2MCMBM.docx

1、2MCMBMSummaryThe QuickPass system allows the tourists to double use the original waiting time and offers them more time for other activities in the park. However, there still exit some problems in the current QP system. In this paper, we analyze the existing QP system, propose better QP schemes, and

2、 test their validity. After the careful analysis of the common pursuit of tourists and CEOs, we conclude that the principle objective of a QP system is to increase the average free time of tourists. This increment is directly reflected in the decrease of the length of a waiting line. Empirically, we

3、 assume that the length of a regular line has an optimal value. We also set a limit to the length of the line for QP holders.When formulating QP schemes, the most important factor is the return time designated to each tourist. First, we propose Scheme 1, a simplified version of the real QP system, i

4、n which the return time is determined by the current length of the regular line. We use the result of this scheme as the baseline of analyzing the later schemes. Then we take into account the number of QP holders in the virtual line and create Scheme 2. This is a FIFO system and thus can avoid the p

5、roblem of the instability of the assigned return time. In Scheme 3, we predict the arrival pattern of the day under discussion using the historical data and come up with an algorithm that guarantees the returning QP holders to avoid the peak time of tourists arrival. Scheme 3 can successfully improv

6、e the performance of the system. Based on Scheme 3, we further record the return time of each QP holder in the virtual line and introduce Scheme 4. We stagger the return time of QP holders and thus control the length of the line for returning QP holders within a desirable level. Finally, we formulat

7、e Scheme 5 from a new perspective. This new scheme will make sure that each designated return time maximizes the free time increment of the system!As the extension of this model, we also propose a system with partial priority for QP holders. We briefly compare the new system with the original QP sys

8、tem with absolute priority and recommend the situations of introducing this partial priority strategy.To test the above schemes, we establish a considerate simulation program, taking into account many complex factors in the real world situation. Then we have the powerful weapon to test our proposed

9、schemes. Based on the results of simulation, we come to some useful conclusions and strong recommendations for the CEOs:The two criteria of evaluating a scheme are the free time increment and the regular line length. The two quantities follow a linear relationship approximately.After the implementat

10、ion of QP systems, the length of regular line reduces by about 20%. To maintain the length of regular line within a proper range, an appropriate number of QP tickets should be issued. It is important to accumulate and update the historical data.The QuickPass Strategy1 Analysis of the ProblemNowadays

11、, the emergence of QuickPass system has reduced the peoples time waiting in line and thus has been widely used in many areas. Especially in amusement parks, the system help the tourists get rid of the horribly long waiting line and offer them more time for other recreational activities. It seems to

12、be a win-win strategy. We have accumulated lots of comments praising the introducing of this system both from tourists and CEOs of the parks. However, does the QuickPass really have the great power to enhance the satisfaction of tourists on one hand and on the other, to bring more profits to the bus

13、inessmen?Actually, we have found some “necessary evils” from the QuickPass system (we will call it QP for short), which we should pay special attention to: A long return time designated by QuickPass (say, 6-8 hours) will block a tourist from getting any further QP for the rest of the day! A tourist

14、may not get a QP from a big attraction late in a day. The return time may become unstable sometimes. For instance, a tourist may find it unfair to be assigned to return 4 hours later when he observes that just a short later on the same ride, the QuickPass was given for an hour or so later. Perhaps t

15、he most dissatisfactory situation is that the QP holders return to the ride happily only to find that they still have to wait in a line nearly as long as the regular lines. According to those drawbacks (may be more), it is clear that theres still great need to improve the current system. Our task is

16、 analyzing the problems in the old system, proposing our better strategies and then testing the validity of our schemes. Moreover, we will come up with some key criteria to evaluate the QP schemes based on our model.Before establishing our math model, it is important to get a deeper understanding of

17、 the “QuickPass” System. The key word in a QuickPass System is “virtual line”. This concept derives from a very simple idea, that is, to use some certain form to record the position of a people in a line, to estimate the time from now on until he gets the service and to assign a return time for the

18、people. The system then allows the people to “idle” during the period of his original waiting time, doing whatever he wants, so long as he returns to accept the service at the designated time. Disneyland is one of the first amusement parks who adopt this kind of system, namely, FastPass, and the com

19、pany has achieved some success. In the past, tourists visiting Disneyland complain ironically that the “most frequent activity” is simply to wait in a line! Although it may be a little exaggerating, the long waiting line is indeed the NO.1 headache of both tourists and the CEO. Obviously, it is caus

20、ed by the contradiction between the ever-increasing tourists and the limited capacity of some hot attractions. Long waiting lines will not only cause large amounts of complaints from tourists but also the lack of time for them to go shopping or dining in the park, which is against the hope of the CE

21、O? (Since tourists do not buy extra tickets after they enter the park, the profit gain from shopping centers or restaurants is the only possible source for profit increment.) Therefore, Disneyland introduces the FastPass system to skillfully allocate tourists time and makes possible the double use o

22、f their time.Now we have got some idea of the reason for introducing the QuickPass system. But we still would like to further explore the expected benefits of the QP system from two different perspectives: the enjoyment related consideration of tourists and the profit related considerations of CEOs.

23、 Tourists1. To play in as many attractions as possibleOf course it is the sincere hope of every tourists and todays QP system facilitate the realization of this hope. Our schemes will further improve the enjoyment of tourists. 2. To reduce the waiting timeQP system will give tourists more time for o

24、ther activities, including playing in more attractions. Therefore, this factor incorporates the first one. CEOs1. To stretch the average free time for each touristThe “average free time of a tourist” is defined as the average value of a tourists total time used in the park minus the time used to wai

25、t in lines and actually play in attractions. The increase of this time means that the likelihood for the tourists to go shopping or dining in the park may become larger and so does the likelihood for the CEOs to earn more profit gains (although we cannot exactly control the behavior of tourists). On

26、 the other hand, tourists also prefer to have more free time for playing or shopping rather than passively wait in an endless line. We put emphasis on the increase of average free time for all the tourists, including QP holders and tourists in the regular line. Obviously, QP system can increase the

27、free time of those QP holders, but at the same time some of the QP strategies may also stretch the waiting time of those in the regular lines. Since to the CEOs the two groups of tourists have equal status, we should take into account the interests of both groups. Some of our QP schemes can increase

28、 the free time for both QP holders and regular tourists. 2. To maintain a waiting line with appropriate length in front of each attraction This statement may seem a little confusing at the first sight, but according to the comments from many CEOS of amusement parks, they hope that there is a waiting

29、 line in front of each attraction because it is a symbol of attractiveness of this attraction. Obviously, the QP rules try to reduce the waiting line. But the goal of our QP system is to maintain a waiting line with appropriate length instead of eliminating the line.From the above analysis, we find

30、that the pursuits of CEO and tourists are quite similar: more free time for tourists. With regard to the second hope of CEO, although it is obviously not the hope of tourists, most tourists are willing to accept a line with an appropriate length, especially in a theme park. 2 Assumptions A tourist o

31、nly buys one ticket to enter an amusement park and no extra money for playing in any attraction. But going shopping or dining in the park is extra cost. Tourists can freely choose whether or not to request a QP ticket. Every tourist is allowed to have only one QP ticket at a time. The length of retu

32、rn time window is a constant value. A certain percentage (1-m%)of QP holders will return to the attraction at the designated time. Overdue QP ticket is invalid. There is no breakdown of an attraction and staffs of the attraction are always working during business hours. Therefore, the capacity of an attraction remains constant during a day. 3 Terms and DefinitionName Definitionrithe arrive time of tourist iqithe length of regular line when tourist i arrivesvithe length of virtual line (the number of the previous valid QP holders) when tourist i arrivesTithe r