## 3 Trust-Optimized 6G-IoT Framework
### Trust Management System
### Delay-Tolerant Routing

These highly dynamic and quite unpredictable network conditions necessitate the employment of delay-tolerant routing to ensure reliable data delivery in TEO-IoT. In this paper, an adaptive and energy-efficient routing protocol is proposed, having the prime motivation of prioritizing critical data with on-time delivery. The protocol will be probabilistic model-based with an optimization of routing decisions, backed by sound theoretical analysis that ensures stability and efficiency, as shown in \[\quad+\alpha_{4}\mathbf{C}_{i}(t)+\alpha_{5}\mathbf{I}_{i}(t)+ \alpha_{6}\mathbf{P}_{i}(t), \tag{13}\]8

The adaptive routing protocol starts its functioning and assigns each possible route \(i\) at time \(t\) with one probability, \(P_{i}(t)\), that depends on distance \(d_{i}(t)\), energy consumption \(E_{i}(t)\), and delay

\(DeltaT_{i}(t)\). The probability distribution is expressed as

\[\quad+\alpha_{4}\mathbf{C}_{i}(t)+\alpha_{5}\mathbf{I}_{i}(t)+ \alpha_{6}\mathbf{P}_{i}(t), \tag{13}\]9 \[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]0

where \(\lambda_{1}\), \(\lambda_{2}\), and \(\lambda_{3}\) are weighting factors balancing the impact of distance, energy, and delay for the routing decision. Thus, the goal will be the minimization of the expected delay \(\mathbb{E}[\Delta T(t)]\), with the preservation of energy efficiency and reliability. The expected delay is given by

\[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]1

\[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]2 Enhanced depiction of the delay-tolerant routing protocol in the TEO-IoT framework. and the overall routing cost function \(J(t)\) is defined as

\[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]3 \[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]4

which represents the reliability of route \(i\), and \(\alpha\) and \(\beta\) are scaling factors. To guarantee the convergence to the optimal routing decision, we define a Lyapunov function \(V(t)\) (Appendix E) as

\[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]5

where \(P_{i}^{*}(t)\) is the optimal probability distribution at time \(t\). The derivative of \(V(t)\) is

\[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]6

For implementing the protocol in an energy-efficient manner, a dynamic adjustment factor \(\eta(t)\) is introduced, modulating the weighing of energy consumption:

\[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]7 \[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]8

\(\eta(t)\) is updated based on current energy reserves of nodes and the priority of data. The updated cost function \(J_{\eta}(t)\) is

\[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]9

For theoretical convergence Appendix F, we ensure a negative definiteness of the Lyapunov function's derivative:

\[\mathbf{I}_{i}(t)=\int_{0}^{t}\rho(\mathbf{y}_{i}(\tau),\mathbf{y}_{i}(\tau- \Delta t))e^{-\beta(t-\tau)}d\tau, \tag{15}\]0 \[\mathbf{I}_{i}(t)=\int_{0}^{t}\rho(\mathbf{y}_{i}(\tau),\mathbf{y}_{i}(\tau- \Delta t))e^{-\beta(t-\tau)}d\tau, \tag{15}\]1

## 4 Simulation and Evaluation

The simulation of the TEO-IoT framework is conducted using the NS-3 network simulator, which provides a detailed and scalable environment for testing the performance of large-scale IoT networks. The datasets utilized for evaluation include Edge-IIoTset [31], N-BaloT [32], and IoT-23 [33]. The simulation parameters used in NS-3 [34] include a bandwidth of 100 Mbps, a packet size of 1024 bytes, a simulation duration of 1000 s, and a mobility model for dynamic IoT nodes. The wireless communication range is set to 250 m, and the simulation environment models both urban and industrial IoT scenarios.