I made my first split about a month an a half ago. Today inspecting a hive I found a lot of drone brood and could not find a queen.
Entrance traffic is very reasonable, but my question is.

How long will a hive last without a queen, with just laying workers. I know bees live for 6 weeks, so by now are they suppose to be all gone? I have read that hive with laying workers "will ultimately fail" But I wonder how long is that. I do not want to introduce a queen, they will tear her apart, and do not want to shake out all the bees- I live in residential neighborhood.

Thank you