On offline scheduling for time-division multiplexing QKD networks

Quantum key distribution (QKD) combined with quantum-safe encryption algorithms offers a practical path to future-proof communication security. Currently, the BB84 QKD protocol is mature and can be deployed over legacy optical fiber infrastructure using commercial products, with trusted key relaying as a workaround for its distance limitations. However, designing cost-effective QKD networks is essential for widespread adoption by end users and telecom operators (Telcos). To address this challenge, we propose and study a novel, to our knowledge, strategy: periodic time sharing of QKD transceivers. This strategy, especially cost saving at low and medium workloads, allows for generating keys for pairs of nodes at deterministic rates decided a priori. This work presents an offline solution for allocating and scheduling QKD transceivers that are shared by the aforementioned time-division multiplexing (TDM) scheme in a QKD network. We propose a mixed-integer linear programming (MILP)-based scheduling (MBS) method to solve this problem, which is computationally expensive, even for small network topologies. As an alternative, we introduce allocation-driven scheduling (ADS), an algorithm that internally breaks the problem into two steps: allocate first and schedule later. The scheduling can be handled by either a relaxed-MBS (rMBS) or a round-robin scheduling (RRS) approach (ADS-rMBS and ADS-RRS, respectively). Both methods yield results comparable to MBS for small networks. Furthermore, simulations illustrate that both ADS-rMBS and ADS-RRS enable a pay-as-you-grow model, reducing the initial capital expenditure in low-load scenarios. Compared with the non-TDM baseline (i.e., QKD transceivers are non-shared), the cost savings range from 30% to 50%, making QKD deployment more economically viable. Moreover, ADS-rMBS generally outperforms ADS-RRS, but requires a higher runtime, reaching up to 2500 s in large networks. Conversely, ADS-RRS maintains a stable 1 ms runtime across all conditions, making both approaches viable depending on the traffic matrix update interval.