  Stochastic Processing Networks (SPNs) can be used to model communication
networks, manufacturing systems, service systems, etc. We consider a real-time
SPN where tasks generate jobs with strict deadlines according to their traffic
patterns. Each job requires the concurrent usage of some resources to be
processed. The processing time of a job may be stochastic, and may not be known
until the job completes. Finally, each task may require that some portion of
its tasks to be completed on time.
  In this paper, we study the problem of verifying whether it is feasible to
fulfill the requirements of tasks, and of designing scheduling policies that
actually fulfill the requirements. We first address these problems for systems
where there is only one resource. Such systems are analog to ones studied in a
previous work, and, similar to the previous work, we can develop sharp
conditions for feasibility and scheduling policy that is feasibility-optimal.
We then study systems with two resources where there are jobs that require both
resources to be processed. We show that there is a reduction method that turns
systems with two resources into equivalent single-resource systems. Based on
this method, we can also derive sharp feasibility conditions and
feasibility-optimal scheduling policies for systems with two resources.
