2017美赛优秀模板篇2017d

1、Team Control Number67316For office use onlyFor office use onlT1 T2 T3T4 F1 F2 F3F4 Problem ChosenD2017MCM/ICMSummary Sheet(Your teams summary should be included as the first page of your electronic submission.)Type a summary of your results on this page. Do not include the name of your school, advis

2、or, or team members on this page.SummaryBottlenecks that passengers take time to take care of their carry-on properties before X-ray scanning and that the structure of the checkpoints is not satisfying are spotted, and detailed recommendations for the airport security management to raise throughput

3、of the security checkpoints, to improve the passengers satisfaction and to keep the cost relatively low are given with cultural factors quantied and their impacts on the models discussed.We divided the security check process into two phases and regard the entire as two queueing models in series. By

4、analyzing the given data, the document check is found to be a Poisson queueing (/) in Kendall notation, and Erlangian process (/) is concerned in the scan check process. Numeric solution of ( /) is introduced using simulation tech- nique.Assumed that arrivals of passengers for a ight obey normal dis

5、tribution, the varying passenger ow in a period of time can be generated from the real data and used for our sim- ulation. We also believe that the mean and the variance of the distribution is culture-re- lated. We also nd that the passenger ow can be changed by recommending the passengers their arr

6、ivals, and thus better result of the passengers waiting time can be achieved.We also suggested several methods to improve the design of the checkpoint, including shortening the distances between identical checkpoints and more rational human resource allocation.Virtual queueing is recommended as an a

7、pproach to improve passengers experience, and modify the conventional First In First Service queueing discipline to partial priority queueing discipline as well. A partial priority queueing discipline is put forward to reduce the remaining time variance of the passengers and to decrease the number o

8、f passengers that missed their ights, thus better passenger satisfaction is reached.We also introduced culture-related factors for passenger arrival recommendation and pri- ority queueing discipline. For the latter, an “acceptability factor” named is used to denote the acceptability of strict priori

9、ty discipline. And the examples of dierent cultures are given to illustrate this idea.Validation of each model are made in our essay to make them convincing. We later assess the models and give a complete guide for the security managers to optimize the airport secu- rity check workow. Weaknesses and

10、 further work that is not implemented in our essay are also pointed out.迈思数模 2018 美赛课程价格表联系/820496864联系电话；/项目名称价格包含内容报名方式内部模拟赛VIP 学员无报名费；普通班学员报名费 80 元；外部学员报名费 200 元；模拟赛，任选近年美赛题目，写出论文，获得视频点评联系工作人员报名美赛报名普通班及VIP 班：700元；外部学员 850 元报名费+美赛证书打印+模拟赛+赛前冲刺课联系工作人员报名普通班（入门班课程）一科 198 元；两科 298元；三科 398 元【限时特惠 168-2

11、68-368】课程更新时间为：11 月 1号，以后每两天更新一节。共计 20 节课https:/chuanke.baid/6313466-237925.html普通班（算法班课程）课程更新时间为：11 月 16 号，以后每两天更新一节。共计 20 节课https:/chuanke.baid/6313466-237851.html普通班（历年赛题分析班）课程更新时间为：12 月 1号，以后每两天更新一节。共计 20 节课https:/chuanke.baid/6313466-237926.htmlVIP 班（入门班课程）一科 598 元；两科 698元；三科 798 元【限时特惠 568-668

12、-768】课程+比赛全天在线指导+模拟赛+辅助报名免手续费先在传课上选择普通班课程进行报名，报名后再支付 400 元到支付宝，支付后，请联系管理员进入内部群（比赛指导将通过 QQ 群进行指导，大家务必迅速加进去）VIP 班（算法班课程）课程+比赛全天在线指导+模拟赛+辅助报名免手续费VIP 班（历年赛题分析班）课程+比赛全天在线指导+模拟赛+辅助报名免手续费Team #67316Page 1Time Counts! Less Waiting & Better AirportsIntroduction1.1BackgroundAirport security check has been imp

13、roved ever since the 911 attack. Although enhanced secu- rity means safer ?ights, however the complicated procedure may also increase the passengers waiting time and add cost to the U.S. Transportation Security Agency (TSA). Under someextreme circumstances, passengers have to wait for hours (and the

14、y are oftenmended tobe earlier for 23 hours, which often lead to confusion) (Hetter, 2016). Thus, to shorten thepassengers waiting and designing a more e?cient security check procedure is vitally important. TSA is now in controversy for causing long queues waiting for security check. We, the Interna

15、l Control Management (ICM) team, trying to ?nd a solution, faces the problems below:Identify the bottlenecks of the current security check work?ow.Improve the process with modi?cations, and illustrate how the modi?cations work.Find how to allow the modi?ed process to be compatible with di?erent cult

16、ure back- grounds and lower the variance of the passengers waiting time.Make suggestions on the policy for the security manager, with concern of the former requirements and corresponding models.1.2Analysis and Approach OverviewFor problem 1, we divide the security check process in two parts: Phase 1

17、, document check; and Phase 2, luggage and body scanning. The former is a Poisson queue, while the latter concerns an Erlangian model. Simulation is practiced as a means of solving multi-server Er- langian model. By testing the total waiting times sensitivity to changes on numbers of parallel server

18、s in the two phases respectively, the bottlenecks of the work?ow can be spotted.To solve problem 2, considering the in?uential factors of a queueing process, modi?cations will be put forward to optimize and avoid congestions.The current TSAmended passengers arrival time is used to build a model of t

19、hepassenger arrival behavior at an airport, and we assume the arrivals in time for one certain?ight obey normal distribution, and in a small time interval, the arrivals of all passengers forall ?ights obey an exponential distribution. We will modify the arrival egy to in?uence passengers arrival beh

20、avior.mendation strat-Another direction to improve the current process is to provide more robust security checkservice with greater capacity. A few suggestions and their veri?cation or explanation will be given.Team #67316Page 2Besides the performance, justi?ability also counts. Virtual queueing und

21、er other discip (Zhao, et al., 2016) will be a good practice. Queueing discipline modi?cation is culture-sensitive, and thus lead to the discussion of the third problem.The following diagram illustrate the above ideas in a more visual way:Figure 1 Optimizing directions and our modi?cations,where “se

22、rvice pattern” concerns the service rate and number of servers.Assumptions1.2.Individual variability is not considered for the servers, the checkpoint structures, etc. Although the number of lanes opened in the scan check process is dynamic, we assume that the service capability is always at its max

23、imum. That is to say, spare lanes will be open, so long as the arrival exceeds the current capability.Assume that every passenger will choose to wait in the queue that minimizes their waiting time at every checkpoint.Points in time that passengers arrive at the airport for a certain ?ight obey norma

24、l distribution.TSA Pre-check wont contribute much to the congestion compared with the normal one. Almost everyone would arrive at the airport for at least half an hour..See 4.1 Security Check ProcessOverview, and 4.3 Queueing Model Speci?cation for de- tailed interpretation and assumptions of

25、 the given datasheet.Symbols and NotationsSymbol or NotationSpeci cationKendall notation, where , , , , and denote the inter-arrival-time( / / ): ( / / )distribution, the service time distribution, the number of parallel servers,Team #67316Page 3Denote an exponential distribution for inter-arrival t

26、ime and service time,i.e. a Poisson distribution for arrival and remove rate. Estimated value of . Arrival and service rates of the scan check process. , Normal distribution with mean , and variance . ( , )Queueing Model for Security Check ProcessSecurity Check ProcessOverview4.1Figure 2 TSA Securit

27、y checkpointThe detailed security check process of one single checkpoint given in the diagram above. Ac- cording to TSAs policy, we classify the security processes in two types (pre-check included and no pre-check concerned process), and divide the each process in two queueing phases. In Phase 1, th

28、e passengers identity documents will be checked, after which they enter Phase 2, where luggage and body screening will be accepted. Two di?erent types are in essence the same queueing with di?erent parameters (number of servers, service time, etc.). And the entire security check process can be seen

29、as two queueing models in series.To better clarify the whole process, a procedure sequence diagram is given below: ( )( ) = e d ,Arrival and service rates of the document check process.Erlang distribution type .queueing discipline, restriction on system capacity, and the source of arrival (usually i

30、n?nity) respectively. (Taha, 2014)Team #67316Page 4ABCDEFGHFigure 3 Procedure sequence diagramA: time waiting for the document check, B: document checking timeC: time waiting for sending luggage for X-ray scanning, D: X-ray scanning time, E: other possible luggage checksF: time waiting for millimete

31、r wave scan, G: body scan time, H: other possible body checks The yellow shaded part is Phase 1 as we introduced in previous paragraphs, and the rest Phase 2.The given Excel datasheet contains time records of the airport checkpoints (whose dier- ences denote the inter-arrival time), time taken of th

32、e ID check process of previous checked passenger (i.e. B in the diagram), millimeter wave scan timestamps (dierences of which are the millimeter wave scanning time, shown as G in the diagram), timestamps that luggage getting out of the X-ray scan (dierences denote E), and time to get scanned propert

33、y (D, E, F, G, H).By analyzing the given datasheet, patterns of the airport security check behaviors, such as the distribution of passengers inter-arrival time and service time at each section, can be dis- covered. Therefore a complete queueing model can be specied.4.2Significance Test on Two TSA Of

34、ficersThe given datasheet involves timing of two dierent TSA ocers, the signicance test here is to verify that individual variability does not contribute much to the service time.Suppose that variances of the service time of the two TSA ocers are equal, = = .22212We make the null hypothesis 0 that s

35、ervice time expectations of both ocers are the same,i.e. 1 = 2.The combined sample variance of the two ocers, = 12.927.2At 5%level, |12| = 1.375 (14) = 2.145, the null hypothesis is not rejected.0.0251/1+1/2Assume that the document check service time obeys the exponential distribution. The pa- ramet

36、er of the distribution, i.e. service rate, is estimated, = 0.09465.4.3Queueing Model SpecificationThe two phases of the process can be specied as a series of queues by giving the arrival and service time distribution pattern.Team #67316Page 54.3.1Arrival3020251520151010550001020304050020406080Figure

37、 4 Frequency histogram of non-pre-check arrivalsFigure 5 Frequency histogram of pre-check arrivalsAccording to the histograms above, we suppose that the time intervals of both the regular and pre-check arrivals obey exponential distribution () = e.Maximum likelihood estimation of the parameter :e (

38、) = ( ) = = e =1=1=1d ln ( ), =ln ( ) = ln = 0d=1=1Therefore= = 1 ,and the expectation, = = , is an unbi- 1 1 ()=1ased estimation. Thus the arrival rates of the regular and pre-check procedures are estimatedto be = 0.077244 and = 0.10882016, respectively.12Here, a goodness of t test is done, and eac

39、h of the procedures are classied into 10 classes.Lets take the regular (without pre-check) procedure as an example:True Frequency211363001101 Predicted Probability0.4610.2480.1340.0720.0390.0210.0110.0060.0030.002 Predicted Frequency21.20411.4306.1613.3211.7900.9650.5200.2800.1510.081Table 1 Regular

40、 procedure, non-pre-check, true frequencies and predicted frequencies10( )= = 15.898 22(9) = 16.9190.05=1Thus we consider the above as an exponential distribution. And similarly, t for the pre-check procedure, 2 = 15.599 0; 0 ) ( ) =( ) with the expectation ( ) = and variance ( ) = . Parameter and i

41、s related with and the service rate (Gross, et al., 1985): = 1? = Fit the distribution for the total service time in Phase 2 (time to get scanned property), our results are, = 4, = 0.0357.Therefore, the Kendall notation of Phase 2 queueing is ( / / ), where the input is identical to the output of Ph

42、ase 1, is an Erlang type = 4, = 0.0357 distribution, and the number of parallel servers (i.e. the number of X-ray scanners and millimeter wave scanners) is depend on speci?c airport.( / / ) queueing does not have a good analytical solution; our numerical solution using simulation technique will be i

43、ntroduced later.4.4Section SummaryThe airport security check process consists of two phases, ?rst of which is an ( / / ) queue- ing process, and the second is an ( / / ?) queueing. Arrival rate of the second is the service rate of the ?rst. Parameters of the distributions can be estimated using the

44、given data.Team #67316Page 7Queueing Simulation and Bottlenecks Spotting5.1Estimating ExpensesAccording to (L;),e of a security o?cer is $28,624$58,987 and ofan airline security screener is $23,262$54,015. That is the human resource expenses of thesecurity check. Costs of security devices are mostly

45、 one-o? consumptions. The price of an airport X-ray baggage scanner is at $20,00050,000 and of a millimeter wave full body scanneris at $100,000 (). And the maintenance cost is mainly from the electricity. Anotherfact is that one single lane of the scan check process requires 4 security screeners on

46、 average.Therefore, we drew a conclusion that the cost of one lane (server) in Phase 2, is about the cost of 4 desks (servers) at Phase 1.5.2Basic IdeasA MATLAB program is written to simulate the entire security check process. To build up the numeric solution, Markov chains are used for Erlangian qu

47、eueing. (Zeng, et al., 2011)Figure 7 MATLAB simulation speci?cationTeam #67316Page 8Since there is no analytical solution of an ( /) (Phase 2) queueing model, a simulof the entire security check process is put forward, and both Phase 1 and Phase 2 are concerned in the model in series.Given the param

48、eters of each probability distribution at the two phases, we generate series of random variates to simulate the process. First, random variates obeying exponential distri- bution is generated as peoples inter-arrival time. We then calculate and store the arrival timestamps, service time (generated r

49、andom variables obeying another exponential distribution) and waiting time (worked out with the previous passengers waiting time, service time and the arrival interval) of each passenger in a table. Besides getting results of waiting time spans, the removal rate of Phase 1 is also observed, which is

50、 used as the arrival of Phase 2. After working on Phase 1, we do the same on Phase 2, but the new service is Erlangian. Finally, expectations of total waiting time are evaluated.To spot the bottlenecks in the process, we tested the improvements of total waiting time expectations when 4 document chec

51、k servers are added (row “Document Check Added” in the table below), and 1 scan check server is added (row “Scan Check Added”).5.3Spot the Bottlenecks!The simulated security process has a changeable arrival rate , and both of the initial numbers of the document check servers and of the scan check se

52、rvers are assigned 5, as is the case in Figure 2, which is a small scale for an airport. The service rate of one document check server is assigned = 0.09465, and that of one scan check service is = 0.0357. Service of Phase 2 is Erlangian type = 4. These three parameters are the same to what we have

53、mentioned before.Below lists the expectations for total waiting time at dierent arrival rates. Row “Original” is the total waiting time expectation of process consist of ( /5) and ( /5). Row “Doc- ument Check Added” for the case that 4 document check servers are added, that is ( /9) for Phase 1 and

54、( /5) for Phase 2. For row “Scan Check Added”, 1 scan check server is added, that is ( /5) and ( /6).3.2473.7104.3294.4784.6384.8105.194Document Check Added31092218781183210671892572153291Table 2 Simulation results of the total waiting time (in seconds)We nd that, the document check process is not t

55、he bottleneck of the process, but the scan check. By adding scan check lanes, service capability of the whole system is signicantly in- creased. We can even observe that some divergent queueing cases converge (e.g. = 5.194).Scan Check Added1825810643304516802718824Original313492263212781108078988739

56、13668Team #67316Page 95.4CommentsBased on the above analysis, bottlenecks restricting the queueing capacity and e?ciency comes from the scan process Phase 2. From the given data, we see that the X-ray scan time is usually fast and steady, and is not likely to be the bottleneck. However, time taken f

57、or the passenger to take o? clothes and to take care of their carry-on properties contribute much to the next passengers waiting (time C in Figure 3), especially when someone is heavy with carry-on properties or not experienced in air travelling.We wouldmend the airport to allow the passengers to ta

58、ke a bin for their to-be-scanned properties before queueing, and thus waiting time in Phase 2 will be reduced.Comments on the SafetyFirstly, on the stand of the airport, any security accident, including terrorist attacks, hijacking or aircraft destroying, if happens, will cause unbearable blame from

59、 the public opinion, which is unacceptable for the airport. Thus it does not sound like a good idea to reduce the links in security check procedure to fasten check-in and to lower the expenses.A fundamental principle of our later discussion is that, no procedure in the security check chain is omitte

60、d. Means like optimizing queueing processes, arranging human resources, guid- ing passengers arrival can be implemented as ways to improve the passenger experience.Passenger Arrival Behavior Modeling7.1Passenger Flow GeneratingFlight records of OHare International Airport on Wednesday, Jan. 18, 2017