## 4 Analysis
### Sensitivity Analysis of All Models
#### 4.4.3. Traffic Flow Sensitivity Analysis  
1. Base travel time adjustment: Travel times are scaled by the sensitivity factor \(f\)  
\[T\prime=T\cdot(1+f)\]  
where T is the original travel time for a vehicle type, and \(f\) is the adjustment factor. 1. Slowdown Probability Adjustment: Random slowdown probabilities were similarly adjusted:  
\[p\prime=p\cdot(1+f)\]
2. Adjust Parameters Travel times and random slowdowns were adjusted by \(\pm\)10% and \(\pm\)20%. For heavy trucks, with f = +0.1: T\({}^{\prime}\) = 45\(\cdot\)(1 + 0.1) = 49.5 min
3. Travel Times Heavy Trucks: \(\circ\) Base: 45 min \(\circ\) f = +0.2: 54 min \(\circ\) f = -0.2: 36 min \(\circ\) Cars: \(\circ\) Base: 30 min \(\circ\) f = +0.2: 36 min \(\circ\) f = -0.2: 24 min \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Route**}} & \multicolumn{1}{c}{**Base**} & \multicolumn{1}{c}{**Base**} & \multicolumn{1}{c}{**Adjusted**} & \multicolumn{1}{c}{**Adjusted**} & \multicolumn{1}{c}{**Adjusted**} & \multicolumn{1}{c}{**Adjusted**} & \multicolumn{1}{c}{**Adjusted**} \\  & **Capacity** & **Demand** & **Capacity** & **Capacity** & **Capacity** & **Capacity** & **Capacity** & **Capacity** \\  & **(Tons/Day)** & **(Tons/Day)** & **(-20\%)** & **(-10\%)** & **(0\%)** & **(+10\%)** & **(+20\%)** \\ \hline Dar es Salaam \(\rightarrow\) Kampala & 60,000 & 2500 & 48,000 & 54,000 & 60,000 & 66,000 & 72,000 \\ \hline Dar es Salaam \(\rightarrow\) Kigali & 36,000 & 1200 & 28,800 & 32,400 & 36,000 & 39,600 & 43,200 \\ \hline Dar es Salaam \(\rightarrow\) Lusaka (Road) & 43,200 & 1800 & 34,560 & 38,880 & 43,200 & 47,520 & 51,840 \\ \hline Dar es Salaam \(\rightarrow\) Lusaka (Rail) & 1500 & 1500 & 1200 & 1350 & 1500 & 1650 & 1800 \\ \hline Dar es Salaam \(\rightarrow\) Bujumbura & 31,200 & 1000 & 24,960 & 28,080 & 31,200 & 34,320 & 37,440 \\ \hline Dar es Salaam \(\rightarrow\) Lliongwe & 28,800 & 1200 & 23,040 & 25,920 & 28,800 & 31,680 & 34,560 \\ \hline Dar es Salaam \(\rightarrow\) Lubumbashi & 48,000 & 2500 & 38,400 & 43,200 & 48,000 & 52,800 & 57,600 \\ \hline \hline \end{tabular}  
Most routes maintain full demand satisfaction, except Dar es Salaam \(\rightarrow\) Lubumbashi, which faces a shortfall at \(-20\%\) and \(-10\%\), reaching full demand from 0% adjustment onwards. As shown in Table 9: Demand satisfaction (adjusted capacities vs. demand)  
\begin{tabular}{l c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Route**}} & \multicolumn{1}{c}{**Factor \(-\)20\%**} & \multicolumn{1}{c}{**Factor \(-\)10\%**} & \multicolumn{1}{c}{**Factor 0\%**} & \multicolumn{1}{c}{**Factor +10\%**} & \multicolumn{1}{c}{**Factor +20\%**} \\ \hline Dar es Salaam \(\rightarrow\) Kampala & 2500 & 2500 & 2500 & 2500 & 2500 \\ \hline Dar es Salaam \(\rightarrow\) Kigali & 1200 & 1200 & 1200 & 1200 & 1200 & 1200 \\ \hline Dar es Salaam \(\rightarrow\) Lusaka (Road) & 1800 & 1800 & 1800 & 1800 & 1800 & 1800 \\ \hline Dar es Salaam \(\rightarrow\) Lusaka (Rail) & 1500 & 1500 & 1500 & 1500 & 1500 & 1500 \\ \hline Dar es Salaam \(\rightarrow\) Bujumbura & 1000 & 1000 & 1000 & 1000 & 1000 \\ \hline Dar es Salaam \(\rightarrow\) Lliongwe & 1200 & 1200 & 1200 & 1200 & 1200 & 1200 \\ \hline Dar es Salaam \(\rightarrow\) Lubumbashi & 2000 & 2250 & 2500 & 2500 & 2500 \\ \hline \hline \end{tabular}  
\end{table} 
Table 9: Demand satisfaction (adjusted capacities vs. demand)The sensitivity analysis offers insights into the models' robustness and parameter responses. For Markov processes, adjusting transition probabilities (\(\pm\)20%) showed notable changes in steady-state probabilities. The \"cargo successfully delivered\" probability rose from 25% to 30% with a 20% delay reduction, emphasizing the need to reduce congestion and improve equipment reliability as shown in Figure 4. However, uniform scaling oversimplifies complexities like weather and equipment failures. In max-flow problems, bottlenecks and excess capacities were identified.