Attempted supersedure in April, May and even June is a real problem in our region because of prevailing temperatures.
Drones require days of at least 65°F to establish good drone congregation areas in which the virgin queens can be successfully mated; however, these temperatures only arrive sporadically in our coastal Washington areas during May and June.
Consistent temperatures over 65°F usually do not occur until after the beginning of July.
If your bees are trying to replace the overwintered queen before local drones are available, and you are finding supersedure cells, built usually in the middle of frames, you can intervene by purchasing an already-mated queen or else combine the colony with another that is queenright.
If you allow the colony to go for too long without a queen (usually defined as about a month), you run the risk of having a hive of laying-workers. And that is a big problem. . . . . . . . Rich