Buffer management and delivery latency in various networks have been extensively studied. However, little work has considered the condition in which the traffic exhibits interpacket dependency, a common occurrence with many applications. Furthermore, the existing work related to such traffic mainly focuses on maximizing goodput and little attention has been paid to delivery latency. This paper concentrates on the delivery latency minimization problem for streaming data with packet dependencies. A novel optimization model is proposed to describe the aforementioned problem and the theoretical lower bound for delivery latency is deduced. Based on this model, a plain buffer management (PBM) algorithm is applied to the implementation of the buffer scheduling process. Afterwards, we improve the PBM algorithm under the guidance of a heuristic idea and put forward an optimal buffer management greedy (OBMG) algorithm. Experiments demonstrate that the OBMG algorithm outperforms the currently best known online (BKO) algorithm as it decreases the average delivery latency by 35.6%. In some cases, delivery latency obtained from the OBMG algorithm can be quite close to the theoretical lower bound. In addition, the OBMG algorithm can reduce CPU computational overhead by more than 12% in comparison to the BKO algorithm.