In this chapter, we evaluate the impact of long-range dependence on a single network element (multiplexer or router) of a data network, this element being modeled as a ¯uid queueing system. Such a system has constant output rate C and is fed by a number N of i.i.d. on=off traf®c sources. The case where the number of sources N is ®xed is treated, for instance, in Boxma and Dumas [4].