Playback delay control is an important mechanism to avoid jitter in video streaming systems. This paper introduces a playback delay minimization problem for multiuser video streaming systems providing a jitter-free video streaming service to end users in the system. In particular, a necessary condition on the playback delay for jitter-free streaming is obtained. Then, based on the derived necessary condition, an optimum rate splitting algorithm that splits available rate to all users is proposed. The proposed algorithm is optimum in the sense that it achieves the minimum system delay, which is defined as the maximum of all initial playback delays, while ensuring jitter-free streaming service to all users. Finally, using these results, an expression for the minimum system delay as a function of system parameters such as total rate and playback curves of requested video files is also derived.