Synchronize the devices to work on the same time frame.
If you knew that your device was going to send data in 5 minutes, you would set the timer to wake the ESP before that time so that it could be ready for the transmission. It would complete the transmission and then go to sleep for another 4 1/2 minutes.
If the other devices are not battery powered then the ESP repeater could wake whenever it wanted and the devices sending through it would keep trying until they hit the available window.
Compromise. And decide what is the least undesirable solution for you.