End-to-End Delay Minimization in Thermally Constrained Distributed Systems

With ever-increasing power densities, managing on-chip temperatures by optimizing mapping and scheduling of tasks is becoming increasingly necessary. We study the minimization of end-to-end delay for thermally constrained scheduling of an application that is specified as a task graph and is executing on parallel processors without speed scaling. We show that task graph scheduling on thermally constrained systems is monotonic, i.e., delaying the execution of a task longer than necessary cannot lead to the early completion of any other task. Using this monotonicity principle, we design the provably optimal schedule for a given mapping, called the JUST schedule. The JUST schedule can be easily implemented using temperature sensors. We then present different thermal-aware modifications to standard mapping heuristics and evaluate them on a large set of problem instances. The experimental results illustrate that with simple thermal-aware modifications, mappings with much smaller end-to-end delay can be identified.