# Modular Bus Unit Scheduling for an Autonomous Transit System under Range and Charging Constraints
## 4 Computational Results
### Effects of the Dispatch Cost and Battery Capacity  
This subsection is devoted to the sensitivity analyses of scheduling solution economics with respect to the dispatch cost and battery capacity. Figure 5 illustrates the total costs of modular bus systems under various MB dispatch costs _c\({}_{m}\)_. The solid lines in four different colors represent four instances, while the corresponding dashed lines denote the total costs of traditional buses only as a control group without fluctuations. From Figure 5, we observe that as the cost of MB units increases, the total cost of the dispatch system gradually rises at a relatively uniform rate. Taking modular bus instance (2) as an illustration, the difference between consecutive points, denoted as \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{**Trip Sequence**} & **Number of Units Equipped with MB Platoon** & **Cumulative Energy Consumption (kWh)** & **Cost (S)** \\ \hline
16 & _o_-2-8-77-17-23-28-\(\varsigma\) & 1 & 15.16 & 50.17 \\
17 & _o_-1-68-9-16-22-\(\varsigma\) & 1 & 16.46 & 43.25 \\
18 & _o_-4-41-13-19-\(\varsigma\) & 3 & 52.13 & 100.79 \\ Total & \
\begin{tabular}{c} satisfying the demands of \\ 30 trips \\ \end{tabular} & 27 &
\begin{tabular}{c} Not exceeding the battery \\ capacity \\ \end{tabular} & 1144.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._C \(-\) A, represents the rate of change. When dispatching costs increase, the total number of modular buses dispatched and the scheme remain unchanged as modular buses are the sole vehicles involved in the scheduling process. Consequently, the increase in C \(-\) A, determined by the change value per modular bus ($5) multiplied by the total number of MB units in the instance, remains consistent throughout.  
Interestingly, the intersections between the solid line representing modular bus and the dashed line representing traditional bus vary across different instances. Specifically, in instances 1-4, these intersections occur at approximately $25, $25, $20, and $28 for the individual bus cost, respectively. This phenomenon primarily relates to the ratio of \((\mathrm{B}-\mathrm{A})/(\mathrm{C}-\mathrm{A})\), as exemplified in instance 2. Here, \(\mathrm{B}-\mathrm{A}\) represents the overall cost gap between the traditional bus system and the modular bus system at a dispatching cost of $5, while \(\mathrm{C}-\mathrm{A}\) represents the cost difference between any two adjacent points. The value of \(\mathrm{B}-\mathrm{A}\) signifies the economic gap between the two scheduling modes. When the modular bus scheduling mode better aligns with the trip organization and passenger demand in a given scenario compared to the fixed-capacity scheduling mode of traditional buses, a larger difference in \(\mathrm{B}-\mathrm{A}\) arises. We qualitatively speculate that in scenarios with low or fluctuating demand between trips, the fixed-capacity scheduling strategy of traditional buses is likely to result in wasted vehicle resources. In contrast, modular buses allow adjustments to capacity with coupling/decoupling techniques, thereby indicating an economic advantage. Based on the calculation of C \(-\) A (modular bus cost change step * total number of vehicles dispatched), the value of C \(-\) A is smaller when the fleet size is smaller. In summary, it is crucial to identify the cost balance between the modular and traditional bus systems, which enables operators to make economically viable decisions by considering the cost range of the modular bus system. For instance, when the advantages of the modular bus system are pronounced, even in the early development stages with higher costs (reflected in a larger \(\mathrm{B}-\mathrm{A}\) value), it can still offer profitability compared to the traditional bus. As modular bus technology advances and the individual vehicle  
Figure 5: The impact of modular bus dispatching cost on total system cost. cost decreases substantially, the modular bus system will increasingly dominate as the preferred option.