# Analyzing the Economic Performance of a TLS-Based Structural Safety Diagnosis Process
## 3 Results
### Queuing Model Results (M/M/1 vs. M/D/1)  
In this study, queueing theory was applied, treating the investigation targets as \"customers\" and deployed personnel as a single \"server\". The traditional manpower-based diagnostic approach, characterized by significant variability due to manual labor, was modeled using an M/M/1 queue, following an exponential distribution. In contrast, the TLS-based 3D scanning reverse modeling diagnostic method employed the M/D/1 model due to the nearly constant service times facilitated by scanning equipment. In Project A, the fire-damaged area was 21,550 m\({}^{2}\), and, assuming an 8 h workday over periods of 40 days (visual inspection method) and 14 days (TLS-based 3D scanning reverse modeling method), the arrival rate (\(\lambda\)) was calculated by dividing the total investigation area by the total work hours. Comparing the service rates (\(\mu\)) based on the actual task duration, the traditional method (M/M/1) achieved a service rate (\(\mu\)) of 538.75 m\({}^{2}\)/hour, while the TLS-based 3D scanning reverse modeling method (M/D/1) increased efficiency to 1538.29 m\({}^{2}\)/hour. As a result, the server utilization (\(\rho\)) decreased significantly from 0.91 to 0.32. Additionally, the average number of customers (L) in the system reduced dramatically from approximately 10 m\({}^{2}\) to 0.47 m\({}^{2}\), and the average waiting time per 1 m\({}^{2}\) (W) was substantially shortened from 1.2 min to approximately 0.06 min (3.6 s). \begin{table}
\begin{tabular}{c c c c c} \hline
**Classification** & **Method** & **Labor Input** & \multicolumn{2}{c}{**Process**} \\ \hline \multirow{4}{*}{Project A} & Visual inspection & \multirow{2}{*}{4 people/40 days} & – & Visual and precise measurement of each fire-damaged area \\  & & & – & Determine the extent of damage \\  & & & – & Analyze and write a report \\ \cline{2-5}  & \multirow{2}{*}{TLS inspection} & \multirow{2}{*}{3 people/14 days} & – & Set up scanning points (89 locations) and scan all of them \\  & & & – & Identify deformation and damage of members with 3D \\  & & & – & models \\  & & & – & Calculate the amount \\ \hline \multirow{4}{*}{Project B} & Visual inspection & \multirow{2}{*}{10 people/ 80 days} & – & Basic visual and sample measurement \\  & & & 80 days & Separate drawing and detailed inspection \\ \cline{2-5}  & \multirow{2}{*}{TLS inspection} & \multirow{2}{*}{6 people/55 days} & – & Scanning (192 points) and point cloud integration \\  & & & – & Modeling of steel member dimensions and corrosion \\  & & & – & Structural analysis and derivation of repair plan \\ \hline \multirow{4}{*}{Project C} & Visual inspection & \multirow{2}{*}{10 people/ 154 days} & – & Measurement of all sections of the site (2743 m) \\  & & & – & Manual drawing \\ \cline{1-1}  & & & – & Structural analysis \\ \cline{1-1} \cline{2-5}  & \multirow{2}{*}{TLS inspection} & \multirow{2}{*}{5 people/66 days} & – & Setting scanning points for 13 sections \\ \cline{1-1}  & & & – & BIM modeling after integrating TLS data \\ \cline{1-1}  & & & – & Displacement analysis and report preparation \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of work inputs and processes between visual inspection and TLS-based 3D scanning reverse modeling methods. In Project B, the service rate (\(\mu\)) increased from 65 m\({}^{2}\)/hour (visual inspection method, M/M/1) to 94.55 m\({}^{2}\)/hour (TLS-based 3D scanning reverse modeling, M/D/1). Consequently, the server utilization (\(\rho\)) decreased from 0.91 to 0.62, the average number of customers in the system (L) dropped from 10 m\({}^{2}\) to 1.15 m\({}^{2}\), and the average waiting time (W) significantly improved from 10.14 min to 1.14 min. In Project C, the service rate (\(\mu\)) more than doubled from 17.81 m\({}^{2}\)/hour (visual inspection method) to 41.56 m\({}^{2}\)/hour (TLS-based 3D scanning reverse modeling method).