Consider a queue with infinite waiting space at which the mean arrival-rate is equal to the mean service-rate. We call this system a balanced queue. Using a mathematical model, this paper proves that the departure process from such a system can be Long-Range Dependent (LRD) when the input process is Short-Range Dependent (SRD). Furthermore, the departure process does not fall within the class of LRD processes normally considered, and its power-spectrum is investigated using non-standard techniques. Simulations and experiments are described which demonstrate that the induced LRD is not a peculiarity of the model chosen, and can occur in real networks. In particular, evidence is presented to show that TCP may itself cause balanced queues. This finding is consistent with the observation that one of the primary goals of TCP is to obtain maximum network throughput without causing over-load, thereby leading to balanced queues throughout a network.