## 4 Performance Evaluation of Proposed Scheme
### Simulation Results
and 31.25% when compared against MRMQoS and MCSTM for a network size of 25. These percentages highlight the environmental benefits of the proposed model, showcasing its capacity to contribute to a more sustainable and eco-friendly transportation system. Overall, the proposed model's superior performance in minimizing CO2 emissions underscores its efficacy and potential for promoting environmentally conscious decision-making in multimodal transportation networks. The performance improvement gain of the proposed model against MRMQoS and MCSTM is given in Table 2.  
In certain instances, the imposition of QoS constraints on a chosen multicast tree often results in its rejection. Consequently, in the subsequent experiments, we explored an extension of our proposed approach wherein the overall weight of a multicast tree must also conform to a budget constraint. This problem is commonly identified as a constrained Steiner tree problem, well-known for its NP-hard nature [31]. A specific manifestation of this model is widely acknowledged as a constrained shortest path problem, a crucial challenge in optimization domains such as transportation, crew scheduling, network routing, and communication networks [32]. The constrained shortest path problem entails identifying the shortest path that adheres to specific constraints, such as delay and cost. Our proposed method was initially employed to calculate the cost, delay, and profit of the selected multicast tree. Subsequently, these metrics were compared with the multicast tree resulting from the variation in MRMQoS using two distinct strategies, with the aim of evaluating the solution quality of the proposed method. Figure 6 visually illustrates the cost comparison of multicast trees obtained for the proposed method and the variable MRMQoS, along with their two strategies. The results align with our expectations, highlighting the proposed method's capacity to discover optimal multicast trees within a reasonable timeframe. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Network**} & \multicolumn{5}{c}{**MRMQoS**} & \multicolumn{5}{c}{**MCSTM**} \\ \cline{2-10}  & \multirow{2}{*}{**Cost**} & & \multirow{2}{*}{**Delay**} & & \multirow{2}{*}{**Profit**} & \multicolumn{2}{c}{**CPU**} & \multicolumn{2}{c}{**CO2**} & \multirow{2}{*}{**Cost**} & & \multirow{2}{*}{**Delay**} & \multirow{2}{*}{**Profit**} & \multicolumn{2}{c}{**CPU**} & \multicolumn{2}{c}{**CO2**} \\  & & & & & & & & & & **Time** & **Emissions** \\ \hline
15 & \(-\)23.53\% & \(-\)5.8\% & \(-\)10.5\% & 14.3\% & 32.1\% & 0.2\% & 0.3\% & 0.2\% & 0\% & 48.5\% \\
25 & \(-\)19.04\% & 0.1\% & \(-\)8.3\% & 9.5\% & 7.26\% & 0\% & 32.9\% & 11.7\% & \(-\)1.6\% & 31.25\% \\
35 & \(-\)29.03\% & \(-\)2.6\% & \(-\)8.2\% & 15.4\% & 4.66\% & 0\% & 13.2\% & 20.8\% & \(-\)1.3\% & 18.3\% \\
45 & \(-\)31.37\% & \(-\)5.9\% & \(-\)28.6\% & 11.1\% & 6.15\% & 0.1\% & 30.5\% & 11\% & \(-\)10\% & 13.9\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance improvement gain of proposed model against MRMQoS and MCSTM. Figure 6: Comparison of proposed model with avg. cost multicast tree fixed delay and avg. cost multicast tree fixed profit. In the initial approach, we evaluated the mean cost of the multicast tree resulting from variations in MRMQoS, where the delay parameter D was held constant, while the profit parameter P was adjusted within the range of \(\text{P}_{\text{DEA}}-10\) to \(\text{P}_{\text{DEA}}+10\). The solution quality is notably influenced by the profit requirement P, and surpassing a specific threshold renders the acquisition of the primal solution unfeasible. Subsequently, in the second approach, we maintained the profit parameter P at the \(\text{P}_{\text{DEA}}\) level and varied the delay parameter D from \(\text{D}_{\text{DEA}}-10\) to \(\text{D}_{\text{DEA}}+10\).