  Task graph scheduling is a relevant problem in computer science with
application to diverse real world domains. Task graph scheduling suffers from a
combinatorial explosion and thus finding optimal schedulers is a difficult
task.
  In this paper we present a methodology for computing near-optimal preemptive
and non-preemptive schedulers for task graphs. The task graph scheduling
problem is reduced to location reachability via the fastest path in Priced
Timed Automata (PTA) and Priced Timed Markov Decision Processes (PTMDP).
Additionally, we explore the effect of using chains to reduce the computation
time for finding schedules.
  We have implemented our models in UPPAAL CORA and UPPAAL STRATEGO. We conduct
an exhaustive experimental evaluation where we compare our resulting schedules
with the best-known schedules of a state of the art tool. A significant number
of our resulting schedules are shown to be shorter than or equal to the
best-known schedules.
