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Network on Chip (NoC) interconnects are some of the most challenging-to-analyse components of multiprocessor platforms. This is primarily due to the following two reasons: (i) NoCs contain numerous shared resources (e.g. routers, links), and (ii) the network traffic often concurrently traverses multiple of those resources. Consequently, complex contention scenarios among traffic flows might occur, some of the important implications being significant performance limitations, and difficulties when performing the real-time analysis. In this work, we propose a slot-based transmission protocol for NoCs (called SBT-NoC), and an accompanying analysis method for deriving worst-case traffic latencies. The cornerstone of SBT-NoC is a contention-less slot-based transmission, arbitrated via a protocol running on a dedicated network medium. The main advantage of SBT-NoC is that, while not requiring any sophisticated hardware support (e.g. virtual channels, a flit-level arbitration), it makes NoCs amenable to real-time analysis and guarantees bounded low latencies of high-priority time-critical flows, which is a sine qua non for the inclusion of NoCs, and multiprocessors in general, in the real-time domain. The experimental evaluation, including both synthetic workloads and a use-case of an autonomous driving vehicle application, reveals that SBT-NoC offers a plethora of configuration opportunities, which makes it applicable to a wide range of diverse traffic workloads.