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.

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