DRL-based progressive recovery for quantum-key-distribution networks

Mengyao Li; Qiaolun Zhang; Alberto Gatto; Stefano Bregni; Giacomo Verticale; Massimo Tornatore

doi:10.1364/JOCN.526014

Journal of Optical Communications and Networking
Vol. 16,
Issue 9,
pp. E36-E47
(2024)
•https://doi.org/10.1364/JOCN.526014

DRL-based progressive recovery for quantum-key-distribution networks

Mengyao Li, Qiaolun Zhang, Alberto Gatto, Stefano Bregni, Giacomo Verticale, and Massimo Tornatore

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Mengyao Li, Qiaolun Zhang, Alberto Gatto, Stefano Bregni, Giacomo Verticale, and Massimo Tornatore, "DRL-based progressive recovery for quantum-key-distribution networks," J. Opt. Commun. Netw. 16, E36-E47 (2024)

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About this Article
History
- Original Manuscript: April 10, 2024
- Revised Manuscript: June 28, 2024
- Manuscript Accepted: July 16, 2024
- Published: August 14, 2024
Virtual Issues
Journal of Optical Communications and Networking Optical Networks and Systems (ONS) Syposium at GLOBECOM 2023 (2024)

Abstract

With progressive network recovery, operators restore network connectivity after massive failures along multiple stages, by identifying the optimal sequence of repair actions to maximize carried live traffic. Motivated by the initial deployments of quantum-key-distribution (QKD) over optical networks appearing in several locations worldwide, in this work we model and solve the progressive QKD network recovery (PQNR) problem in QKD networks to accelerate the recovery after failures. We formulate an integer linear programming (ILP) model to optimize the achievable accumulative key rates during recovery for four different QKD network architectures, considering different capabilities of using trusted relay and optical bypass. Due to the computational limitations of the ILP model, we propose a deep reinforcement learning (DRL) algorithm based on a twin delayed deep deterministic policy gradients (TD3) framework to solve the PQNR problem for large-scale topologies. Simulation results show that our proposed algorithm approaches well compared to the optimal solution and outperforms several baseline algorithms. Moreover, using optical bypass jointly with trusted relay can improve the performance in terms of the key rate by 14% and 18% compared to the cases where only optical bypass and only trusted relay are applied, respectively.

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Reach (km)	10	20	30	40	50
Key rate (kb/s)	23	13	7	3.5	1.9

Set	Description
$N_{p}$	Set of QKD nodes in the network
$E_{p}$	Set of physical links in the network
$E_{a}$	Set of links in the fully connected graph
$E_{f}$	Set of failed links in the network
$N_{f}$	Set of failed nodes in the network
$P$	Set of node pairs for paths in the topology
$W$	Set of channels
$T$	Set of stages
$Φ$	Set of physical routes that use the same end nodes as auxiliary link $e \in E_{a}$
$D$	Set of requests
$S^{+} (i)$	Set of outgoing links from node $i$
$S^{-} (i)$	Set of incoming links for node $i$

Parameter	Description
$O_{n}$	Integer, number of QKD modules on node $n$
$h_{ϕ, e}$	Binary, equals 1 if link $e \in E_{p}$ in route $ϕ$
$k_{d}$	Integer, the required key rate of request $d \in D$
$l_{ϕ}$	Integer, the key rate can be supplied by route $ϕ$
$α_{d}$	Real, the weight of request $d \in D$
$υ_{e}$	Integer, recovery resources needed by link $e \in E_{p}$
$ω_{n}$	Integer, recovery resources needed by node $n \in N_{p}$
$δ$	Integer, node recovery resources available at each stage
$ϵ$	Integer, link recovery resources available at each stage
$θ$	Integer, the number of seconds for one stage

Variable	Description
$f_{e, w}^{p, t}$	Binary, equals 1 if quantum channel $w$ on link $e \in E_{a}$ is allocated for the path between node pair $p$ at stage $t$
$x_{e, w}^{p, t, ϕ}$	Binary, equals 1 if route $ϕ$ is selected for connection between the end nodes of link $e \in E_{a}$ in the QKD path between node pair $p$ at channel $w$ at stage $t$
$p_{e, w}^{p, t}$	Binary, equals 1 if link $e \in E_{a}$ used the quantum channel between node pair $p \in P$ on channel $w \in W$ at stage $t \in T$
$q_{e, w}^{p, t}$	Binary, equals 1 if path $p$ contains auxiliary link $e \in E_{a}$ based on a QKP on channel $w$ at stage $t$
$u_{p, w}^{t}$	Integer, key rate generated for path $p$ on channel $w$ at stage $t$
$z_{p, w}^{t}$	Binary, equals 1 if the QKD path between node pair $p \in P$ uses quantum channel $w \in W$ at stage $t$
$B_{i}^{t}$	Binary, equals 1 if node $i \in N_{p}$ works at stage $t$
$C_{e}^{t}$	Binary equals 1 if link $e \in E_{a}$ works at stage $t$
$B_{i (e)}^{t}$	Binary equals 1 if end node $i \in N_{p}$ of link $e \in E_{p}$ works at stage $t$
$g_{p}^{t}$	Integer, stored keys in a QKP for path between node pair $p$ at stage $t$
$y_{d}^{t}$	Binary equals 1 if request $d$ is served at stage $t$
$γ_{e, w}^{p, t}$	Integer, key rate provided from a QKP for link $e$ in the QKD path between node pair $p$ in channel $w$
$η_{t}$	Integer, available recovery resources for links at stage $t$
$β_{t}$	Integer, available recovery resources for nodes at stage $t$

Reach (km)	10	20	30	40	50
Key rate (kb/s)	23	13	7	3.5	1.9

Abstract

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Equations (20)

Journal of Optical Communications and Networking