A Mixed Criticality System (MCS) combines real-time software tasks with different criticality levels. In a MCS, the criticality level specifies the level of assurance against system failure. For high-critical flows of messages, it is imperative to meet deadlines, otherwise the whole system might fail, leading to catastrophic results, like, loss of life or serious damage to the environment. In contrast, low-critical flows may tolerate some delays. Furthermore, in MCS, flow performances such as the Worst Case Communication Time (WCCT) may vary depending on the criticality level of the applications. Then, execution platforms must provide different operating modes for applications with different levels of criticality. To conclude, in Network-On-Chip (NoC), sharing resources between communication flows can lead to unpredictable latencies and subsequently turns the implementation of MCS in many-core architectures challenging. In this article, we propose and evaluate a new NoC router to support MCS based on an accurate WCCT analysis for high-critical flows. The proposed router, called DAS (Double Arbiter and Switching router), jointly uses Wormhole and Store And Forward communication techniques for low and high-critical flows respectively. It ensures that high-critical flows meet their deadlines while maximizing the bandwidth remaining for the low-critical flows. We also propose a new method for high-critical communication time analysis, applied to Store And Forward switching mode with virtual channels. For low-critical flows communication time analysis, we adapt an existing wormhole communication time analysis with share policy to our context. The second contribution of this paper is a multi-abstraction level evaluation of DAS. We evaluate the communication time of flows, the system mode change, the cost and 4 properties of DAS. Simulations with a cycle-accurate SystemC NoC simulator show that, with a 15% network use rate, the communication delay of high-critical flows is reduced by 80% while communication delay of low-critical flow is increased by 18% compared to solutions based on routers with multiple virtual channels. For 10% of network interferences, using system mode change, DAS reduces the high-critical communication delays about 66%. We synthesize our router with a 28nm SOI technology and show that the size overhead is limited of 2.5% compared to the solution based on virtual channel router. Finally, we applied model checking verification techniques to automatically prove several DAS properties required by critical systems designers.