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Chapter 4
Numerical Results
In this chapter, we outline the numerical results of the three cases. First of all, there are extensive discussions on these cases by using the date collected in Taoyuan International Airport.
We will get some useful conclusions of the proposed model. In the final part of this Chapter, we will use the data collected in the other two international airports to strengthen our conclusions.
To begin with Case A, Table 4.1 presents the parameters computed using the proposed esti-mation method.
Table 4.1: Numerical results of Case A
a b aR bR c2S EWA
1
1771.75 0.0016 1771.751 0.0022 1.6336 1.434
Thus, we obtain the numerical results of Case B, as shown in Table 4.2.
Table 4.2: Numerical results of Case B
SH SM SL WH WM WL EWB
22.64 28.77 62.72 7.668 1.626 7.080 3.86
It should be noted that Case C achieves an average waiting time shorter than that of Case B,
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as anticipated. In the following, we present the optimal numerical results obtained via simulated annealing with a given fixed minimum requirement D. Table 4.3 below presents the range of controllable parameters used in simulated annealing.
Table 4.3: The range of parameters used in simulated annealing at Taoyuan airport
M h m pM pL
[70, 100] [1, 20] [1, 20] [0, 1] [0, 1]
Then, the optimal solutions can be found in Table 4.4, we assume D = 0.02 in this part, and the process of finding the optimal solutions is presented in Figure 4.1, the upper part of this figure shows that the changing of feasible solutions varies with iterations, the lower part demonstrates the changing of optimal solutionEWC. In the search for an optimal solution, we also record the changes in proportion p of all passengers transferred from M-lane to H-lane.
Figure 4.2 presents a comparison between p and the current feasible solution EWC.
Table 4.4: Optimal solutions by simulated annealing of Case C with fixedD at Taoyuan airport
D M h m pM pL EWC WH WM WL
0.02 100 2 4 0.28 0.99 2.359 10.419 1.403 1.474
As indicated above, the relationship between EWC and p is unpredictable rather than linear.
Nonetheless, the simulation has an optimal solution, which can be found via simulated anneal-ing. Compared to Case B, Case C shortens the average waiting time in L-lane and M-lane but extends the waiting time in H-lane, resulting in an overall decrease. A lack of passengers in higher level lanes will tend to attract passengers from lower level lanes. However, it is neces-sary to ensure that p is not less than D at any point during this period. Thus, in the following, we discuss the changes to the configuration of parameters and the average waiting time with different values forD.
Table 4.5 lists the optimal parameter configurations with various values forD. An increase in D was shown to increase EWC; however, the effect is not significant. Figure 4.3 can reflect
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Figure 4.1: Process of finding the optimal solution withD =0.02 at Taoyuan airport
Figure 4.2: Comparison between proportionp and current average waiting time EWCwithD = 0.02 at Taoyuan airport
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this trend more directly. The thresholdsh and m can be adjusted in accordance with the value for D. As shown in Figure 4.4, an increase in D makes the requirements for the security inspection system more stringent, which leads to an increase inh, while the value of m remains unchanged.
Table 4.5: Optimal solutions at Taoyuan airport by simulated annealing of Case C with different D at Taoyuan airport
In the next part, we discuss the issue of proportions pM andPL, which send passengers to a higher level lane from lower lane. Figure 4.5 presents the results of this situation. The result is somewhat non-intuitive: an increase in D results in the transfer of a smaller proportion of arriving passengers from M-lane to H-lane, such that the value of pMdrops steadily, as shown in Figure 4.5. Nonetheless, we know that the thresholdh gradually increases, which drives up the overall number of passengers being transferred. At the same time, the threshold ofM-lane remains constant; therefore, the value of pL remains equal to 1.
Following the statements above, we will change some of the model configurations to check that the conclusions are still holds. Table 4.6 shows the arrival schedules at Narita Airport which are collected from 10:30 to 14:30. So we have the average total arrival rate during the period at Narita Airport is 1770.5 per hour, which is very close the data we collected at Taoyuan airport.
But we use different proportions to assign the number of passengers to the three lanes. In this time, we assume that 70% of arrival passengers, in which 65% of them are assigned toM-lane and 5% of them are assigned toH-lane. Thus 30% of arrival passengers are allocated to L-lane.
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Figure 4.3: The average waiting timeEWC of differentD at Taoyuan airport
Figure 4.4: The thresholdsh and m of different D at Taoyuan airport
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Figure 4.5: The proportions pMandpL of differentD at Taoyuan airport
Since the number of arrival passenger is close to that at Taoyuan airport, we use the same service rates of three lanes. Table 4.7 demonstrates this assignment. The range of parameters we used in simulated annealing method is still the same as we did at Taoyuan airport.
Table 4.6: Arrival schedules at Narita airport
Time Period Number of Flights Number of Passengers
10:30 - 11:30 16 4075
11:30 - 12:30 5 986
12:30 - 13:30 3 630
13:30 - 14:30 6 1391
We directly obtain the optimal solutions via simulated annealing method with different D in the Table 4.8. In this configuration, we can still get the similar conclusions. Nevertheless, the only difference is that the optimal configurations ofM at Taoyuan airport occur at the upper bound of its range, while at Narita airport, the optimal configurations ofM become varied with the increase of the minimum requirement D but there is no strict rules. It can be intuitively
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Table 4.7: Parameters used in simulation at Narita airport Classes Proportion Arrival Rate Total Service Rate
H-class 5% 88.525 185
M-class 65% 1150.825 1100
L-class 30% 531.15 540
observed from Figure 4.6. As the same methods we dealing with at Taoyuan airport, the com-parison between proportion p and current average waiting time EWC at Narita airport is given in Figure 4.7, the average waiting timeEWCof differentD is given in Figure 4.8, and the thresholds h and m of different D are given in Figure 4.9. Also, Figure 4.10 demonstrates the proportions pMand pL of differentD.
Table 4.8: Optimal solutions by simulated annealing with differentD at Narita airport
D M h m pM pL EWC
Since the average arrival rates collected at Taoyuan airport and Narita airport are almost equal, we have collected data from different time periods at Sydney International Airport. Ta-ble 4.9 gives the arrival schedules.
From Table 4.9, the average arrival rate at Sydney airport during 18:00-22:00 is 1140.5 per hour, which is quite smaller than that at Taoyuan airport. We allocate the passengers according to the same proportions at Taoyuan airport. Therefore, 60% of them and 10% of them are assigned toM-lane and H-lane. On contrary, 30% of arrival passengers are allocated to L-lane. Similarly,
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Figure 4.6: The buffer sizeM of different D at Narita airport
Figure 4.7: Comparison between proportionp and current average waiting time EWCwithD = 0.2 at Narita airport
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Figure 4.8: The average waiting time EWC of differentD at Narita airport
Figure 4.9: The thresholdsh and m of different D at Narita airport
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Figure 4.10: The proportions pMandpL of differentD at Narita airport
Table 4.9: Arrival schedules at Sydney airport Time Period Number of Flights Number of Passengers
18:00 - 19:00 8 1956
19:00 - 20:00 3 595
20:00 - 21:00 0 0
21:00 - 22:00 6 2311
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we give the appropriate service rate in this case, Table 4.10 summarizes the information about parameters used in simulation at Sydney airport.
Table 4.10: Parameters used in simulation at Sydney airport Classes Proportion Arrival Rate Total Service Rate
H-class 10% 114.05 125
M-class 60% 684.30 720
L-class 30% 342.15 380
After optimization using the simulated annealing method, we get the optimal solutions at Sydney airport. Table 4.11 demonstrates the configuration of parameters with different D.
Therefore we can find that, although the number of passenger is declined, the parameters with two sets of data have the same variation with increase of D. Figure 4.11 to Figure 4.14 are showing the changing of various parameters, which all have maintained the same trend with the previous case at Taoyuan airport.
Table 4.11: Optimal solutions by simulated annealing with differentD at Sydney airport
D M h m pM pL EWC
0 100 1 2 0.99 0.99 1.752
0.05 100 2 2 0.26 1 1.782
0.10 100 3 2 0.12 0.99 1.809 0.15 100 3 2 0.05 0.99 1.824 0.20 100 4 2 0.04 0.99 1.836
0.25 100 5 2 0.03 1 1.849
0.30 100 6 2 0.02 0.99 1.864
0.35 100 7 2 0.02 1 1.873
0.40 100 7 2 0.01 0.99 1.879 0.45 100 9 2 0.01 0.99 1.890 0.50 100 10 2 0.01 1 1.896
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Figure 4.11: Comparison between proportion p and current average waiting time EWC with D=0.2 at Sydney airport
Figure 4.12: The average waiting time EWC of differentD at Sydney airport
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Figure 4.13: The thresholdsh and m of different D at Sydney airport
Figure 4.14: The proportionspMand pLof differentD at Sydney airport
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Chapter 5
Conclusions
This thesis reports a tiered security screening system for airports based on a two-dimensional Markov process and a Markov modulated Poisson process. The proposed model was evaluated using the matrix geometric method, wherein the optimal configuration of parameters is deter-mined using simulated annealing. The proposed security screening system was shown to reduce the overall average waiting time, even as security was improved. We also constructed a compre-hensive queueing strategy and a novel approach to calculating optimal model parameters. This makes it possible to adjust the configuration of the model according to the number of arriving passengers or the specific requirements of the system security.
The efficacy of the proposed methodology depends on the validity of profiling, in the form of a background pre-check by the TSA and the airline company. This makes it possible to send passengers to different queueing lanes according the risk they pose.
We present the following recommendations for future study. Despite reductions in the com-putation time of the proposed model, it still lags behind real-time calculations. Enabling calcu-lations in real time will require adjustment of the queueing strategy according to the number of passengers arriving in real time. Secondly, in the determination of optimal solutions, it will be necessary to take into account not only the overall average waiting time but also the inspection cost and inconvenience cost of passengers.
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