2018 International Conference on Physics, Mathematics, Statistics Modelling and Simulation (PMSMS 2018) ISBN: 978-1-60595-558-2
Airport Security Management Model Based on PSO Algorithm Zhi-qiang REN, Guo-rong ZHANG, Yong-gen CAO, Zhen DONG, Hai-lun CHEN and Cheng-ling LU* College of Electrical and Optical Engineering, West Anhui University, Lu'an 237010, China *Corresponding author
Keywords: Queuing theory, Multi-objective programming, PSO algorithm.
Abstract. This paper aims at the airport's service process and establishes a mathematical probability model to simulate the queuing situation of passengers. Firstly, based on the queuing theory, we use a model to reflect the changing number of queues in different areas of the airport over time. Then, according to the queuing characteristics of each region, a multi-objective planning model is established to solve reasonable safety personnel and safety inspection equipment setting plans. In order to optimize the speed and accuracy of the solution, we have introduced the particle swarm algorithm, which can be used to obtain practical solution in a short period of time.
Introduction At present, American researchers use virtual queuing model to reduce the waiting time of passengers. Robertde Lange takes the European airport as the research object, through the analysis to the traditional queuing theory, obtains the virtual queuing implementation factor. The virtual queuing model can reduce the cost of airport security inspection and improve airport efficiency [1] . Robert Cope uses virtual queuing model to solve the problem of long waiting time for visitors to Disneyland. In this paper, the FASTPASS virtual queuing system, which can solve the problem of tourists queuing, is put forward, which can not only bring benefits to Disneyland, but also reduce the waiting time of passengers and increase passenger satisfaction [2] .
Passenger Flow Model Based on Queuing Theory As is shown in figure 1, the process of security inspection is generally divided into document inspection, personal inspection and baggage inspection. We can regard the personal examination and baggage inspection as a parallel system, which may be carried out at the same time. The review process is simplified as shown in the following figure:
Figure 1. The simplified process of security inspection. The flow of checkpoints can be represented by queuing theory [3] , of which consists six parts who are represented by X / Y / Z / A / A / B / C [4] , as follows: In order to simplify the model, from a macro point of view, we assume that the passengers arrive at the airport individually, so there is no phenomenon of batch arrival. Through the data
preprocessing, we find that the interval of arrival of passengers is a negative exponential distribution of the parameter λ as follows:
ft( ) =λ e−λt , t ≥ 0 (1) The airport queuing system can be regarded as a balanced state. For the number of passengers waiting, the average number of times entering the airport per unit time should be equal to the average leaving number of times. That is, the number of passenger remains conservative as shown in the figure 2:
Figure 2. State transition law of passengers. According to the state transition law shown above, we can obtain the state equilibrium equation of the queueing system as follows:
µ11p= λ 00 p λp+ µ p =() λµ + p 00 22 1 11 (2) λnn−−11p+ µ nn ++ 11 p =() λµ nnn + p where, when the queue number is n, λn is the average number of passengers arriving per unit time;
µn is the average number of passengers processed in the unit time of the service desk; pn represents the probability that the number of passengers in the queuing system. It is necessary to discuss the two cases: Case 1. the number of passengers exceeds the number of service desks. Case 2. the number of passengers does not exceed the number of service desks.
pn can be obtained from the above equilibrium equation, and the results are as follows: ρ n p0 , n= 1,2, , s n! pn = (3) ρ n p, n≥ s s! s n− s 0 −1 s−1 ρn ρ s In case one, p0 =∑ + . Taking into account that when the number of passengers is n=0 n! s !() 1 − ρ greater than the number of passengers at the service desk, subsequent passengers will have to wait, so the probability of passenger waiting F( s , ρ ) can be calculated through pn as follows: ∞ s ρ Fs(),ρ =∑ pn = p 0 (4) n= s s!() 1 − ρ In case two , when the number of passengers is larger than the amount of service stations, the queue length will become longer. Through the analysis, we know that the queue length is related to the number of service stations, the number of passengers and the probability of the number of passengers in the queuing system, so we can get: ∞
Lq=∑ () nsp − n (5) n= s + 1 Combined with the equation (4) and (5), the final expression of queue length can be obtained as follows: F( s ,ρ) ρ L = (6) q 1− ρ Establishment of Multi-objective Programming Model Through the analysis, we can know that there are two zones with serious problems in the airport queuing process: the pre-checked passenger channel in zone B and the baggage collection area in zone C. So the two zones need to be reconfigured to increase passenger throughput and reduce the difference in waiting time, and we optimize the existing scheme by establishing a multi-objective programming model, as follows: Constraint 1: Restrictions on the number of channels The number of regular passenger channels can’t be less than the number of pre-checked passenger channels, that is:
N0+ pc≤ M 0 − nc (7)
Where N0 indicates the initial number of pre-checked passenger channels and M0 indicates that the initial number of regular passenger channels, pc and nc is the number of pre-checked channel and regular channel after optimizing. Constraint 2: Safety first The security of the modified inspection process cannot be lower than the security before the modification. The security standard for the airport can be defined as the number of security personnel on duty on each inspection channel, the more security personnel, the higher the corresponding security. The number of channels checked before modification is M0+ N 0 and the number of modified channels is M0+ N 0 + pc − nc , so we can get: P P+ p 0≤ 0 ro (8) M0+ N 0 M 0 ++− N 0 pcnc where, P0 indicates the number of TSA stuffs prior to the modification and the number of additional
TSA stuffs is pro . According to international airport experience, the number of airport security personnel is 18% of the number of passengers per day. Constraint 3: Velocity priority The daily throughput of passengers at the airport cannot be less than the throughput before the modification. The daily throughput of passengers is the sum of the number of passengers entering the airport and the number of passengers leaving the airport, that is
λνt+( M00 +≤+ N) λν t( M 00 ++− N pcnc ) (9) where v represents the number of passengers who check the service in unit time. Objective function 1: Fairness of passengers’ waiting time
In order to ensure the minimum difference of passengers' waiting time, wt1, w t 2 , w t 3 is used to represent the waiting time of passengers in zone A, zone B and zone C respectively, which can be calculated by queuing theory model. The least variance is used to represent the least difference. As follows: n 1 2 min S =∑ ( wti− w ti ) (10) n −1 i=1 Objective function 2: Cost as low as possible The costs required to ensure that the modifications are minimal, including the cost of the baggage check belt, and the alteration of the human body examination passage, as well as the salary costs of the corresponding security personnel, it can be expressed as follows:
minMon = cb ( pc+ nc ) + cbc m + c p pro (11) where, cb indicates the cost of the renovation of body scanner, the construction cost of the baggage check passage is cm , cp indicates the salary cost of the security personnel, and the increased number of baggage check bands is bc . Solution Based on Particle Swarm Optimization
We express the objective function one as F1 and the objective function two as F2 . Considering that all the objective functions are required to calculate the minimum value, we first consider to add
up them. However, there are differences in the order of magnitude thereby we standardize them firstly, then we establish a process function F [5] . So the ultimate objective function is: F F F =1 + 2 (12) F1max F 2 max Because the objective function needs to traverse the parameters in turn to achieve the optimal solution of the multi-objective programming, considering the need to traverse the first scheme and the cleaning time of each scheme respectively. There are many computations and the results are not accurate. We use PSO algorithm [6] to solve the model. The specific steps are as follows: Step1:Firstly, determine the 3D particle ( pc, nc , bc , pro ) about increased number of pre-checked channel, reduced number of regular passenger channel, increased number of baggage check bands and increased number of TSA staff, and the 4D particles are assigned according to the constraint conditions in the topic: pc= rand (0,5 ) nc= rand ()0,3 bc= rand ()0,5 pro= rand ()0,20 Step2:Under certain constraint conditions, the first selection is carried out. then we set up 30 particles, and the particles evolve in the global range according to the law of particle motion. Select the smallest ( pc, nc , bc , pro ) from the particle swarm as the next upper limit: pcmax, nc max , bc max , pro max . Step3:The larger ( pc, nc , bc , pro ) is chosen from the particle swarm as the lower limit of the next selection pcmin, nc min , bc min , pro min : Step4:Then substituted the three-dimensional particle into the constraint condition to calculate
P0 P 0 + p ro whether the N0+ pc≤ M 0 − nc and ≤ are satisfied. If the content is satisfied, M0+ N 0 M 0 ++− N 0 pcnc the target function F is recorded. If the particle is not satisfied, the particle is re selected. Step5:After 200 iterations, the smallest objective function and its corresponding three-dimensional particle are selected as the final solution. Therefore, the optimal solution of the final four-dimensional particle ( pc, nc , bc , pro ) is obtained. We use the Monte Carlo method to randomly generate a sequence of passenger arrival intervals and millimeter-wave inspection times, as shown in the Figure 3:
Figure 3. The result of passenger arrival intervals.
Summary Because of the limitations on data and time, there are still some factors not taken into account in our model. In the future, we will make the following adjustments: Arrange suitable passage for passengers of different gender and age. In the process of security screening, female security personnel conduct physical examinations for female passengers. Therefore, female-specific lanes can be added. Similarly, for the elderly and children, special security lanes and personnel can be added to improve airport inspection efficiency. Airport security personnel and inspection channels need to be reorganized, especially the holidays and the peak tourist season. Since the flow of passengers at the checkpoint has changed greatly in a year, especially during the holidays, it is necessary to reschedule the security channels and increase the security personnel.
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