Control Variates (CV) is a Variance Reduction technique used in order to shorten simulation experiments. In a previous work we presented Time-to-idle as a stochastic process strongly correlated with the queue waiting time processes in the different queues of a polling service discipline network. Time-to-idle sample values are asynchronous with respect to those of queuing times, that is, they are generated at unpredictable times in an unpredictable order with respect to each other. This inherent characteristic allows it to be used in a network of queues (through batch means methods and taking care of synchronization between batches of both processes) but can hinge its performance in the single queue case. In this paper we evaluate its performance through simulation of the single queue case, comparing it with the service time and/or interarrival time synchronous random variables in the D/M/1, M/D/1 and M/M/1 queues where actual mean queue waiting times are known. We observe a slightly lower efficiency of Time-to-idle CV as was expected and we conclude that new techniques for synchronization of batches should be explored in order to minimize it.