The multi-core systems are usually implemented on homogeneous or heterogeneous cores, in order to design the better NOC (network on chip), it must consider the performance, scalability, simplifies hardware design and arbitration strategy at the on chip network. The routers are designed with circuit-switched network, circuit switching is asynchronous circuits and routers have no queuing (buffering), therefore, it is simple and efficient in implementation. Synchronous circuit is network with a clock source, but the distributing global clock has many problems such as power consumption, increasing the area and Clock skew. Ring topology with multi-transaction bus architecture. It could make multiple packets to access the bus at the same time, so that the multi-transaction bus architecture is better to get more throughputs. When the number of cores increase, the central arbiter circuit is more complexity, this thesis presents an SAP (self-adjusting priority) schedule that can fairly adjust priorities of each component by appropriately exchanging weighting at distributed arbiter. When numerous requests encounter contention on a network, a winner owning the highest priority will exchange its priority with the lowest priority of these requests. This principle guarantees that winners will decreased the opportunity of incurring network at the next time. In opposition, these losers can obtain the higher priority than that of the original. Therefore, the proposed scheme not only offers fair strategy, but also simplifies hardware design.