This paper studies realization of relaxed memory consistency models in the network-on-chip based distributed shared memory (DSM) multi-core systems. Within DSM systems, memory consistency is a critical issue since it affects not only the performance but also the correctness of programs. We investigate the scalability of the relaxed consistency models (weak, release consistency) implemented by using transaction counters. Our experimental results compare the average and maximum code, synchronization and data latencies of the two consistency models for various network sizes with regular mesh topologies. The observed latencies rise for both the consistency models as the network size grows. However, the scaling behaviors are different. With the release consistency model these latencies grow significantly slower than with the weak consistency due to better optimization potential by means of overlapping, reordering and program order relaxations. The release consistency improves the performance by 15.6% and 26.5% on average in the code and consistency latencies over the weak consistency model for the specific application, as the system grows from single core to 64 cores. The latency of data transactions grows 2.2 times faster on the average with a weak consistency model than with a release consistency model when the system scales from single core to 64 core