How long does a queen bee live?
Queen bee
When a young virgin queen emerges from a queen cell, she will generally seek out virgin queen rivals and attempt to kill them. Virgin queens will quickly find and kill (by stinging) any other emerged virgin queen (or be dispatched themselves), as well as any unemerged queens.  Queen cells that are opened on the side indicate that a virgin queen was likely killed by a rival virgin queen.  When a colony remains in swarm mode after the prime swarm has left, the workers may prevent virgins from fighting and one or several virgins may go with after-swarms.  Other virgins may stay behind with the remnant of the hive. Some virgins have been seen to escape the hive to avoid being killed and seek out another without a queen, such as in the eusocial bee Melipona scutellaris.[3] As many as 21 virgin queens have been counted in a single large swarm. When the after-swarm settles into a new home, the virgins will then resume normal behavior and fight to the death until only one remains. 
If the prime swarm has a virgin queen and the old queen, the old queen will usually be allowed to live.  The old queen continues laying.  Within a couple of weeks she will die a natural death  and the former virgin, now mated, will take her place.