# Journal-First: Minimal-Overlap Centrality for Multi-Gateway Designation in Real-Time TSCH Networks

Miguel Gutiérrez Gaitán, Luís Almeida, Pedro M D'orey, Pedro M Santos, Thomas Watteyne

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Miguel Gutiérrez Gaitán, Luís Almeida, Pedro M D'orey, Pedro M Santos, Thomas Watteyne. Journal-First: Minimal-Overlap Centrality for Multi-Gateway Designation in Real-Time TSCH Networks. RTAS 2025 - Real-Time and Embedded Technology and Applications Symposium, IEEE, May 2025, Irvine, CA, United States. hal-05065435

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# Journal-First: Minimal-Overlap Centrality for Multi-Gateway Designation in Real-Time TSCH Networks<fnref n="1" />

Miguel Gutiérrez Gaitán

Pontificia Universidad Católica de Chile

Santiago, Chile

miguel.gutierrez@uc.cl

Luís Almeida

Universidade do Porto

Porto, Portugal

lda@fe.up.pt

Pedro M. d'Orey

CISTER/ISEP

Porto, Portugal

ore@isep.ipp.pt

Pedro M. Santos

CISTER/ISEP

Porto, Portugal

pss@isep.ipp.pt

Thomas Watteyne

INRIA

Paris, France

thomas.watteyne@inria.fr

**Abstract**—This extended abstract introduces the novel minimal-overlap (MO) centrality metric for gateway designation in low-power real-time wireless sensor networks (WSNs) operating under the time-synchronized channel hopping (TSCH) mode. The MO metric quantifies how much routing paths of active data flows overlap when directed to a candidate gateway—higher overlaps imply more contention and reduced schedulability. By selecting gateways that minimize this overlap at design time, the proposed approach improves real-time performance without requiring additional infrastructure. The method supports both single- and multiple-gateway designation by applying MO centrality globally or within network clusters, respectively. Simulation results under earliest-database-first (EDF) scheduling and shortest-path routing show that our method significantly outperforms classical centrality-based strategies (eigenvector, closeness, betweenness, degree), improving schedulability by up to 40%, and enabling over 2× more schedulable flows compared to worst-case gateway designation.

## I. INTRODUCTION

Low-power wireless sensor networks (WSNs), widely used in Industrial Internet-of-Things (IoT) applications, play a central role in enabling real-time communication with cost-effective and flexible infrastructure. These networks often operate under the time-synchronized channel hopping (TSCH) mode of IEEE 802.15.4e, which provides enhanced reliability and predictability through slot-based scheduling and channel diversity [2]. In such systems, sensor and actuator nodes generate periodic data flows subject to strict deadline constraints, which must be transmitted to gateway nodes responsible for collecting and forwarding information to higher layers.

While considerable research has focused on optimizing scheduling and routing mechanisms to meet real-time requirements, the role of gateway designation—i.e., selecting which nodes serve as gateways—has received less attention. Poorly chosen gateways can result in excessive traffic overlap, increased contention, and degraded schedulability.

In this work, we address the problem of gateway designation at the system design stage, where the network topology and flow information are assumed known. We propose a novel centrality metric, termed minimal-overlap (MO) centrality, that quantifies the degree of path overlap among active flows when routed to a candidate gateway. Unlike classical centrality metrics that rely solely on topological properties (e.g., degree, betweenness), MO centrality captures flow-induced interference. To our knowledge, this is the first use of a flow-informed centrality metric explicitly designed to improve traffic schedulability in TSCH WSNs.

This approach is applicable to both single- and multi-gateway scenarios. In the latter case, we combine MO centrality with spectral clustering to partition the network and designate one gateway per cluster. Simulation results show significant improvements in schedulability over classical centrality-based approaches, validating the effectiveness of minimizing route overlaps as a design principle.

## II. MINIMAL-OVERLAP CENTRALITY FOR GATEWAY DESIGNATION

In TSCH-based WSNs, flow paths may traverse overlapping sets of intermediate nodes before reaching their destination. These overlaps create transmission conflicts and contention for shared links, degrading the network's ability to deliver messages within deadline bounds. We propose a graph-theoretic formulation that quantifies this overlap and enables the designation of gateways that minimize it.

### A. Minimal-Overlap Centrality (Single-Gateway Case)

Let the network be modeled as an undirected graph $G = (V, E)$, where $V$ is the set of nodes and $E$ is the set of wireless links. Each data flow $f_i$ originates at a source node and is routed via shortest paths toward a designated gateway node $v_q \in V$. For a given node $v_q$, we define the minimal-overlap (MO) centrality as:

$$MO(v_q) = \frac{1}{\sum_{i \neq j} \Delta_{i,j}(v_q) + 1}, \quad (1)$$

<footnote n="1">¹This work is an extended abstract of the journal article: M. Gutiérrez Gaitán et al., “Minimal-Overlap Centrality for Multi-Gateway Designation in Real-Time TSCH Networks,” *ACM Transactions on Embedded Computing Systems*, vol. 23, no. 1, Article 9, Jan. 2024. DOI: 10.1145/3610583 [1].</footnote>
<figure><img src="image_2.png" /><figcaption>(a) A graphical representation of the minimal-overlap (b) A toy example of the centrality-driven multi-gateway designation framework in [3] for k = 3 clusters/gateways.</figcaption></figure>

<caption>Fig. 1: Overview of the MO centrality framework: (a) single-gateway designation reduces routing path overlap based on flow-aware centrality; (b) spectral clustering partitions the network to enable scalable multi-gateway designation.</caption>

where $\Delta_{i,j}^{(v_q)}$ represents the number of shared hops in the routing paths of flows $f_i$ and $f_j$ when both are directed to node $v_q$. The summation accounts for all pairs of flows, and the +1 prevents division by zero. A higher MO score indicates lower cumulative overlap, and hence a better candidate gateway.

This computation is performed at design time, assuming that flow periodicity, deadlines, and network topology are known—a common case in industrial WSNs. The node with the highest MO score is selected as the gateway. Figure 1a illustrates this idea: flows directed to a gateway with low MO score lead to overlapping paths, whereas routing them to a high-MO node (GW') yields more disjoint paths and lower contention.

## B. Multi-Gateway Designation via Clustering

To generalize the method to multiple gateways, we partition the network into $k$ clusters using spectral clustering based on the normalized Laplacian of the adjacency matrix of $G$. Each cluster is treated as a subgraph, and MO centrality is computed locally. The node with the highest local MO score in each cluster is designated as the cluster's gateway.

This clustering-based approach ensures that routing remains localized within clusters, reducing contention and overlap. It is especially effective in large or high-density networks, and it does not require node position information. As shown in Figure 1b, the multi-gateway designation is based on cluster-wise topology and centrality, providing a scalable, position-agnostic framework for real-time WSN design.

## III. EVALUATION SUMMARY

Figures 1a and 1b illustrate the core ideas of MO centrality in both single- and multi-gateway contexts. To evaluate its effectiveness, we conducted simulations on synthetic TSCH network topologies with varying node densities and flow loads. All experiments assume shortest-path routing and earliest-deadline-first (EDF) scheduling.

In single-gateway scenarios, MO designation improves schedulability by up to 40% compared to classical metrics such as degree, closeness, betweenness, and eigenvector centrality. In multi-gateway configurations, combining spectral clustering with MO centrality enables over 2× more flows to meet deadlines compared to random or worst-case gateway choices.

These results confirm that minimizing flow path overlap using MO centrality is a judicious and effective strategy for enhancing real-time performance in TSCH-based wireless sensor networks.

## IV. CONCLUSION

This work presents a centralized framework for gateway designation in TSCH wireless sensor networks using a novel minimal-overlap (MO) centrality metric. The metric captures flow path overlap to better reflect contention in the network and guides the selection of gateways that improve schedulability. The approach applies to both single- and multi-gateway cases, using spectral clustering for the latter. Evaluation results show that MO centrality significantly outperforms classical graph metrics by enabling more flows to meet their deadlines. These findings support the use of flow-aware gateway designation as a design-time strategy for improving the real-time performance of industrial WSNs. Future work includes integrating MO centrality with joint routing and scheduling strategies, as a preliminary step explored in [4], to form a unified co-design framework for real-time TSCH networks.

## ACKNOWLEDGMENT

This document was issued within the frame and for the purpose of the OpenSwarm project. This project has received funding from the European Union's Horizon Europe Framework Programme under Grant Agreement No. 101093046. Views and opinions expressed are however those of the author(s) only and the European Commission is not responsible for any use that may be made of the information it contains. The work also received funding by the FONDECYT Iniciación project No. 11241221 and the Competence Center START 4.0 under the Safepath project (CUP: J57H24000330004); also by the CISTER Research Unit (UIDP/ UIDB/04234/2020) through FCT/MCTES (Portuguese Foundation for Science and Technology) National Funds.

## REFERENCES

[1] M. G. Gaitán, L. Almeida, P. M. D'orey, P. M. Santos, and T. Watteyne, "Minimal-overlap centrality for multi-gateway designation in real-time TSCH networks," *ACM Transactions on Embedded Computing Systems*, vol. 23, no. 1, pp. 1-17, 2024.

[2] T. Watteyne, J. Weiss, L. Doherty, and J. Simon, "Industrial ieee802.15.4e networks: Performance and trade-offs," in *2015 IEEE International Conference on Communications (ICC)*. IEEE, 2015, pp. 604-609.

[3] M. G. Gaitán, D. Dujovne, J. Zuñiga, A. Figueroa, and L. Almeida, "Multi-gateway designation for real-time tsch networks using spectral clustering and centrality," *IEEE Embedded Systems Letters*, 2022.

[4] M. G. Gaitán, L. Almeida, T. Watteyne, P. M. D'Orey, P. M. Santos, and D. Dujovne, "Joint scheduling, routing and gateway designation in real-time tsch networks," in *RTNS 2022-30th International Conference on Real-Time Networks and Systems*, 2022.