Shared-memory concurrency is the prevalent paradigm used for developing parallel applications targeted towards small- and middle-sized machines, but experience has shown that it is hard to use. This is largely caused by synchronization primitives which are low-level, inherently nondeterministic, and, consequently, non-intuitive to use. In this paper, we present the Nornir run-time system. Nornir is comparable to well-known frameworks like MapReduce and Dryad, but has additional support for process structures containing cycles. It is based on the formalism of Kahn process networks, which we deem as a simple and deterministic alternative to shared-memory concurrency. Experiments with real and synthetic benchmarks on up to 8 CPUs show that performance in most cases improves almost linearly with the number of CPUs, when not limited by data dependencies.