so opening a new tab and navigating to the same page will close the previous connection.

I was thinking of maintaining a map with the session id as the key; however, as the map would have to be constantly adjusted in size as more and more clients connect I am afraid of it having performance problems, and since it's accessed concurrently you would probably have to do some kind of locking.

Any ideas for performance efficient ways of ensuring a unique connection per client? Would love to hear suggestions, thank you.