## 5 Discussion  
The analysis of Dar es Salaam Port using Markov processes, cellular automata, and max-flow models provides a comprehensive view of the port's operational dynamics and reveals several key insights into its performance and areas for improvement. The Markov process model illustrates the flow of cargo through various stages: waiting at the port, in transit, delayed, and successfully delivered. Based on the transition probabilities, cargo \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Parameter Adjusted** & **Sensitivity Factors** & **Key Observations** & **Insights for Optimization** \\ \hline Markov Processes & Transition Probabilities & \(\pm 10\%\), \(\pm 20\%\) & \begin{tabular}{c} A delay reduction of \\ 20\% increased cargo \\ delivery probability \\ from 25\% to 30\% \\ \end{tabular} & \begin{tabular}{c} Reducing congestion \\ and improving \\ equipment reliability \\ enhances cargo \\ handling efficiency \\ \end{tabular} \\ \hline Max-Flow Problems & Capacity Adjustments & \begin{tabular}{c} \(-20\%\), \(-10\%\), \(0\%\), \\ +10\%, +20\% \\ \end{tabular} & \begin{tabular}{c} Bottleneck identified on \\ Lubumbashi route (500-ton/day shortfall); \\ excess capacity can be \\ observed in Kigali \\ (300-ton/day unused) \\ \end{tabular} & \begin{tabular}{c} Expansion required for \\ bottleneck routes; \\ excess capacity can be \\ allocated for future \\ demand \\ \end{tabular} \\ \hline Traffic Flow Models & Travel Time and & \begin{tabular}{c} \(\pm 10\%\), \(\pm 20\%\) \\ Slowdowns \\ \end{tabular} & \
\begin{tabular}{c} Heavy truck travel time \\ increased from 45 min \\ to 54 min (+20\%) under \\ rainy conditions; \\ slowdown probability \\ rose from 0.3 to 0.5 \\ \end{tabular} &
\begin{tabular}{c} Road maintenance and \\ improved congestion \\ management are \\ crucial for traffic \\ efficiency \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Summary of sensitivity analysis results. Figure 6: Traffic flow sensitivity analysis: travel time under slowdown variations. spends approximately 15% of its time waiting at the port. This figure suggests that there could be inefficiencies in port handling or capacity constraints that need addressing. Improving port operations or expanding capacity could potentially reduce this waiting time, thereby increasing overall throughput. Cargo in transit represents 50% of the time, which is a substantial portion of the cargo's lifecycle. This indicates that the transit phase is a major component of the overall process, and optimizing this phase could lead to significant improvements. Enhancing route planning, employing real-time traffic data, and reducing bottlenecks in the transportation network are potential strategies to address this. Delays account for 10% of the time, reflecting issues such as equipment failures, congestion, or other disruptions. Addressing the root causes of these delays is crucial for improving overall efficiency. Investments in infrastructure maintenance, better traffic management, and improved equipment reliability could help reduce this delay rate. The model also reveals that only 25% of the cargo is delivered successfully. This lower-than-expected delivery rate highlights the need for improved mechanisms in the final delivery phase. Strategies such as better coordination with hinterland destinations, optimizing delivery routes, and improving handling processes could help increase the delivery success rate. The cellular automata model simulates traffic flow on a 20 km stretch of road connecting Dar es Salaam Port to the primary highway network. The simulation considers road conditions, vehicle types, and environmental factors, offering a detailed picture of traffic dynamics. The simulation starts with 900 vehicles distributed across the 20 km stretch, with a mix of 60% heavy trucks and 40% smaller vehicles. Heavy trucks face significant delays, averaging 45 min for the 20 km stretch, primarily due to poor road conditions and construction zones.