# Delays in mempool - based blockchains under realistic conditions: case of narwhal and droneVet application

Khouloud Hwerbi, Ichrak Amdouni, Cédric Adjih, Leila Azouz Saidane, Anis Laouiti

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Khouloud Hwerbi, Ichrak Amdouni, Cédric Adjih, Leila Azouz Saidane, Anis Laouiti. Delays in mempool - based blockchains under realistic conditions: case of narwhal and droneVet application. Annals of Telecommunications - annales des télécommunications, 2026, 10.1007/s12243-026-01153-0. hal-05472747

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Delays in Mempool - based Blockchains under Realistic
Conditions: case of Narwhal and DroneVet Application

Khouloud Hwerbi (Corresponding author), Email Address of the Corresponding Author: khouloud.hwerbi@ensi-uma.tn<sup>a,b</sup>, Ichrak Amdouni<sup>a</sup>, Cédric Adjih<sup>c</sup>, Leila Azouz Saidane<sup>a</sup>, Anis Laouiti<sup>b</sup>

<sup>a</sup>ENSI, University of Manouba, Tunis, Tunisia, name.surname@ensi-uma.tn

<sup>b</sup>Telecom SudParis, Institut Polytechnique de Paris, France, name.surname@telecom-sudparis.eu

<sup>c</sup>Inria, France, name.surname@inria.fr

**Abstract**

This study focuses on modeling and analyzing the delay in consensus protocols within mempool-based blockchains. In such systems, unconfirmed transactions are temporarily stored in a memory pool (mempool) before being selected, ordered, and committed to blocks by the consensus mechanism.

In a previous work, we designed a generic model of a mempool-based blockchain, capturing core protocol behaviors. The model involves *n* nodes (potentially including Byzantine nodes) that exchange blocks and await one or two quorums of acknowledgments before producing new blocks and advancing to the next round. Based on this framework, we derived two Markov chains to characterize round durations and validated them through simulations.

In this paper, we extend that work in three key directions: (1) We focus on Narwhal, a specific mempool protocol, describing its operations and its round duration formula. (2) We introduce DroneVet, an application leveraging UAVs to monitor livestock health and shares collected data across stakeholders via blockchain technology. DroneVet is implemented using Narwhal and includes realistic environmental constraints such as packet loss, network latency, and UAV-energy limitation. (3) We develop DroneVet and compare its round duration with the theoretical round duration of Narwhal.

By taking into account the environmental factors specific to agricultural deployments, this work highlights how such conditions impact the reliability and responsiveness of blockchain-based systems. Our findings provide valuable insights for deploying secure, resilient, and transparent blockchain solutions in rural settings to support reliable livestock monitoring.

**Keywords:** Blockchain, Delay Analysis, Markov Chain, Exponential Distribution, Simulation, realistic network conditions, Narwhal, DroneVet.
# Contents

1 Introduction 3

2 State of the Art 4

<table><tr><td>2.1 Mempool Protocol</td><td>4</td></tr><tr><td>2.2 Blockchain Integration with UAVs</td><td>5</td></tr><tr><td>2.3 Blockchain and UAVs in Agriculture</td><td>5</td></tr><tr><td>2.4 Blockchain Performance Evaluation</td><td>6</td></tr></table>

3 Delay Analysis of Mempool protocol with Markov Chain 6

<table><tr><td>3.1 System Model</td><td>6</td></tr><tr><td>3.2 Notations and Assumptions</td><td>7</td></tr><tr><td>3.3 Mempool Protocol with one quorum of messages</td><td>7</td></tr><tr><td>3.4 Mempool Protocol with two quorums of messages</td><td>9</td></tr><tr><td>3.5 Simulation Results</td><td>11</td></tr></table>

4 Case Study of a Mempool Protocol: Narwhal Protocol 13

<table><tr><td>4.1 Overview</td><td>13</td></tr><tr><td>4.2 Narwhal Protocol Messages</td><td>13</td></tr><tr><td>4.3 Protocol Workflow</td><td>14</td></tr><tr><td>4.4 Analysis of Data Dissemination delays in Narwhal</td><td>14</td></tr></table>

5 DroneVet Application: Blockchain and UAV for Cattle Health Monitoring 15

<table><tr><td>5.1 Motivation and System Overview</td><td>15</td></tr><tr><td>5.2 Architecture and System Workflow</td><td>16</td></tr></table>

6 DroneVet under Realistic Network Conditions 17

<table><tr><td>6.1 UAV-based Challenges</td><td>17</td></tr><tr><td>6.2 Network-based Challenges</td><td>18</td></tr><tr><td>6.2.1 Packet Loss and Reliability</td><td>18</td></tr><tr><td>6.2.2 Signal Propagation Effects</td><td>18</td></tr></table>

7 Simulation of DroneVet under Realistic Conditions 18

<table><tr><td>7.1 Application Scenario</td><td>19</td></tr><tr><td>7.2 Impact of Network Latency Variability</td><td>19</td></tr><tr><td>7.2.1 Simulation Scenario and Setup</td><td>19</td></tr><tr><td>7.2.2 Simulation Results</td><td>20</td></tr><tr><td>7.3 Impact of Packet Loss</td><td>21</td></tr><tr><td>7.3.1 Simulation Scenario and Setup</td><td>21</td></tr><tr><td>7.3.2 Simulation Results</td><td>22</td></tr><tr><td>7.4 Impact of UAV Energy Constraints and Node Failures</td><td>23</td></tr><tr><td>7.4.1 Simulation Scenario and Setup</td><td>23</td></tr><tr><td>7.4.2 Simulation Results</td><td>25</td></tr><tr><td>7.5 Discussion: Importance of Round Duration Evaluation</td><td>25</td></tr></table>

8 Conclusion 26

9 Author Contributions 27
# 1. Introduction

A deep understanding and accurate modeling of delay in blockchain consensus protocols is essential to enhance their scalability, responsiveness, and applicability in real-world scenarios. Consensus delays influence not only system throughput and user experience but also the network's ability to maintain synchronization, especially under dynamic or resource constrained conditions. Although considerable research has been devoted to delay analysis in general consensus mechanisms, increasing attention is now being directed toward specific architectures most notably, mempool-based blockchains which exhibit unique transaction propagation behaviors and round coordination dynamics that merit dedicated investigation.

Mempool-based blockchains temporarily store unconfirmed transactions in a memory pool (mempool) before they are selected, ordered, and added to blocks by the consensus protocol. The efficiency of the mempool in disseminating and aggregating transaction blocks plays a vital role in determining the overall delay of the blockchain. This is especially relevant in systems where blocks are propagated in rounds and nodes must wait for a quorum of acknowledgments before proceeding. One prominent example is Narwhal [12], a high-performance mempool protocol used in the Sui blockchain, which we study in this work.

In parallel, blockchain technology is showing increasing promise in the agricultural domain. It enables secure, transparent, and tamper-proof data management that is essential for trust and automation in agricultural supply chains [3]. In particular, blockchain has been integrated with UAVs and IoT systems to improve traceability, automate decisions, and monitor livestock health [21]. These developments align with the goals of Agriculture 5.0, where advanced technologies are used to enhance sustainability and efficiency in farming operations [34] [22] [53].

As a concrete example, we consider the DroneVet application [21], which uses UAVs to collect physiological data (e.g., temperature, activity) from IoT-equipped livestock. This data is recorded and shared on a blockchain with stakeholders such as farmers, veterinary services, and drone operators. DroneVet benefits from blockchain's transparency and security guarantees, enabling coordinated and trustworthy monitoring. However, the performance of the underlying blockchain system—particularly its delay behavior—is crucial for the application's responsiveness and practical deployment.

In prior work, we established a generic analytical model for mempool-based blockchains involving n nodes (potentially Byzantine), where nodes exchange blocks and wait for either one or two quorums of block acknowledgments before generating new blocks. These blocks form a Directed Acyclic Graph (DAG), with nodes moving to new rounds based on quorum conditions. We modeled round durations using two Markov chains and validated our results through simulation, confirming the accuracy of our probabilistic delay estimations.

In this paper, we build upon that foundation by applying our model to the Narwhal protocol. We begin by describing Narwhal and recalling the theoretical round duration derived from our Markov-based analysis. We then integrate Narwhal into the DroneVet application and simulate its operation in realistic agricultural environments characterized by network latency, mobility, and packet loss [18] [27]. These conditions reflect common constraints in UAV-based systems, including intermittent connectivity, changing topology, and energy limitations.

Finally, we evaluate the round duration of the DroneVet system in simulation and compare it with our theoretical predictions. This comparison enables us to assess how
well the modeled behavior aligns with real-world performance under environmental con-
straints.

By conducting this delay analysis within a concrete agricultural context, our study bridges theoretical modeling and practical deployment. It provides valuable insights for adapting blockchain technologies to resource-constrained and infrastructure-limited environments, ultimately supporting reliable, secure, and efficient livestock health monitoring in smart agriculture.

By integrating UAVs and blockchain technology, our study enhances the understand-
ing of blockchain performance under realistic conditions, paving the way for more resilient
and efficient solutions particularly in smart agriculture.

Section 2 presents the state of the art, covering mempool protocols, Blockchain and UAV integration, blockchain use in agriculture, and existing performance evaluation methods. Section 3 revisits our delay analysis model for a mempool protocol using Markov chains. Section 4 focuses on the Narwhal-mempool protocol as a case study. Section 5 introduces the DroneVet application for livestock health monitoring. In Section 6, we discuss realistic agricultural challenges including latency, packet loss, and energy limitation. Section 7 presents simulation results of DroneVet under these conditions. Finally, Section 8 concludes the paper and outlines future directions.

## 2. State of the Art

This section reviews recent advancements in blockchain research relevant to our study, focusing on three main domains: mempool protocol architectures, blockchain integration with UAV systems, and blockchain performance evaluation methodologies. These works collectively form the foundation for our study on how environmental constraints in agricultural UAV deployments influence blockchain consensus performance.

Blockchain has evolved significantly over the past few years, extending beyond cryp-
tocurrency applications to support decentralized decision-making and data integrity in
various domains. Recent studies highlight its adaptability and potential across sectors.
For instance, authors in [2] propose an efficient blockchain framework for decentralized
Attribute-Based Access Control (ABAC) policy decision points, improving scalability
and trust in distributed systems. Similarly, in this paper authors [1] assess the viabil-
ity of blockchain technology in renewable energy supply chains, demonstrating its role
in enhancing transparency and coordination among stakeholders. These recent works
illustrate the growing relevance of blockchain as a foundational technology for secure and
decentralized operations, motivating its adoption in UAV-based agricultural systems.

2.1. *Mempool Protocol*

The mempool is a fundamental component of blockchain networks, serving as a temporary repository where unconfirmed transactions are stored before they are selected, ordered, and added to blocks by the consensus protocol.

Efficient mempool design is a key to enhance blockchain scalability, throughput, and
resilience against attacks.

Gai et al. [16] propose a robust and shared mempool structure aimed at improving transaction propagation and reducing latency in consensus mechanisms. By treating the mempool as a shared resource among nodes, the proposed design improves synchronization and accelerates transaction finality.
Security aspects have also been extensively explored. Wang et al. [52] examine Ethereum vulnerability to asymmetric Denial-of-Service (DoS) attacks via symbolic stateful fuzzing, revealing exploitable weaknesses in mempool logic. Similarly, Saad et al. [43, 42] introduce optimization techniques that adaptively structure mempool management to counteract Distributed Denial-of-Service (DDoS) attacks, improving resilience under adversarial conditions.

Mempool efficiency and privacy have been further addressed. Choudhuri et al. [10] propose a batched threshold encryption method to protect transaction confidentiality. Meanwhile, Sarenche et al. [44] analyze how dynamic mempool statistics influence Bitcoin mining strategies, especially under variable block rewards.

Together, these works underscore the importance of both performance and security in mempool design, setting the foundation for our modeling of mempool protocols in constrained environments.

## 2.2. Blockchain Integration with UAVs

Blockchain technology is increasingly deployed in UAV and IoT-based systems to enhance security, accountability, and data integrity. UAVs function as mobile blockchain nodes, particularly in scenarios such as disaster recovery, package delivery, and agricultural monitoring.

For instance, Gupta et al. [17] present a secure communication framework for UAVs operating in 6G environments. Their architecture integrates blockchain with the Inter-Planetary File System (IPFS), reducing data storage costs and improving communication reliability. Related work by Vangala et al. [51] further explores smart secure sensing in agriculture using blockchain enhanced IoT infrastructures. Environmental factors significantly affect blockchain performance in UAV networks. Hossain et al. [18] conduct empirical evaluations of private blockchains in UAV settings, showing that area coverage, altitude, and network parameters influence throughput and latency, highlighting the impact of mobility and topology dynamics.

Smirnov and Teslya [48] discuss smart contracts for coordinating robot coalitions in precision agriculture, leveraging blockchain to manage distributed decision making in mobile UAV fleets. Similarly, Pokhrel and Choi [38] propose a decentralized federated learning model for autonomous vehicles, which shares architectural parallels with UAV-based blockchain systems.

## 2.3. Blockchain and UAVs in Agriculture

Agricultural scenarios introduce specific challenges where UAVs must operate under poor connectivity and energy constraints. Blockchain technology provides a trusted data layer for coordinating sensor data, drone telemetry, and system authentication.

Bera et al. [6] introduce AKMS- AgriIoT, a private blockchain-based authentication protocol tailored for drone-enabled IoT farms. Vangala et al. [50] propose a generalized blockchain architecture for smart agriculture, addressing key security concerns.

Chinnaiyan et al. [9] employ permissioned blockchains to manage UAV and IoT sensor data, ensuring secure and auditable communications. Dawaliby et al. [13] integrate UAV maintenance automation with blockchain by detecting erroneous data via a smart contract-powered Zscore algorithm, initiating autonomous repair operations.

These efforts demonstrate blockchain's utility in addressing fraud, sensor failures, and trust management in agricultural environments.
## 2.4. Blockchain Performance Evaluation

Evaluating blockchain performance involves both empirical testing and formal modeling. Benchmarking tools such as Hyperledger Caliper [25] and DAGbench [14] offer metrics on throughput, latency, and scalability for conventional and DAG-based blockchains. BlockSim [4] provides a PoW-oriented simulation framework to assess block creation latency and confirmation times.

Recent surveys such as [15] review benchmarking and simulation approaches used to evaluate blockchain systems, highlighting the diverse metrics and environments used in comparative assessments.

Analytical approaches include queuing theory [39, 29], stochastic Petri nets [55], and game theory [28], offering mathematical insights into blockchain delay, mining strategies, and transaction prioritization. Ricci et al. [41] combine queuing models with machine learning to predict Bitcoin confirmation times under network load. Li et al. [29] investigate Markov processes in blockchain consensus, particularly in the context of dynamic network behaviors.

Further contributions include conceptual models for blockchain analytics in Ethereum [11], modeling of permissioned systems like Hyperledger Fabric [47], and consensus specific studies such as performance modeling of the HotStuff protocol [45].

While these works provide a strong foundation for performance modeling, few of them consider dynamic, real world conditions such as message loss, node failures, or variable latency factors prevalent in UAV-based agricultural deployments.

This review highlights a growing body of work on mempool based blockchains, blockchain and UAV integration, and performance analysis. However, a gap remains in studying how agricultural environmental conditions affect the performance of advanced mempool protocols like Narwhal. Our work bridges this gap by modeling Narwhal's behavior under real world UAV deployment constraints in the DroneVet application.

# 3. Delay Analysis of Mempool protocol with Markov Chain

In this section, we establish a generic model of a mempool that consists of a DAG as a data structure for the transactions management, by considering the key fundamentals of such protocols. Then, we will model it using Markov chains. Finally, we will determine the round duration formula and compare it with the round duration obtained by simulating the protocol.

## 3.1. System Model

The mempool protocol studied operates within a network of $n$ nodes, where $n = 3f+1$ and $f$ represents the number of Byzantine nodes. A round $r$ is a designated period or phase in the protocol for each node $i$ to propose a block of transactions $B_{i,r}$. When a node broadcasts such a block, it waits to receive a quorum of $q = 2f+1$ block acknowledgments $A_{b}^{j,i}$ from other nodes $j$ to form a quorum $Q_{i,r}^{(1)}$ before it can broadcast a new block of transactions in the next round $r+1$. Each block is associated with a specific round number, ensuring that a node can propose only one block of transactions per round. The blocks broadcast by the nodes form a Directed Acyclic Graph (DAG), where each vertex represents a block and edges are the dependencies between these blocks. This structure ensures that the protocol can handle Byzantine faults while maintaining a consistent and verifiable order of transactions.
## 3.2. Notations and Assumptions

To facilitate the modeling and analysis of the consensus delay and communication in the protocol, we define the key notations used throughout this work. These notations capture the structure of block propagation, acknowledgment reception, and state transitions in a round-based BFT consensus process. Table 1 summarizes the main symbols used in our formalization.

<table><caption>Table 1: Notation Used in the Models Establishment</caption><thead><tr><th>Symbol</th><th>Description</th></tr></thead><tbody><tr><td>$B_{i,r}$</td><td>A block $B$ broadcast by node $i$ in the round $r$.</td></tr><tr><td>$A_b^{j,i}$</td><td>A block acknowledgment sent from node $j$ to node $i$.</td></tr><tr><td>$A_q^{j,i}$</td><td>A quorum acknowledgment sent from node $j$ to node $i$.</td></tr><tr><td>$Q_{i,r}^{(1)}$</td><td>A quorum of $q$ block acknowledgments $A_b$ received by node $i$.</td></tr><tr><td>$Q_{i,r}^{(2)}$</td><td>A quorum of $q$ quorum acknowledgments $A_q$ received by node $i$.</td></tr><tr><td>$X_{i,r}(t)$</td><td>The number of messages received by node $i$ in round $r$.</td></tr><tr><td>$P_i(t)$</td><td>The probability of being in state $i$ at time $t$.</td></tr></tbody></table>

Our analysis is grounded on the following modeling assumptions, which define the operating environment and communication characteristics of the mempool protocol:

**A1.** A message transmission time is exponentially distributed with mean $\mu$ and rate parameter $\lambda$. The message transmission time refers to the end-to-end delay experienced when a message (e.g., transaction or block) is propagated between two nodes.

**A2.** All nodes in the network have equal capacity and computational power.

**A3.** Nodes operate over a fully connected peer-to-peer (P2P) network in which they are directly connected pairwise (i.e., each node is directly connected to $n-1$ nodes).

**A4.** Message transmission is assumed to be lossless for both broadcast and unicast communications. The term “lossless” refers to an idealized condition in which all transmitted messages are successfully delivered to their intended recipients without packet drops, corruption, or omission.

## 3.3. Mempool Protocol with one quorum of messages

We are interested in modeling the described protocol from the point of view of validator (acting as a miner) node $V_i$, denoted $i$ as well. The protocol starts when $i$ broadcasts a message $B_{i,r}$ in the round $r$ to the network. Then, it waits for a quorum $Q_{i,r}^{(1)}$ of block acknowledgment $A_b^{j,i}$ from other nodes $j$. Fig. 1 describes the defined protocol. We will model this mempool protocol with one quorum using a Continuous-Time Markov Chain (CTMC). The CTMC framework is particularly suitable for modeling the stochastic nature of the system, capturing the random arrival and processing of transactions. Its transition rate diagram, depicted in Fig. 2, illustrates the various states and the rates at which transitions occur between these states. Here, $\lambda$ represents the average message arrival rate, which determines how frequently new messages are proposed by nodes $j$.
<figure><img src="image_2.png" /><figcaption>Figure 1: Exchanged Messages from the point of view of validator $V_i$</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: Markov Chain for the Described Protocol</figcaption></figure>

Let $X_{i,r}(t)$ be the number of messages (i.e. block acknowledgment $A_b^{j,i}$) received by $i$, according to assumption A1, $\{X_{i,r}(t)\}_{t \in \mathbb{R}_+}$ be a continuous-time Markov chain.

The balance equations (or equilibrium equations) are given by:

$$ \begin{aligned} \lambda P_1 &= \lambda P_0 \\ \lambda P_2 &= \lambda P_1 \\ \vdots \\ \lambda P_{q-1} &= \lambda P_{q-2} \end{aligned} $$

Thus,

$$ P_0 = P_1 = \dots P_{q-2} = P_{q-1} = \frac{1}{q} \qquad (1) $$

Let $R = n - 1$. A node generates a new message in the next round, i.e. $B_{i,r+1}$ when it reaches the quorum, that is when it becomes at the state $q-1$ with probability $\frac{1}{q}$. The average message arrival rate for node $i$ is then given by:

$$ \lambda = \frac{nR}{q} \qquad (2) $$
For a round to end, $q$ messages (i.e. block acknowledgment) must be received, thus $q$ transitions must end. Each transition happens at an average rate $\lambda$, following an exponential distribution. The distribution of the duration of a round $r$, denoted by $f_{1round}(t)$, is given by:

$$f_{1round}(t) = \bigotimes_{q \text{times}} \lambda e^{-\lambda t} \qquad (3)$$

Or,

$$F_{1round}^{*}(s) = \left(\frac{\lambda}{\lambda + s}\right)^{q} \qquad (4)$$

Where $F_{1round}^{*}(s)$ is the Laplace transform of $f_{1round}(t)$.

### 3.4. Mempool Protocol with two quorums of messages

Let $X_{i,r}^{(1)}(t)$ be the number of acknowledgments $A_b^{j,i}$ received by node $i$ (in order to reach $Q_{i,r}^{(1)}$), and, let $X_{i,r}^{(2)}(t)$ be the number of acknowledgments $A_q^{j,i}$ received by node $i$ (in order to reach $Q_{i,r}^{(2)}$). According to assumption A1, $\{X_{i,r}^{(1)}(t), X_{i,r}^{(2)}(t)\}_{t \in \mathbb{R}_+}$ is a continuous-time Markov chain described in Fig. 3. We define:

<figure><img src="image_4.png" /><figcaption>Figure 3: Markov Chain for the two quorums Protocol</figcaption></figure>

* $\lambda_1$ is the average message, $A_b^{j,i}$, arrival rate,

* $\lambda_2$ is the average message, $A_q^{j,i}$, arrival rate.

Note that $\lambda_1$ is defined by Assumption A1, while $\lambda_2$ will be determined later. To determine $\lambda_2$, we model the broadcasting of both the block $B_{i,r}$ and the quorum $Q_{i,r}^{(1)}$ using the queuing network shown in Fig. 4. This model allows us to analyze the dynamics and interactions affecting $\lambda_2$.
In this model, broadcasting a message (either $B_{i,r}$ or $Q_{i,r}^{(1)}$) to $n-1$ nodes (denoted as $R$) involves creating $R$ duplicate copies of the message, assuming an infinite number of servers.

<figure><img src="image_5.png" /><figcaption>Figure 4: Two stations queuing network for messages broadcast</figcaption></figure>

As $k$ acknowledgments are received from nodes confirming the message, there are $R-k$ nodes that still need to receive it. Consequently, $R-k$ copies of the message remain being transmitted across the network.

The first station represents the block transmission, and the second represents the $Q_{i,r}^{(1)}$ transmission. Both stations have an infinite number of servers (without waiting times), and $R$ is the total number of customers in the queuing network. The state of each station corresponds to the number of customers in each state. A Continuous-time Markov chain models this system. To determine the mean message generation rate, we focus on station 2. Fig. 5 describes the transition rate diagram of this second station using a Markov chain.

<figure><img src="image_6.png" /><figcaption>Figure 5: Messages generation rate for station 2</figcaption></figure>

Let $P_k$ the probability to have $k$ $A_b^{j,i}$ being transmitted. $P_k$ is given by:

$$P_k = P_0 \frac{R * (R-1) \dots (R-k+1)\mu}{k!\mu}$$

where, $R$ is the total number of possible $A_b^{j,i}$, $k$ is the specific number of $A_b^{j,i}$ we're interested in, $P_0$ is the probability of having 0 $A_b^{j,i}$ transmitted, and $\mu$ is the generation
rate associated with each $A_b^{j,i}$. The expression $R \times (R-1) \times \cdots \times (R-k+1)$ can be written as $\frac{R!}{(R-k)!}$. Thus, the probability $P_k$ simplifies to:

$$P_k = P_0 \times C_R^k \qquad (5)$$

By normalization of probability, $\sum_{k=0}^{R} P_k = 1$. Using Eq. 5, this becomes: $\sum_{k=0}^{R} P_0 \times C_R^k = 1$. Knowing that $\sum_{k=0}^{R} C_R^k = 2^R$, $P_0$ is given by $P_0 = \frac{1}{2^R}$. Thus, $P_k$ is then given by: $P_k = \frac{C_R^k}{2^R}$.

The mean generation rate $\lambda_2$ of $Q_{i,r}^{(1)}$ can be derived from the expected number of $A_b^{j,i}$ transmitted, denoted by $\bar{N}_2$: $\bar{N}_2 = \sum_{k=0}^{R} k \times P_k$.

Substituting this into the expression for the mean generation rate $\lambda_2$, we obtain:

$$\lambda_2 = \mu \times \bar{N}_2 = \mu \sum_{k=0}^{R} k \times P_k \qquad (6)$$

Here, $\mu$ represents the rate at which each $A_b^{j,i}$ is generated. Given that $P_k$ follows a binomial distribution, $P_k = \frac{C_R^k}{2^R}$, where $C_R^k$ is the binomial coefficient, the mean generation rate $\lambda_2$ can be rewritten as:

$$\lambda_2 = \mu \sum_{k=0}^{R} k \times \frac{C_R^k}{2^R} \qquad (7)$$

The duration of a round corresponds to $q$ vertical transitions and $q$ horizontal transitions to go from state (0,0) to state $(q, q)$ in the diagram of Fig. 3 and this whatever the path followed. Thus the distribution of the duration of a round is given by:

$$f_{2round}(t) = \bigotimes_{q \text{times}} \lambda_1 e^{-\lambda_1 t} \bigotimes_{q \text{times}} \lambda_2 e^{-\lambda_2 t} \qquad (8)$$

Or,

$$F_{2round}^{*}(s) = \left(\frac{\lambda_1}{\lambda_1 + s}\right)^q \left(\frac{\lambda_2}{\lambda_2 + s}\right)^q \qquad (9)$$

### 3.5. Simulation Results

In this section, we present the simulation results of the protocol for both one and two quorum configurations. We compare the distribution of the simulation outcomes with the theoretical distributions derived in equations 3 and 8. To ensure accuracy, we conducted simulations over 1000 rounds.

The plots in Fig. 6 and Fig. 7 visually confirm the close agreement between the simulated data (histograms) and the theoretical distributions: $f_{1round}(t)$ in Eq. 3 and $f_{2round}(t)$ in Eq. 8 (red lines). This strong alignment indicates that our mathematical model accurately captures the behavior of the mempool process, supporting the validity of our theoretical expectations.

In Fig. 7, we observe that the round durations are longer compared to those in Fig. 6. This increase is due to the additional communication overhead and potential delays associated with the requirement of waiting to receive two quorums of messages for each node to move to a new round and propose a new block. This approach significantly enhances the integrity and robustness of the system, reducing the risk of conflicting blocks.

The plot in Fig. 8 helps us understand how delays are distributed in the system and provide a critical value $T$ which can be used to make informed decisions about system
<figure><img src="image_7.png" /><figcaption>Figure 6: Distribution of Round Duration for the protocol based on One-Quorum of messages</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7: Distribution of Round Duration for the protocol based on Two-Quorums of messages</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 8: Distribution of the CDF for the Exponentially distributed Delays</figcaption></figure>

performance and reliability. The green vertical line at $x = T$ (where $T \approx 2.8214$) tells us that about 67% of all delays will be less than or equal to $2.8214\mu$. This means if we set a timeout or an expectation for delay at around $2.8214\mu$, we can be confident that approximately 67% of the delay instances will fall within this time frame.

# 4. Case Study of a Mempool Protocol: Narwhal Protocol

## 4.1. Overview

To validate and extend our analytical findings on mempool-based blockchain protocols, we now focus on a concrete example: the Narwhal protocol.

Narwhal is a mempool protocol that reliably broadcasts transactions from the mempool. This mempool serves as a buffer for transactions waiting to be validated and included in a block. Narwhal proceeds in rounds and builds its DAG during these rounds. Each vertex is linked to a specific round. The DAG structure efficiently organizes and creates a causal order of transactions, enhancing the robustness of the blockchain and the parallel processing of transactions. By maintaining a structured round-based DAG, Narwhal ensures efficient data availability and transaction integrity. Nodes which are responsible for processing and validating transactions, operate in rounds and exchange messages. Narwhal is designed as a robust and asynchronous mempool protocol that decouples transaction dissemination from consensus, thereby improving throughput and fault tolerance. This case study bridges the gap between abstract modeling and real-world deployment.

## 4.2. Narwhal Protocol Messages

Narwhal considers three types of messages: the block of transactions, the signature of a block, and the certificate of availability of a block:

1. **Block**: A block is a message broadcasted by a node $i$ to the network. Each block includes the signature of the generator node, a list of transactions, and a list of certificates of availability of blocks from the previous round.
<figure><img src="image_10.png" /><figcaption>Figure 9: Exchanged Messages from the point of view of validator $V_i$ [20]</figcaption></figure>

2. **Signature**: A signature is a message that is relative to a specific block. It is sent by a node when this latter validates (or approves) this block. A specific quorum of such signatures constitutes a certificate of availability relative to the block in question.

3. **Certificate of availability**: A certificate message is associated to a block. It contains the hash of this block, along with a quorum of signatures received from other validators that approved this block and the round number r.

### 4.3. Protocol Workflow

The Narwhal protocol operates as the following (Fig. 9):

1. Each validator node continually receives client transactions and creates a local transaction list. It also receives certificates, which are stored in a certificate list.

2. Upon receiving a block, a validator first validates the block signature, ensuring that the block contains $q = 2f + 1$ certificates from the previous round and is the first block it receives from this validator in the current round. If these conditions are satisfied, the validator signs (approves) it.

3. Once a validator receives a quorum $q$ signatures for the block it has broadcast, it generates a certificate of availability for the block and broadcast this certificate to the network.

4. Upon receiving certificates of availability of his block, from a quorum $q$ of validators for the current round, the validator advances to the next round and broadcasts a new block containing its current transactions.

After the transactions are disseminated through the DAG, a separate consensus protocol takes over to determine the final order in which these transactions are included in the blockchain. This protocol introduces no additional message overhead, as nodes are not required to exchange extra messages. Instead, each node independently inspects its local DAG and applies predefined rules to determine the transaction order.

### 4.4. Analysis of Data Dissemination delays in Narwhal

In a previous study [20], we analyzed the round duration of the Narwhal protocol under the assumption that message delays follow a normal distribution. Specifically, we
modeled the transmission and reception times of protocol messages, beginning by defining the start time of round r for node i as a Gaussian variable:

$$t_{i,r}^{\text{round}} \sim \mathcal{N}(\mu_r, \sigma_r^2).$$

We then derived the distribution of the start time for the subsequent round,

$$t_{i,r+1}^{\text{round}} \sim \mathcal{N}(\mu_{r+1}, \sigma_{r+1}^2),$$

by establishing recursive equations linking $(\mu_r, \sigma_r^2)$ to $(\mu_{r+1}, \sigma_{r+1}^2)$.

As $r \to \infty$, the asymptotic round duration converges to the following expression:

$$(\mu_{r+1} - \mu_r) \approx 3\mu + \left(\sqrt{2} + \sqrt{\frac{2\beta + 1}{1 - \beta}}\right) \alpha\sigma. \qquad (10)$$

# 5. DroneVet Application: Blockchain and UAV for Cattle Health Monitoring

This section presents the DroneVet application that we have previously proposed in [21].

## 5.1. Motivation and System Overview

There is increasing global concern about food safety, especially when it comes to contamination stemming from animal-based products. A significant contributor to this issue is the failure, in some cases, of farmers to adhere to proper vaccination protocols, thereby heightening the risk of diseased animals entering the food supply. Yet, many livestock health issues are manageable if detected early, which is crucial not only for containing disease outbreaks but also for mitigating financial losses in the agricultural sector [33].

This underscores the critical need for proactive and reliable animal health monitoring systems [54]. In response, the DroneVet application is an innovative solution, leveraging unmanned aerial vehicles (UAVs) for livestock health monitoring. Given the presence of potentially conflicting interests among stakeholders such as farmers, veterinarians, and regulators blockchain technology is employed to ensure data integrity, transparency, and tamper resistance through immutable, timestamped records of health information [26].

DroneVet is particularly geared toward supporting governmental authorities in overseeing the health status of livestock destined for markets. In DroneVet, UAVs, operated by certified private entities, collect biometric data from RFID-tagged, sensor-equipped cattle [54]. This data is securely submitted as blockchain transactions, ensuring traceability. Furthermore, drone operators are compensated based on mission validation, promoting accountability and service quality.

The goals of this system are twofold: (i) At the consumer level, it aims to enhance food quality and reduce the risk of contamination. (ii) At the national level, it supports the preservation of livestock health and enables the collection of valuable statistics for forecasting consumption patterns and planning potential exports [21].

As a proof of concept, we implemented the system on the Sui blockchain platform¹, which is built upon the Narwhal mempool protocol discussed earlier.
<figure><img src="image_11.png" /><figcaption>Figure 10: System overview: Participants, Components, Access Right [21]</figcaption></figure>

## 5.2. *Architecture and System Workflow*

Figure 10 presents an overview of the proposed system. The monitoring process is managed by autonomous drones. A government authority launches a tender for a monitoring mission based on drones. A drone operator obtains this tender and drones start their missions on a predefined farm. They collect data from the cattle, which are equipped with sensors. The drone task assignment and the payment of drone operators are made via blockchain technology. Thus, the system can be seen as a marketplace where the drone owners are the service providers and the government authorities are the service requesters. Each drone task starts every day: it collects data from the assigned farm and uploads the collected data to the blockchain network in real-time. The data collected by the drones will be managed transparently via the blockchain so that it is secure and immutable.

Actors benefit from the system as follows:

* **Farmers** play a central role in animal welfare. They are expected to follow good husbandry practices, provide proper nutrition, and adhere to vaccination schedules. The system allows farmers to access and update their livestock's health records regularly.

* **Consumers** benefit from greater transparency in food supply chains. They can verify whether meat products come from healthy livestock, including details such as vaccination status and feeding history.

* **Veterinarians** have an important role in our system. They are actively involved in the welfare of animals by providing care in a preventive (prevention of disease) or curative (treatment of disease) manner. When a farmer brings his/her animal to the veterinarian, this latter will be able to: consult the previous records about the cattle or update these records with new information like the new vaccines for instance.

<footnote n="1">¹https://sui.io</footnote>
* **The government authorities** like the ministry of commerce and the ministry of agriculture can consult or update information about the cattle health (vaccines, cattle number, measures collected by drones, health status) and manage the marketplace.

* **Some organizations** (like consumer protection organization) can benefit from the system by consulting the health status of the livestock.

* **Research labs** can base their studies on the cattle health information data they consult on the system and may add new information (results).

* **Drone operators** use the system as a marketplace where they find new offers and livestock monitoring tenders in which they can participate. The system will enable them to register the work done by the drones that they possess and to be paid accordingly.

This architecture demonstrates how blockchain and UAV technologies can jointly support a transparent, accountable, and secure infrastructure for livestock health monitoring, thereby benefiting stakeholders from farmers to researchers and regulatory authorities.

# 6. DroneVet under Realistic Network Conditions

The objective of this section is to discuss the challenges of DroneVet application under realistic conditions. In our analysis we distinguish between *UAV-based challenges* that stem from physical and operational limitations of drones, and *network-based challenges* that arise from the communication environment.

## 6.1. *UAV-based Challenges*

Unmanned Aerial Vehicles (UAVs) in DroneVet are not only mobile but also energy-constrained computing nodes. This role introduces many challenges to the UAVs to participate in the consensus. These challenges can be summarized as follows [19]:

*Energy Limitations..* Battery capacity remains the most restrictive factor for UAV [19]. A significant portion of the onboard energy is consumed by propulsion, which leaves only a fraction for communication and computation. Participation in consensus involves continuous sensing, message exchange, and cryptographic verification, all of which consume the limited resources. This limits the service time of the UAVs, reduces their availability for consensus runs, and involves trade-offs between flight autonomy and participation in the consensus protocol. Energy consumption can lead to unexpected node failures, which can disrupt consensus unless protocols are designed to be energy aware.

*Mobility and Coverage Transitions..* Agricultural UAVs cover vast and heterogeneous areas where connectivity is far from uniform. At higher altitudes, they may enjoy improved line-of-sight, but lateral movement across large fields exposes them to shadowing from trees, barns, or rolling terrain. Moreover, frequent transitions between coverage zones or gateways create abrupt topology changes. These dynamics produce fluctuating link quality, variable delay, and occasional disconnections, which directly translate into inconsistent message exchange during the consensus protocol [37, 32].
*Environmental and Operational Instability.* In addition to terrain-related disturbances, environmental factors such as wind, humidity, and precipitation can affect both flight stability and wireless propagation. Strong winds force UAVs to use more energy to stabilize themselves, while humidity in the atmosphere increases signal attenuation. These persistent, yet subtle influences complicate the already delicate balance between mobility, communications reliability, and energy sustainability [32].

## 6.2. Network-based Challenges

Beyond the physical constraints of UAVs, DroneVet must also deal with the realities of wireless communication in open environments. Unlike urban areas with dense infrastructure, rural agricultural areas offer limited support in terms of base stations, resulting in a reliance on multi-hop links, shared spectrum, and long-distance transmissions. These conditions give rise to several network challenges.

### 6.2.1. *Packet Loss and Reliability*

Open-air communication is subject to signal loss, interference, and congestion, all of which increase packet error rates. A single lost or corrupted message can require costly retransmissions, consuming more bandwidth and energy while prolonging consensus processes. Prolonged packet loss, particularly during bad weather or long-distance transmissions, can result in a complete loss of consensus among nodes. Reliability therefore becomes a decisive factor in the robustness of the system [32].

*Interference and Spectrum Sharing.* Modern agricultural fields are increasingly equipped with IoT devices such as soil sensors, actuators, and weather stations. These devices often share the same frequency bands as UAVs, leading to spectrum conflicts, collisions, and increased retransmission rates [24]. In large-scale deployments, UAVs may also experience handoffs between heterogeneous networks (LoRa, Wi-Fi, 4G/5G, or satellite). Such coexistence amplifies interference and degrades quality of service, further complicating blockchain communication.

### 6.2.2. *Signal Propagation Effects*

Although the fields appear clear, long-distance wireless propagation suffers from attenuation and limited reflection. At lower frequencies, uneven terrain and sparse obstacles (isolated trees or farm buildings) still disrupt line-of-sight communication. At higher frequencies, signals are more vulnerable to atmospheric absorption and rain fading. These propagation effects reduce the reliability of critical communication phases, such as block exchange and acknowledgment, ultimately slowing down consensus progression [5].

In summary, DroneVet faces a confluence of UAV-level and network-level challenges that may impact the consensus protocol performance. While these constraints are diverse and often interdependent, three stand out as particularly critical for blockchain operation in agricultural UAV networks: **energy limitations**, **latency variability**, and **packet loss**. The following section explicitly models and simulates these factors to evaluate their impact on DroneVet's consensus round duration and overall system performance.

# 7. Simulation of DroneVet under Realistic Conditions

Building on the challenges outlined in Section 6, we now evaluate DroneVet's performance when subject to realistic environmental constraints. In particular, we concentrate on two dominant network-level factors—**latency variability** and **packet loss**—as well
as the role of **energy limitations** on UAV. These parameters were identified as the most
critical disruptors of consensus stability in agricultural UAV deployments.

To this end, we extend our simulator to incorporate variable message delays, probabilistic packet losses, and node duty-cycle restrictions that emulate real-world conditions. Our objective is to quantify how these factors influence the Narwhal protocol, which underpins DroneVet’s mempool-based consensus, with respect to round duration, reliability, and system resilience.

7.1. Application Scenario

We consider a peer-to-peer blockchain network including four nodes implementing the
DroneVet application in a rural agricultural field. The network participants represent key
stakeholders in livestock health monitoring:

* a **UAV** that periodically monitors the field and collects health-related data from livestock via embedded IoT sensors,

* a **veterinarian station** responsible for validating and interpreting diagnostic results,

• a **farmer** who provides local oversight and acts on health alerts,

* a **governmental ministry** that ensures regulatory compliance and maintains authoritative health records.

In this setup, the veterinarian, farmer, and ministry nodes are assumed to operate with
stable and reliable network connectivity, reflecting their fixed infrastructure and access
to wired or high-quality wireless links. By contrast, the UAV node is highly dynamic
and experiences intermittent connectivity due to mobility, environmental conditions, and
limited energy supply. As a result, communication between the UAV and the other nodes
is subject to variable latency and packet loss.

Figure 11 depicts this architecture, in which the UAV serves as a mobile data source with unstable links, while the remaining nodes maintain relatively stable peer-to-peer connections. This allows us to explicitly examine how DroneVet’s consensus protocol behaves when a single resource-constrained and delay-prone participant interacts with otherwise stable peers. In the following sections, we investigate how the three key environmental constraints—**latency variability**, **packet loss**, and **energy limitation**—affect consensus delay within this application scenario.

7.2. Impact of Network Latency Variability

7.2.1. *Simulation Scenario and Setup*

In the DroneVet application, the UAV hovers over livestock in agricultural fields to collect health data. Depending on herd distribution, the UAV may remain in a stable area or move across distant zones, requiring it to switch between different ground stations for connectivity. This mobility, combined with environmental factors such as vegetation, terrain elevation, and electromagnetic interference, introduces variability in wireless communication quality.

To model this behavior, we simulate randomized transmission delays using a uniform
distribution bounded by a configurable maximum latency while taking into account the
underlying communication technology. Empirical latency ranges are informed by prior
<figure><img src="image_12.png" /><figcaption>Figure 11: Application scenario of DroneVet in an agricultural field. Red dashed links represent unstable UAV connections subject to latency variability, packet loss, and energy constraints. Black solid links represent stable peer-to-peer connections between ground nodes.</figcaption></figure>

studies such as [7, 9, 23], which analyze wireless performance in outdoor and rural scenarios. Indeed, In UAV and IoT-based agricultural networks, latency strongly depends on the communication technology. For example, in Wi-Fi (2.4 GHz), the latency typically ranges between 10–100 ms. For cellular networks (3G/4G), it is between 20–200 ms, while LoRaWAN may introduce delays from 500 ms up to several seconds under poor link conditions [49].

Thus, we simulate the following 3 scenarios :

• **Scenario 1 – Minor network instability:** Maximum latency of 0.1 seconds, corresponding to stable Wi-Fi or low-latency LoRaWAN.

• **Scenario 2 – Moderate latency:** Maximum latency of 0.5 seconds, capturing typical delays in 3G/4G or moderately degraded Wi-Fi conditions.

• **Scenario 3 – Severe congestion:** Maximum latency ranging from 1.0 to 5.0 seconds, reflecting high interference or unstable LoRaWAN links.

### 7.2.2. Simulation Results

Figure 12 shows the round duration distribution for the three latency variability scenarios. Surprisingly, the distributions remain almost indistinguishable: the median round duration is consistently around 3.2 s, with extremely narrow interquartile ranges and no significant outliers. Even in the severe scenario, where one node exhibits latencies of several seconds, the consensus latency is unaffected.

This result can be explained by the quorum rule ($q = 3$ out of 4): consensus progress depends only on the three fastest nodes, effectively masking the instability of the single UAV node. Consequently, as long as the number of unstable nodes remains below the quorum threshold, the protocol demonstrates strong resilience to latency variability.

These findings nuance our understanding of Narwhal's performance. While prior expectations suggested that increasing network delays would directly inflate round duration distributions, the simulation shows that fault-tolerant consensus can endure considerable link variability without visible degradation. This highlights the robustness of the protocol
<figure><img src="image_13.png" /><figcaption>Figure 12: Round Duration Distribution under Different Network Latency Conditions.</figcaption></figure>

design and proves the importance of quorum-based mechanisms in real-world UAV-based agricultural deployments.

### 7.3. Impact of Packet Loss

#### 7.3.1. Simulation Scenario and Setup

To simulate the effect of packet loss, we randomly discard a fraction of the transmitted messages (including blocks, signatures, or certificates) during consensus rounds. Each dropped message impacts the quorum formation and can delay or prevent round completion at some nodes.

In the simulation, packet loss is modeled by randomly assigning an infinite delay to some messages. They will be considered as lost messages. These delays are excluded from the round duration computation, which means that rounds can only proceed with the available subset of messages. If no valid quorum can be formed, no possible block can be associated to this round.

Prior studies of wireless sensor networks and UAV communications like [30], [23], [46] show that packet loss strongly depends on environmental and operational conditions. We distinguish:

* Low mobility scenarios (e.g., hovering UAVs, short range): 1–5% loss probability

* Moderate mobility (e.g., UAVs patrolling fields, switching stations): 5–15% loss

* High mobility or long-range transmission (e.g., fast UAVs, LoRaWAN links): 20–40% loss

In line with these empirical ranges, we simulate the following packet loss levels:
* **Minor loss:** 1% message drop probability

* **Moderate loss:** 5% message drop probability

* **Severe loss:** 10% message drop probability

### 7.3.2. Simulation Results

<figure><img src="image_14.png" /><figcaption>Figure 13: Round Duration Distribution under Varying Packet Loss Rates. Invalid rounds (no quorum) are discarded from the dataset.</figcaption></figure>

Figure 13 presents the distribution of round duration for the three packet loss scenarios compared with the Gaussian-only baseline. The statistics obtained from the simulation are summarized below:

* **Minor loss (1%):** Mean round duration ≈ 0.151 s, with standard deviation 0.0067. The distribution is close to baseline, but occasional rounds are delayed by lost messages.

* **Moderate loss (5%):** Mean duration increases to ≈ 0.156 s with higher variance (0.0084). The distribution broadens, with heavier tails and more outliers, indicating rounds that take longer due to quorum delays.

* **Severe loss (10%):** Mean duration rises further to ≈ 0.160 s, with similar variance (0.0087). Although the increase is not dramatically wider than the 5% case, the higher mean reflects more frequent quorum slowdowns. Some rounds are excluded entirely when too many messages are lost to form a quorum.
Overall, packet loss introduces both additional latency and variability in consensus performance. Even modest loss rates (5–10%) significantly broaden the latency distribution. At higher loss levels, the filtering of invalid rounds conceals the worst-case behavior, but in practice these correspond to failed or stalled consensus rounds. These findings highlight the importance of reliability mechanisms such as retransmissions, forward error correction, or timeout-based recovery in UAV-based blockchain systems, where unstable wireless links are unavoidable.

## 7.4. Impact of UAV Energy Constraints and Node Failures

### 7.4.1. Simulation Scenario and Setup

Agricultural UAVs, unlike fixed infrastructure nodes, are battery powered with limited flight endurance. Their energy is consumed not just by communication and consensus participation, but also by propulsion, sensing, data acquisition, and mobility. When the UAV is depleted of energy, it becomes a failed node, unable to take part in further consensus rounds, which reduces the number of available replicas and can threaten quorum formation.

Different UAV platforms offer varying levels of battery endurance depending on their design and configuration. For instance, small fixed-wing UAVs with a payload capacity of around 1 kg and a take-off weight of about 6 kg can achieve up to 2 hours of endurance. Similarly, long-endurance gasoline-powered quadrotor prototypes with a take-off weight of 10 kg have demonstrated flight times between 2 and 3 hours. In contrast, in the context of “small commercial UAVs”, the typical flight autonomy is limited to 20–30 minutes, whereas larger platforms may sustain several hours of operation depending on their configuration. These values are inspired by findings reported in previous studies [35, 36, 31].

To model realistic UAV energy constraints, we define $T_{battery}$ while considering two different cases:

* A nominal flight autonomy of $T_{battery} = 20$ minutes under typical operations (hov-ering, moderate payload, communication load). This fits many consumer-grade or small agricultural quadcopters.

* A more capable fixed-wing UAVs with an endurance $T_{battery} \approx 1-2$ hours under favorable conditions, particularly when they are optimized for endurance with lighter payloads.

Using the measured round durations of $T_{round} \approx 3.0–3.5$ seconds per consensus round, we compute MaxRounds, the maximum number of rounds a UAV can sustain:

$$ \text{MaxRounds} = \frac{T_{\text{battery}}}{T_{\text{round}}} $$

- For $T_{battery} = 20$ min (1200 s):

$$ \text{MaxRounds ranges from } \frac{1200}{3.5} \approx 343 \text{ rounds to } \frac{1200}{3.0} = 400 \text{ rounds} $$

- For $T_{battery} = 60$ min (3600 s):

$$ \text{MaxRounds ranges from } \frac{3600}{3.5} \approx 1029 \text{ rounds to } \frac{3600}{3.0} = 1200 \text{ rounds} $$
To obtain a more realistic simulation environment, we extend this model by introducing variable UAV energy levels rather than assuming a fixed maximum flight duration. In practice, the available battery capacity of each UAV is rarely constant or equal to its nominal value. Several factors can lead to partial or degraded energy availability:

* **Battery aging and usage history:** Over time, repeated charge/discharge cycles reduce the effective energy capacity.

* **Environmental conditions:** High or low ambient temperatures can significantly affect discharge rates and battery efficiency.

* **Manufacturing variability:** Slight differences in cell quality or assembly lead to non-uniform battery performance across UAVs.

* **Mission conditions:** Payload mass, flight altitude, and maneuver aggressiveness also influence real energy consumption.

To reflect these heterogeneous operating conditions, each UAV in the simulation is assigned a random available battery duration within an interval defined by:

$$T_{\text{battery}} \in [T_{\text{min}}, T_{\text{max}}]$$

where $T_{\text{min}}$ represents a partially depleted or degraded energy state, and $T_{\text{max}}$ corresponds to the nominal full-charge duration computed above. Specifically, we set $T_{\text{min}} = 0.5 T_{\text{max}}$, meaning that UAVs may start the consensus process with as little as half their full battery capacity.

This stochastic modeling approach captures realistic variability in UAV endurance: some nodes may fail earlier due to reduced energy reserves, while others remain operational longer. Consequently, the achievable number of consensus rounds

$$N_{\text{rounds}} = \frac{T_{\text{battery}}}{T_{\text{round}}}$$

becomes a random variable, producing a distribution of sustainable rounds across the UAV population rather than a single deterministic value. This allows the simulation to better reflect energy-related heterogeneity and the resulting asynchrony in node participation.

To analyze the effects of different endurance profiles, we further categorize UAVs into three qualitative energy-constraint scenarios that correspond to different regions of the sampled endurance interval:

* **High energy availability:** UAVs operating in the upper 80-100% range of the endurance interval, remaining active for nearly the full mission duration (approximately 340-400 consensus rounds in the 20-minute case, and 1000-1200 rounds in the 60-minute case).

* **Moderate autonomy:** UAVs with endurance within the mid-range, roughly 50-80% of the maximum battery capacity. These UAVs remain active for around 170-200 rounds (20-minute case) or 500-600 rounds (60-minute case).

* **Severe constraint:** UAVs whose endurance lies below 50% of the nominal $T_{\text{battery}}$, resulting in early depletion and disconnection after approximately 70-80 rounds in the 20-minute case, or 200-250 rounds in the 60-minute case.
This categorization provides a structured interpretation of UAV autonomy levels within the stochastic endurance model, enabling the evaluation of how energy variability influences consensus sustainability, fault tolerance, and overall network resilience.

### 7.4.2. Simulation Results

Figure 14 and Figure 15 illustrate the outcomes of the stochastic endurance model under two UAV configurations with nominal flight autonomies of 20 and 60 minutes, respectively. Each UAV was assigned a random available energy capacity within [0.5 $T_{max}$, $T_{max}$], and the corresponding number of consensus rounds was computed according to

$$N_{\text{rounds}} = \frac{T_{\text{battery}}}{T_{\text{round}}}, \quad T_{\text{round}} \in [3.0, 3.5] \text{ s.}$$

*Distribution of Sustainable Rounds.* The histogram in Figure 14 shows the distribution of achievable consensus rounds across simulated UAVs. For the 20-minute UAVs, the number of rounds ranges approximately between 170 and 400, with the majority clustered around 250–320 rounds. In contrast, 60-minute UAVs achieve between roughly 500 and 1200 rounds, displaying a broader and flatter distribution due to their larger endurance interval. These results confirm that introducing variable energy levels produces heterogeneous participation times among nodes, mimicking realistic degradation and operational variability.

*Statistical Dispersion.* The boxplot in Figure 15 further emphasizes the dispersion in achievable rounds. While both UAV categories show proportional scaling with battery capacity, the interquartile range (IQR) expands significantly for long-endurance UAVs, reflecting the wider variability in sustained participation. Specifically, 50% of small UAVs complete between approximately 230 and 320 rounds, whereas long-endurance UAVs span a range between roughly 700 and 950 rounds. This variability indicates that some nodes may deplete their energy prematurely, leading to gradual replica loss and reduced fault-tolerance margins during prolonged operation.

*Interpretation.* Overall, the results demonstrate that even moderate heterogeneity in UAV energy reserves can translate into noticeable disparities in consensus longevity. Such disparities cause asynchronous node dropouts over time, which can compromise quorum formation if not accounted for in protocol design. These findings highlight the importance of adaptive participation mechanisms and dynamic quorum management in energy-constrained UAV networks.

### 7.5. Discussion: Importance of Round Duration Evaluation

The evaluation of round duration provides fundamental insights into the performance of mempool-based consensus protocols. Round duration defines the time within which nodes collect, disseminate, and organize transactions before reaching agreement on their inclusion in the distributed ledger. As such, it is a critical design parameter that influences transaction throughput, consensus stability, and overall system security [40].

A key trade-off emerges between **short** and **long** round durations. Shorter rounds enable transactions to be confirmed more frequently, improving responsiveness and user experience. However, excessively short rounds may also lead to highly fragmented directed acyclic graphs (DAGs), with many blocks being proposed in parallel, thereby increasing protocol complexity and resource overhead. In contrast, longer round durations simplify the DAG structure and reduce communication overhead, but at the cost of
<figure><img src="image_15.png" /><figcaption>Figure 14: Distribution of consensus rounds under variable UAV battery levels.</figcaption></figure>

slower transaction finality (i.e., the time until a transaction is validated and irreversibly included in a block) and reduced throughput.

From a system design perspective, round duration directly affects **scalability**, **security**, and **reward mechanisms** [40]. Shorter rounds increase block generation rate and improve network scalability but require higher bandwidth and synchronization accuracy. Conversely, longer rounds limit throughput and may reduce validator rewards if transaction inclusion is delayed, thereby weakening liveness guarantees reported in prior blockchain studies [56].

For UAV-based blockchain applications such as DroneVet, the measured round duration of approximately 3.0–3.5 seconds offers a practical balance: it is short enough to support timely health monitoring and alert dissemination, while still maintaining a manageable DAG complexity. These observations do not introduce new conclusions but rather situate the measured values within known trade-offs discussed in the literature.

More broadly, round duration analysis provides guidelines for blockchain designers: the parameter should be calibrated by considering the holistic trade-off between performance, reliability, and security under resource-constrained conditions [40].

## 8. Conclusion

This work presented a delay analysis of a DAG-based mempool protocols in the context of UAV-assisted agricultural monitoring, using the DroneVet application as a representative scenario under realistic environmental constraints.

Simulations show that variable UAV endurance introduces asynchronous node dropouts, reducing available replicas and limiting sustainable consensus rounds. Longer battery autonomy enhances robustness, whereas packet loss remains the main performance bottleneck, and latency variation has minor impact when quorum is quickly reached. These results highlight the need for energy aware and adaptive quorum mechanisms to ensure reliable UAV-based blockchain operation in real world agricultural settings.
<figure><img src="image_16.png" /><figcaption>Figure 15: Boxplot of consensus rounds distribution under random battery levels.</figcaption></figure>

# 9. Author Contributions

K. Hwerbi designed and wrote the manuscript. I. Amdouni designed and revised the manuscript. K. Hwerbi, I. Amdouni, C. Adjih, L. Azouz Saidane and A. Laouiti discussed the research idea and jointly proposed the contribution.

# Acknowledgment

Funding Declaration: This research was conducted under the project PHC-Maghreb ANGEL 24MAG18.

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