This paper extends the useful concept of open systems proposed by W.S. Liu, et al. (1997) in scheduling real-time applications and non-real-time applications, where the schedulability of each real-time application can be validated independently of other applications in the system. We replace the underlying earliest-deadline-first OS scheduler of the open system architecture by W.S. Liu, et al. (1997) with a rate-monotonic OS scheduler. The motivation behind this work is that many existing operating systems may not support the earliest deadline first scheduling very well. We propose to use the idea of sporadic servers to preserve CPU cycles for applications. We also develop schedulability tests for real-time applications which adopt the rate monotonic scheduling algorithm, the earliest deadline first scheduling algorithm, the priority ceiling protocol, and the stack resource policy. We allow tasks in each application to share local and global non-preemptable resources. A global resource synchronization mechanism is proposed. This paper provides a fixed-priority-based alternative for the important open system architecture.