## 6 Results and Discussions
### Simulation of the Monitoring and Control of Parking Lots in the North of a City
#### 6.2.3 Sensitivity of the M/M/c/N Submodel Parameters
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Performance Measures**} & \multicolumn{5}{c}{**N = c + QC**} \\ \cline{3-8}  & \multicolumn{1}{c}{\(\mathbf{20}\)} & \multicolumn{1}{c}{\(\mathbf{40}\)} & \multicolumn{1}{c}{\(\mathbf{60}\)} & \multicolumn{1}{c}{\(\mathbf{80}\)} & \multicolumn{1}{c}{\(\mathbf{100}\)} \\ \hline \multirow{4}{*}{\(\lambda=18\)} & Lq & 9.7680287 & 8.7731639 & 4.2386577 & 0.0574124 & 0.0000000 \\ \cline{3-8}  & Wq & 2.9049968 & 0.8819170 & 0.2617368 & 0.0031796 & 0.0000000 \\ \cline{3-8}  & Ls & 19.7674165 & 38.7650848 & 53.0444338 & 53.7451905 & 53.7221771 \\ \cline{3-8}  & Ws & 5.8802601 & 3.8972909 & 3.2707136 & 2.9995683 & 2.9906034 \\ \hline \multirow{4}{*}{\(\lambda=19\)} & Lq & 9.7857790 & 8.8963941 & 5.0577142 & 0.1548115 & 0.0000210 \\ \cline{3-8}  & Wq & 2.9516445 & 0.8956879 & 0.3057474 & 0.0084220 & 0.0000027 \\ \cline{3-8}  & Ls & 19.7851786 & 38.8888549 & 54.2292723 & 56.9578859 & 57.3252534 \\ \cline{3-8}  & Ws & 5.9698368 & 3.9152395 & 3.2833324 & 3.0026420 & 3.0083440 \\ \hline \multirow{4}{*}{\(\lambda=20\)} & Lq & 9.7993401 & 8.9989178 & 6.0102552 & 0.4050986 & 0.0000000 \\ \cline{3-8}  & Wq & 2.9356919 & 0.9007006 & 0.3658240 & 0.0208122 & 0.0000008 \\ \cline{3-8}  & Ls & 19.7987141 & 38.9913721 & 55.6044419 & 60.1219889 & 60.3234000 \\ \cline{3-8}  & Ws & 5.9333933 & 3.9023497 & 3.3791768 & 3.0301136 & 3.0038029 \\ \hline \multirow{4}{*}{\(\lambda=21\)} & Lq & 9.8094943 & 9.0844409 & 6.6684213 & 0.8048002 & 0.0006822 \\ \cline{3-8}  & Wq & 2.9403526 & 0.9062943 & 0.4025095 & 0.0384241 & 0.0000318 \\ \cline{3-8}  & Ls & 19.8089609 & 39.0789421 & 56.4512113 & 62.7442819 & 62.3487029 \\ \cline{3-8}  & Ws & 5.9367949 & 3.9008090 & 3.4017842 & 3.0320373 & 2.9949809 \\ \hline \multirow{4}{*}{\(\lambda=22\)} & Lq & 9.8192339 & 9.1647395 & 7.1485597 & 1.4979797 & 0.0087552 \\ \cline{3-8}  & Wq & 2.9595867 & 0.9134098 & 0.4304650 & 0.0703336 & 0.0003686 \\ \cline{3-8}  & Ls & 19.8187323 & 39.1588491 & 57.0144941 & 65.9122711 & 65.8330126 \\ \cline{3-8}  & Ws & 5.9753214 & 3.9008317 & 3.4366650 & 3.0676521 & 3.0016503 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The effect of variation of parameter \(\lambda\) on performance measures, expected number of customers in system (Ls), expected number of customers in queue (Lq), expected waiting time in system (Ws), and expected waiting time in queue (Wq). Effect of Changes in the Service Rate  
These effects were analyzed using the following settings:  
\(\lambda\) = 20 cars/hour;  
\(\mu\) = [0.20, 0.25, 0.333, 0.40, 0.45];  
N = [20,40,60,80,100];  
QC = 10. The effect of system parameters on performance measures is summarized in Table 12. An increase of \(\mu\) caused the expected number of customers in queue and the expected waiting time in the queue to decrease. Additionally, an increase of \(\mu\) produced a decrease in the expected number of customers and in the expected waiting time in system. Both the increase in the number of parking spaces and the increase in the value of \(\mu\) caused the expected number of customers in queue to decrease. The effect of \(\lambda\) on system congestion was the reverse of the effect of \(\mu\). Furthermore, since c and \(\mu\) affect system congestion in the same way, the effects of these parameters on the system were similar.