In this paper, we proposed a model for controlling the group velocity of the transmitted and reflected pulses in a slab medium doped by four-level quantum dot nanostructure. Here, an infrared signal field interacted by quantum dot nanostructure can affect the behavior of reflected and transmitted pulses. We show that in the presence and absence of infrared pulses, the other controllable parameters have essential roles for controlling the slow and fast light propagation through the medium. Moreover, we found that the simultaneous slow and fast light can be obtained for the transmitted and reflected pulses by infrared signal field. Our proposed model may be useful for ultrahigh density optical memories in quantum communication systems or in various fields of all-optical systems.
