  In some important application areas of hard real-time systems, preemptive
sporadic tasks with harmonic periods and constraint deadlines running upon a
uni-processor platform play an important role. We propose a new algorithm for
determining the exact worst-case response time for a task that has a lower
computational complexity (linear in the number of tasks) than the known
algorithm developed for the same system class. We also allow the task
executions to start delayed due to release jitter if they are within certain
value ranges. For checking if these constraints are met we define a constraint
programming problem that has a special structure and can be solved with
heuristic components in a time that is linear in the task number. If the check
determines the admissibility of the jitter values, the linear time algorithm
can be used to determine the worst-case response time also for jitter-aware
systems.
