## 4 Analysis
### Markov Processes (Uncertainty Modeling)
#### 4.1.1 Defining the States  
Each state in the Markov process represents a key stage in the cargo movement process, capturing different conditions during transportation. These states help model transitions and help better understand cargo flow dynamics from Dar es Salaam Port to its hinterland destination.  
Cargo Waiting at Port represents goods awaiting processing and dispatch at the port. Delays may be caused by congestion or waiting for available transportation. Optimizing this state reduces waiting times and speeds up cargo turnover.  
Cargo in Transit refers to goods moving through the transport network. Factors like road conditions, travel distance, and traffic influence transit time. Reducing disruptions and improving network conditions can optimize this state.  
Cargo Delayed accounts for cargo experiencing delays due to issues like equipment failures or traffic disruptions. This state highlights the uncertainty in the transportation process, and understanding it helps manage risks and improve reliability.  
Cargo Successfully Delivered marks the completion of the journey, with goods reaching their destination. This state indicates a successful, efficient transport process. Optimizing this state ensures timely deliveries and enhances overall transport system performance.  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Month** & **Total Cargo (Tons)** & **Cargo Waiting at Port** & **Cargo in Transit** & **Cargo Delayed** & **Cargo Successfully Delivered** \\ \hline January & 1,400,000 & 210,000 & 700,000 & 140,000 & 350,000 \\ \hline February & 1,480,000 & 222,000 & 740,000 & 148,000 & 370,000 \\ \hline March & 1,620,000 & 243,000 & 810,000 & 162,000 & 405,000 \\ \hline April & 1,520,000 & 228,000 & 760,000 & 152,000 & 380,000 \\ \hline May & 1,570,000 & 235,500 & 785,000 & 157,000 & 392,500 \\ \hline June & 1,700,000 & 255,000 & 850,000 & 170,000 & 425,000 \\ \hline July & 1,560,000 & 234,000 & 780,000 & 156,000 & 390,000 \\ \hline August & 1,580,000 & 237,000 & 790,000 & 158,000 & 395,000 \\ \hline September & 1,650,000 & 247,500 & 825,000 & 165,000 & 412,500 \\ \hline October & 1,480,000 & 222,000 & 740,000 & 148,000 & 370,000 \\ \hline November & 1,460,000 & 219,000 & 730,000 & 146,000 & 365,000 \\ \hline December & 1,620,000 & 243,000 & 810,000 & 162,000 & 405,000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Monthly data: cargo flow in tonnage.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Month** & **Cargo Waiting at Port (\%)** & **Cargo in Transit (\%)** & **Cargo Delayed (\%)** & **Cargo Successfully Delivered (\%)** \\ \hline January & 14.00\% & 45.00\% & 8.00\% & 23.00\% \\ \hline February & 14.50\% & 46.00\% & 8.80\% & 24.00\% \\ \hline March & 15.50\% & 51.00\% & 11.00\% & 25.00\% \\ \hline April & 14.50\% & 47.00\% & 10.00\% & 24.50\% \\ \hline May & 14.70\% & 49.00\% & 10.50\% & 25.00\% \\ \hline June & 16.00\% & 55.00\% & 11.00\% & 25.00\% \\ \hline July & 14.60\% & 49.00\% & 10.00\% & 27.00\% \\ \hline August & 14.90\% & 50.00\% & 10.50\% & 25.00\% \\ \hline September & 15.50\% & 54.00\% & 10.00\% & 27.00\% \\ \hline October & 15.50\% & 48.00\% & 9.00\% & 24.00\% \\ \hline November & 15.00\% & 47.00\% & 9.00\% & 25.00\% \\ \hline December & 15.00\% & 54.00\% & 11.00\% & 25.00\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Cargo percentages for each month.  
These states and their transitions are probabilistic, informed by historical data, and guide efforts to improve cargo flow, reduce delays, and optimize transport efficiency.  
\(S_{1}\)\(\bullet\) Cargo waiting at port (before it gets processed for dispatch).  
\(S_{2}\)\(\bullet\) Cargo in transit (currently moving through the transport network).  
\(S_{3}\)\(\bullet\) Cargo delayed (either due to equipment failure or external disruptions).  
\(S_{4}\)\(\bullet\) Cargo successfully delivered (arrived at the hinterland destination).