## 6 Results and Discussions
### Simulation of the Monitoring and Control of Parking Lots in the North of a City
#### 6.2.4 Selecting the Level of Service in a Parking Lot System  
In general, it is possible to generate through the simulation a series of measures that can be evaluated by decision-makers for the dimensioning of an IoT system model that includes an M/M/c/N queue system. For this, we carried out a series of simulation experiments to find the optimal values of the system dimensioning. The input parameters \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Performance Measures**} & \multicolumn{4}{c}{**N = c + QC**} \\ \cline{3-6} \multicolumn{2}{c}{} & **20** & **40** & **60** & **80** & **100** \\ \hline \multirow{4}{*}{\(\mu\) = 0.20} & Lq & 9.8863932 & 9.5689731 & 9.0070227 & 7.6498940 & 4.7682230 \\ \cline{2-6}  & Wq & 4.8665900 & 1.5941355 & 0.9007077 & 0.5445835 & 0.2680882 \\ \cline{2-6}  & Ls & 19.8858434 & 39.5632003 & 58.9874069 & 77.5478518 & 93.5819453 \\ \cline{2-6}  & Ws & 9.7894685 & 6.5909675 & 5.8971575 & 5.5409546 & 5.2532598 \\ \hline \multirow{4}{*}{\(\mu\) = 0.25} & Lq & 9.8555745 & 9.3928611 & 8.3538130 & 5.1568331 & 0.5429347 \\ \cline{2-6}  & Wq & 3.9298670 & 1.2437033 & 0.6710817 & 0.2962513 & 0.0267680 \\ \cline{2-6}  & Ls & 19.8550151 & 39.3872245 & 58.3196181 & 74.2702010 & 79.3120437 \\ \cline{2-6}  & Ws & 7.9156135 & 5.2155032 & 4.6785485 & 4.2805763 & 4.0008064 \\ \hline \multirow{4}{*}{\(\mu\) = 0.333} & Lq & 9.8026714 & 8.9884630 & 6.0432631 & 0.4625112 & 0.0002394 \\ \cline{2-6}  & Wq & 2.9802091 & 0.9024992 & 0.3654972 & 0.0231127 & 0.0000122 \\ \cline{2-6}  & Ls & 19.8020543 & 38.9818001 & 55.6618919 & 60.3579146 & 59.8714172 \\ \cline{2-6}  & Ws & 6.0222461 & 3.9150850 & 3.3678719 & 3.0178405 & 2.9874388 \\ \hline \multirow{4}{*}{\(\mu\) = 0.40} & Lq & 9.7510344 & 8.4962144 & 2.8260818 & 0.0077262 & 0.0000000 \\ \cline{2-6}  & Wq & 2.4585182 & 0.7082706 & 0.1488769 & 0.0004131 & 0.0000000 \\ \cline{1-1} \cline{2-6}  & Ls & 19.7504318 & 38.4837565 & 50.2103554 & 50.0408668 & 49.6733216 \\ \cline{1-1} \cline{2-6}  & Ws & 4.9807359 & 3.2049578 & 2.6380632 & 2.4969140 & 2.5017118 \\ \hline \multirow{4}{*}{\(\mu\) = 0.45} & Lq & 9.7096445 & 8.0197927 & 0.9182672 & 0.0000100 & 0.0000000 \\ \cline{1-1} \cline{2-6}  & Wq & 2.1612553 & 0.5973917 & 0.0468604 & 0.0000003 & 0.0000000 \\ \cline{1-1} \cline{2-6}  & Ls & 19.7089036 & 37.9874633 & 44.8559913 & 44.4241978 & 44.5504995 \\ \cline{1-1} \cline{2-6}  & Ws & 4.3871795 & 2.8274819 & 2.2700039 & 2.2243556 & 2.2287925 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: The effect of variation of parameter \(\mu\) 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). for the simulations were \(\lambda\) = 20 cars/h, \(\mu\)= 0.333 cars/h, and QC = 10 cars. Table 13 shows some results obtained in each simulation that allows us to observe some variations in performance measures for various dimensions of the system (c). Figure 23 summarizes the system performance measures for some variations in the number of parking spaces using an M/M/c/N queue system with \(\lambda\)= 20 cars/h, \(\mu\)= 0.333 cars/h, and QC = 10 cars. Additionally, to establish an appropriate service level, the use of the aspiration level model was promoted. This model provides a balance between service level and waiting [39]. Given the experimental scope of our study, we had put aside the use of the cost model due to the difficulty of estimating waiting costs. The problem reduced to determining the number of servers c such that:  
The constants a and b are the levels of aspiration specified by the decision-maker. We can determine an acceptable number of servers around these criteria as shown in Figure 24. For example, for a = 3.5 h and b = 5%, we had an aspiration level with an average system time (h) \(\leq\) 3.5 and average number of idleness servers (%) \(\leq\) 5, which resulted in a number of servers between 42 and 62.