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The increasing speed of internet access links motivated the shift in applications, used to remotely access the computers, from the text-based terminal connections to graphical remote desktop systems (GRDS). Because these services are highly interactive, user-perceived latency is more important than in other different types of internet applications (such as Web, Video streaming, and Peer-to-Peer File transfer), which usually attract the researchers' attention. In previous studies, the traffic performance is shown to be mainly affected by the statistical nature of applications' packet arrival process at network level. This paper describes characterization and modeling of graphical remote desktop system's network traffic at the IP level. Following the past researches, we have evaluated self-similar processes and noticed a very good fit at timescales ranging from 100 ms to 5 s and from 10 to 200 s. We provide the reasons for this self-similar traffic behavior and discuss its consequences at the development of synthetic workloads and performance studies of GRDS systems.