Modelling Mappings of Parallel Programs onto Parallel Architectures with the Prm-net Model

For parallel systems constituted by communicating sequential processes executing on multiprocessor hardware with distributed memory, a Petri net based hierarchically de-composable integrated model, the PRM-net model has been developed. PRM-nets (Program Resource Mapping-nets) provide a modular concept for modelling parallel programs or algorithms with a Petri net like graphical formalism called P-nets. P-nets model (multiple) ows in parallel programs making concurrency, sequential execution, communication and synchro-nisation points explicit. Synthesis rules are given to model complex structures of processes by hierarchically folding process graphs to single transitions to allow investigations at any desired level of abstraction. Modelling the pool of resources (processors, communication media) and their arrangement (connectivity, topology etc.) is also done by a Petri net like formalism: R-nets. Finally the assignmet of the P-net (parallel program) to the R-net (resources) is modelled by arcs with origin in one net and sink in the other net. Performance indices of the system are derived by simulation of the PRM-net, where deterministic ring delays of process transitions are generated at the ring instant. The modelling power of PRM-nets is illustrated in an example modelling the mapping of a neural network onto a distributed memory multiprocessor system and nding the optimal mapping in terms of achievable speedup.