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Deterministic IP (DIP) networking is a promising technique that can provide delay-bounded transmission in large-scale networks. Nevertheless, DIP faces several challenges in the mixed traffic scenarios, including (i) the capability of ultra-low latency communications, (ii) the simultaneous satisfaction of diverse QoS requirements, and (iii) the network efficiency. The problems are more formidable in the dynamic surroundings without prior knowledge of traffic demands. To address the above-mentioned issues, this paper designs a flexible DIP (FDIP) network. In the proposed network, we classify the queues at the output port into multiple groups. Each group operates with different cycle lengths. FDIP can assign the time-sensitive flows with different groups, hence delivering diverse QoS requirements, simultaneously. The ultra-low latency communication can be achieved by specific groups with short cycle lengths. Moreover, the flexible scheduling with diverse cycle lengths improves resource utilization, hence increasing the throughput (i.e., the number of acceptable time-sensitive flows). We formulate a throughput maximization problem that jointly considers the admission control, transmission path selection, and cycle length assignment. A branch and bound (BnB)-based heuristic is developed. Simulation results show that the proposed FDIP significantly outperforms the standard DIP in terms of both the throughput and the latency guarantees.