Modern vehicles are embedding increasing levels of automation, connectivity, and intelligence, which require advanced in-vehicle networks and computational platforms to support the dependability and deterministic requirements of critical in-vehicle functions. To this end, the automotive industry is shifting towards software-defined vehicles (SDVs) and zonal E/E architectures with centralized computing nodes. Realizing the full potential of these new architectures requires an efficient management of the in-vehicle’s computational workload. In this context, this paper introduces a deterministic task scheduling approach for in-vehicle networks (IVN), and demonstrates that it can better guarantee deterministic service levels than alternative approaches based on the shortest path or the objective to minimize task execution time. Our evaluation also demonstrates that a deterministic task scheduling can satisfactorily support increasing in-vehicle computational workloads and tasks, and achieve a more balanced workload and resource utilization across the IVN. These gains are validated across a variety of IVN topologies, and in hybrid wireless-wired IVN implementations, where a gradual introduction of wireless offers increased in-vehicle connectivity diversity.