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Chapter 3
Simulation Study
Simulations were conducted using the actual data pertaining to Taiwan Taoyuan International Airport and other two international airports in order to determine the extent to which the tiered security system enhances airport security and reduces the expected waiting time.
The simulation results demonstrate that the proposed tiered security system is able to achieve both of these goals in (2.2.6).
3.1 Simulation setup
In the following, we consider three cases: (A) a single-queue aggregated system without differentiation of different type of passengers; (B) a three-independent-lane without sharing sys-tem; (C) a three-lane with sharing system. The purpose of simulation is to evaluate the efficacy of the model by comparing simulation results with data collected from three international air-ports. Finally, the simulation results are analyzed to find optimal queueing policy of the model for Case C.
Assume that when passengers join the security system, historical records of the passengers are used to categorized them H-, M-, L-classes in the formulation of the model.
Data included the scheduled times of departure on the website of Taiwan Taoyuan
Interna-‧
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tional Airport(http://www.taoyuan-airport.com/english/flight_depart/) for February 10th, 2015. The following fixed key parameters were used in the study: (1) arrival rate of passengers; (2) service rate of passengers.
In the Taoyuan International Airport website, we collect the scheduled fight between 10:30 and 14:30 in Terminal 1. According to the aircraft type of the flight, we can estimate the total number of passengers arriving the airport. Table 3.1 gives information about the arrival process.
Table 3.1: Arrival schedules at Taoyuan airport Time Period Number of Flights Number of Passengers
10:30 - 11:30 9 1675
11:30 - 12:30 4 1057
12:30 - 13:30 8 2100
13:30 - 14:30 9 2255
The average arrival rate of passengers for the period 10:30-14:30 was 1771.75 per hour. We assume that 60% of them are assigned to M-class and 10% of them are assigned to H-class.
On contrary,30% of arrival passengers are allocated to L-class. We divide it into three classes according to this proportion.
It was also assumed that security lanes in different security level have the different service rate. We assume that the average service rates of each corresponding lane in H-lane, M-lane and L-lane are 185, 220 and 270 per hour respectively. Thus, the total average service rates of H-lane, M-lane and L-lane are 185, 1100 and 540 per hour respectively. Specific data is listed in Table 3.2.
In addition to the data collected in Taoyuan International Airport, we also have collected the scheduled times of departure on the website of Narita International Airport(http://www.
narita-airport.or.jp/ais/flight/today/e_inter_dep.html) for July 4th,
2015 and on the website of Sydney Airport(http://www.sydneyairport.com.au/flights/
flight-arrivals-and-departures/international-departures.aspx) for July 13th, 2015. Also, we use the data to validate the proposed model as well. The detailed data
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and numerical results will be presented in the next Chapter.
Table 3.2: Parameters used in simulation at Taoyuan airport
Classes Proportion Arrival Rate Total Service Rate Service rate per lane× Number of lanes
H-class 10% 177.175 185 185×1
M-class 60% 1063.05 1100 220×5
L-class 30% 531.525 540 270×2
3.2 Simulation assumptions
Investigation of the queueing system, requires a number of assumptions based on findings in the existing literature. The simulations do not account for flight delays, mechanical problems, balking, reneging, or the effects of dealing with families or groups.
3.2.1 Case A: A single-queue aggregated system
A single-queue aggregated system is an M/G/3 queueing system. Passengers arrive at the airport according to a Poisson process with mean arrival rateΛ and service time’s cdf B(t)is a mixture of cdf’s. According to Choi et al. [7], theM/G/3 queueing model can be approximated by GI/G/c/c+r, where c = 3 and r is the length of the queue, which can be set sufficient large. The specific method of the approximation is outlined in Appendix A.
In the study, arrivals occur at rate Λ according to a Poisson process and service time has a hyper-exponential distribution. Then we obtainc2A =1 and
c2S = Var[S] (E[S])2,
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Therefore, the estimated value of the average waiting time in Case A is given by the follow-ing
3.2.2 Case B: A three-independent-lane without sharing system
As described in Chapter 2, we designate a three-independent-lane without sharing system is a three independentM/M/1 system. This simulation includes a novel measure for the estimation the average waiting time of Case B, which is given as follows:
EWB = SH +SM+SL
Λ ,
where Si is the estimated average queue length of the M/M/1 queue for H, M, L classes, respectively.
EWB is set up to enable a comparison of the overall differences between Case B and Case C.
This type of comparison provides a more direct indication of the performance of the proposed model as the three lanes are considered as a whole. Using this kind of objective function also
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makes it possible to determine the average waiting time for each lane in the numerical results.
KeepingEWB as an average upper bound of Case C, the same method is used to assess the model performance in Case C.
3.2.3 Case C: A three-lane with sharing system
An optimization model provides an alternative means by which to obtain an optimal solu-tion to the proposed tiered model. In this thesis, we employed simulated annealing to find the optimal solution for Case C. This begins with the establishment of an objective function of for the simulated annealing model, as follows:
EWC = SH+SM+SL
Λ .
Simulated annealing method is based on the pre-given domain of these controllable param-eters to determine the range to find the optimal feasible solution. Begin with initial point x0, simulated annealing algorithm looks for the best neighbor point ofx0and make it bexk. After found every possible solutionxk+1, the algorithm will make surexk+1satisfy the conditions in mathematical programming, only coincident solution will be outputted. Otherwise it will use some specific approaches to deal with, which include the physics concepts of annealing, more material of simulated annealing method may be found in Appendix B.
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