Schedulability analysis is a cornerstone of modern real-time scheduling theory development. Utilization- bound based schedulability test is considered one of most efficient and effective schedulability tests, because of its extremely low runtime overhead. Deriving the utilization bound for a given real-time system has, nevertheless, been a challenging task as it usually requires comprehensive modeling and understanding of the system and payload tasks. This paper is focused on deriving utilization bounds for weighted round robin schedulers. We demonstrate how to establish a unified modeling framework and then use it to derive utilization bounds. We obtain the optimal parameter selection that maximizes the utilization bound, then compare the new bound with those of fixed priority schedulers, and timed token ring schedulers. The new bound is further extended to systems with sporadic job requests. We argue that our modeling framework is highly versatile, and hence, can be easily tailored for analysis of other types of real-time systems.