The Stack Resource Policy (SRP) is a real-time synchronization protocol with some distinct properties. One of such properties is early blocking; the execution of a job is delayed instead of being blocked while requesting shared resources. If SRP is used in dynamic priority scheduling such as in the Earliest Deadline First (EDF), the early blocking requires that a scheduler should select the highest-priority job among the jobs that will not be blocked, incurring a runtime overhead. In this paper, we analyze the runtime overhead of EDF scheduling when SRP is used. We find out that if jobs share resources using SRP the overhead of selecting a job when using the conventional implementations of a ready queue becomes serious as the number of jobs increases. To solve this problem, we propose an alternative data structure for the ready queue and an algorithm that can significantly reduce the overhead. This paper also describes the design and implementation of a real-time layer that employs the proposed scheme in Linux.