  This work studies fixed priority (FP) scheduling of real-time jobs with
end-to-end deadlines in a distributed system. Specifically, given a multi-stage
pipeline with multiple heterogeneous resources of the same type at each stage,
the problem is to assign priorities to a set of real-time jobs with different
release times to access a resource at each stage of the pipeline subject to the
end-to-end deadline constraints. Note, in such a system, jobs may compete with
different sets of jobs at different stages of the pipeline depending on the
job-to-resource mapping. To this end, following are the two major contributions
of this work. We show that an OPA-compatible schedulability test based on the
delay composition algebra can be constructed, which we then use with an optimal
priority assignment algorithm to compute a priority ordering. Further, we
establish the versatility of pairwise priority assignment in such a multi-stage
multi-resource system, compared to a total priority ordering. In particular, we
show that a pairwise priority assignment may be feasible even if a priority
ordering does not exist. We propose an integer linear programming formulation
and a scalable heuristic to compute a pairwise priority assignment. We also
show through simulation experiments that the proposed approaches can be used
for the holistic scheduling of real-time jobs in edge computing systems.
