In this paper we study the problem of transmitting different quality of service (QoS) data classes on a broadcast erasure channel where each data class is intended for a group of users depending on their erasure rate. For real-time applications such as multimedia, data block length is typically small. Over a small data block length, the behavior of the erasure channel may significantly differ from its average. Thus, to guarantee a certain QoS, a considerable overhead may be needed. We provide a finite block length analysis of the effect of erasure on the overhead. We use this analysis to investigate a packet construction method that mitigated the effect of short block length.