  The scheduling of task graphs with communication delays has been extensively
studied. Recently, new results for the common sub-case of fork-join shaped task
graphs were published, including an EPTAS and polynomial algorithms for special
cases. These new results modelled the target architecture to consist of
homogeneous processors. However, forms of heterogeneity become more and more
common in contemporary parallel systems, such as CPU--accelerator systems, with
their two types of resources. In this work, we study the scheduling of
fork-join task graphs with communication delays, which is representative of
highly parallel workloads, onto heterogeneous systems of related processors. We
present an EPAS, and some polynomial time algorithms for special cases, such as
with equal processing costs or unlimited resources. Lastly, we briefly look at
the above described case of two resource-types and its implications. It is
interesting to note, that all results here also apply to scheduling independent
tasks with release times and deadlines.
