## 5 Simulation Results and Discussions
### Routing Overhead  
In the evaluation of routing overhead, this study considers two key dimensions: communication overhead and storage overhead. For communication overhead, as outlined  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Number of Nodes** & **30** & **40** & **50** & **60** & **70** & **80** & **90** & **100** \\ \hline Traj-Q-GPSR & 27.1 & 53.3 & 112.5 & 172.3 & 232.8 & 290.1 & 345.5 & 374.7 \\ GPSR & 48.9 & 83.7 & 153.2 & 199.8 & 266.6 & 332.1 & 420.3 & 453.7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Energy consumption (J) based on the number of nodes.  
Figure 7: Curve of energy consumption (J) vs. number of nodes.  
in the system model section, trajectory information is periodically disseminated through HELLO packets that encapsulate positional beacons. The structure of the HELLO packet, as detailed in Tables 3 and 4, extends the standard GPSR format by embedding trajectory-related fields, without introducing additional control message types. To rigorously quantify the cost of control traffic, we adopt the Byte-Level Routing Overhead Ratio (BROR) as a measurement metric [45]. This indicator captures the proportion of routing-related bytes relative to the total transmission, offering a fine-grained view of protocol efficiency at the byte level. The BROR is defined as  
\[\text{BROR}=\frac{\text{Control~{}Bytes}}{\text{Control~{}Bytes}+\text{ Average~{}Data~{}Payload~{}Bytes}}\]  
This formulation enables an objective assessment of protocol-induced overhead throughout the simulation period, independent of packet counts or sizes.  
Figure 8 and Table 5 present a comparative analysis of the byte-level routing overhead ratio (BROR) for Traj-Q-GPSR and the conventional GPSR protocol under varying node densities. As anticipated, Traj-Q-GPSR incurs a slightly higher overhead due to the incorporation of trajectory-related information in control packets. Nevertheless, as the network density increases, improved connectivity and higher throughput contribute to a steady decline in BROR for both protocols. Importantly, the overhead gap between Traj-Q-GPSR and GPSR diminishes from 0.57% at low density to 0.32% in high-density scenarios. These findings suggest that, while the proposed protocol introduces marginally greater control traffic, this cost is effectively amortized in denser topologies. More significantly, the gains in routing stability and overall network efficiency justify the additional overhead introduced by the trajectory-aware mechanism.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Field Name** & **Size (Bytes)** \\ \hline Packet Type & 1 \\ Number of Neighbors & 2 \\ Node ID & 2 \\ Current Coordinates \((x,y,z)\) & 24 \\ Current Queue Length & 1 \\ Current Energy Level & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: A format table of packet header.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Field Name** & **Size (Bytes)** \\ \hline Packet Type & 1 \\ Number of Neighbors & 2 \\ Node ID & 2 \\ Current Coordinates \((x,y,z)\) & 24 \\ Current Queue Length & 1 \\ Current Energy Level & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: A HELLO packet header format table.  
This work extends the conventional one-hop neighbor table to a time-aware two-hop structure and employs Q-tables within a Q-learning framework, thereby incurring greater memory overhead compared to GPSR. Since storage requirements grow with neighbor count, node density is the dominant factor affecting memory cost.  
Table 6 presents the average number of neighbor entries maintained by Traj-Q-GPSR and GPSR under different node densities. The results indicate that Traj-Q-GPSR experiences accelerated growth in storage load as density increases, yet remains within acceptable limits, reflecting a balance between enhanced topological awareness and resource efficiency.