## 2 Problem Statement  
Several researchers have proposed various approaches and solutions for quantum network construction. In terms of the physical layer and communication, [PERSON] et al. proposed an experimental QKD system that can tolerate channel losses exceeding 140 dB and achieve a secure distance of 833.8 km, setting a new record for fiber-based QKD [18]. [PERSON] and [PERSON] et al. presented an experimental system that realized DI-QKD based on entangled states of radium atoms prepared and analyzed at a distance of 400 m within a building, demonstrating the capability of generating keys in the system [19].  
Researchers in the academic community have also actively participated in related studies in the field of networking. [PERSON] and [PERSON] proposed a three-node remote quantum network based on the photonic coupling of solid-state spin qubits [20]. [PERSON] and [PERSON] et al. explored a QSDC network based on time-energy entanglement and frequency conversion, which included a fully connected QSDC network with 15 users. Experimental results demonstrated the feasibility of this QSDC network, laying a foundation for satellite-based remote QSDC implementation [21]. [PERSON] et al. presented a fully connected quantum communication metropolitan area network without active switching or trusted nodes. This network can easily be scaled to accommodate more users while minimizing the required infrastructure and hardware, thus reducing network construction costs [22]. [PERSON] and [PERSON] et al. investigated the deployment of QKD with hybrid trusted/untrusted relay nodes based on an optical backbone network. They designed an integer linear programming model and a heuristic algorithm to optimize deployment costs while maintaining a higher level of security compared to traditional point-to-point QKD protocols with only trusted relay nodes [23]. Furthermore, [PERSON] authored a review article to introduce the fundamental knowledge of quantum key distribution (QKD) and review the development of QKD networks as well as their implementation in practice. Subsequently, the general architecture, components, interfaces, and protocols of QKD networks were described, and relevant physical layer and network layer solutions were summarized, providing guidance for the design of QKD networks [24].  
In network research, routing is a critical problem. [PERSON] and [PERSON] investigated the performance of balancing the allocation of quantum key resources in optical data center networks using Quantum Key Distribution (QKD). In order to effectively utilize quantum key resources, they proposed three efficient load balancing routing, wavelength, and time-slot allocation (LB-RWTA) methods, which have high efficacy in quantum key resource allocation and network performance management [25]. [PERSON] and [PERSON] et al. studied the key routing in different typical network topologies under partially trusted relay scenarios and proposed a secret key distribution (SKP)-based collaborative routing algorithm for finding the optimal key relay routing path. The experimental results show that compared with traditional schemes based on trusted relays, the SKP-CR algorithm has significant advantages in terms of a key distribution success rate in a mesh topology [26].  
This article presents a novel approach that differs from traditional network schemes utilizing a single quantum key distribution (QKD) protocol. Instead, it proposes a hybrid QKD network model consisting of two links, namely the BB84 protocol and the MDI-QKD protocol. Furthermore, this approach establishes a unique linear programming mathematical model based on the key bit generation characteristics of BB84 and MDI-QKD. A dynamic routing algorithm is designed based on the remaining key quantities at each node, and a new queuing theory for encrypted data packets is integrated to alleviate the overall congestion in the quantum network. This approach aims to reduce the packet loss rate and improve quantum key utilization.