Generalized processor sharing (GPS) is an efficient and flexible scheduling mechanism for sharing server capacity and providing differentiated quality-of-service (QoS) owing to its appealing properties of fairness, traffic isolation, and work conservation. This paper analytically investigates the loss probabilities of individual traffic flows in GPS systems subject to heterogeneous long-range dependent (LRD) and short-range dependent (SRD) traffic, which have not been studied in the open literature. We derive and validate the closed-form expressions of the loss probabilities of both traffic flows. We then evaluate the effects of Hurst parameter of LRD traffic on the performance of GPS systems in terms of traffic loss probability.