condition_variable without mutex in a lock-free implementation

I have a lock-free single producer multiple consumer queue implemented using std::atomics in a way similar to herb sutters CPPCon2014 talk.

Sometimes, the producer is too slow to feed all consumers, therefore consumers can starve. I want to prevent starved consumers to bang on the queue, therefore I addedd a sleep for 10ms. This value is arbitrary and not optimal. I would like to use a signal that the consumer can send to the producer once there is a free slot in the queue again. In a lock based implementation, I would naturally use std::condition_varialbe for this task. However now in my lock-free implementation I am not sure, if it is the right design choice to introduce a mutex, only to be able to use std::condition_variable. I just want to ask you, if a mutex is the right way to go in this case.