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Three-dimensional network-on-chip (3D NoC) has been proposed to solve the complex on-chip communication issues in future 3D multicore systems. However, the thermal problems of 3D NoC are more serious than 2D NoC due to chip stacking. To keep the temperature below a certain thermal limit, the thermal emergent routers are usually throttled. Then, the topology of 3D NoC becomes a Nonstationary Irregular Mesh (NSI-Mesh). To ensure the successful packet delivery in the NSI-Mesh, some routing algorithms had been proposed in the previous works. However, the network still suffers from extremely traffic imbalance among lateral and vertical logic layer. In this paper, we propose a Topology Aware Adaptive Routing (TAAR) to balance the traffic load for NSI-Mesh in 3D NoC. TAAR has three routing modes, which can be dynamically adjusted based on the topology status of the routing path. In addition to increasing routing flexibility, the TAAR also increases both vertical and lateral path diversity to balance the traffic load. Compared with the related adaptive routing methods, the experimental results show that the proposed TAAR can reduce 19 to 295 percent traffic loads in the bottom logic layer and improve around 7.7 to 380 percent network throughput. According to our proposed VLSI architecture, the TAAR only needs less than 24.8 percent hardware overhead compared with the previous works.