Proceeding of the IEEE International Conference on Automation and Logistics Chongqing, China, August 2011
A Fast Method to Evaluate the Runway Capacity at the Airport Based on Arrival/Departure Capacity Curve* Shidong Wang, Yue Zhang and Haiyang Yu
Peihan Wen
Institute of Civil Aviation Development China Academy of Civil Aviation Science and Technology Beijing, China {wangsd&zhangyue&yuhy}@ mail.castc.org.cn
Department of Industry Engineering Chongqing University Chongqing, China
[email protected] number of everyday’s flight. Then statistical method is applied to evaluate the runway’s capacity, so this requires more data than FAA model and the result is usually conservative which means the calculated capacity can’t exceed the history. 3)Simulation Tool There are also some simulation software to solve the problem, such as TAAM, SIMMOD[4]. The runway’s configuration, the facility, the slot time and flight’s time table is set in the software, then flight’s taxiing, take-off and landing will be simulated which will demonstrate every detail in operating runway. The result is usually accurate and the procedure is flexible, but the cost is high and the technology is complex. The pros and cons of different method are listed in TABLE I.
Abstract - With the development of civil aviation and the increasing demand of good service, the importance of evaluating the capacity of the runway at the airport is obvious. The paper proposes a fast method to evaluate the runway which is based on the arrival-departure curve and statistical analysis and overcome the boundedness of historical data. This method can make a balance between the precision and implementing difficulty comparing with the traditional methods. Meanwhile, the calculations to the expectation value of capacity under the different situation (busy, balanced and idle) are also discussed. Finally, the idea to collaborate with other technologies are proposed. Index Terms - air transpiration; evaluation of the capacity of runway; arrival-departure curve.
TABLE I
I. INTRODUCTION
THE COMPARISON OF EVALUATING METHOD
With the prosperous Chinese economic development, the civil aviation has been the critical logistical industry. There are almost 190 airports in China, but the air transportation service has still some quality problem, especially, the flight delay. Among those factors, the capacity of runway is very important, so the effectiveness and accuracy will not only influence the air transportation flow’s management but also support the construction of airports. The paper uses the airport arrival/departure capacity cure and discusses the runway capacity under whole constraint capacity which considers all the limitation, such as ground, and airspace, etc. The ground constraint is the influence made by the layout of runway, taxiway and apron, and the airspace[1]. There are three kinds of method to evaluate the runway capacity. 1)FAA Theoretical Model[2] Considering the physical layout and configure of runway, and the number of flight, the method can calculate the maximum capacity except the airspace, weather, and controller. This simple model requires less data, and low cost, the process is short, too. Because the model gets rid of some factors, there usually has gap between the result and actual capacity. The result’s adjustment varies in experience. The abnormal factors usually occur unpredictable, and the duration and scope is also hard to determine and they can take place in both busy time and idle time. 2) Arrival/Departure capacity Curve[3] The whole runway system is seen as a “black box” without analyzing the influencing factors specially and use the *
Method /Indicator Cost
Low
Arrival/Departure Curve Low
Technology
Easy To Get
Easy To Get
Development Accuracy
Fast Low
Fast Middle
Data
Little, Such As Runway Configuration
Moderate, Including Runway And The Everyday’s Flight
Simulation Tool High Hard To Learn Slow High Much, The Whole And Detailed Data About Runway
II. A FAST METHOD The paper proposes a fast method based on the arrival/departure capacity curve in airport, and the advantage is using the statistical analysis to evaluate the runway’s capacity beyond the flight data from history. The structure of method is listed as Fig.1.
The work is supported by the National Soft Science Research Program (2010GXS1B105)
978-1-4577-0302-07/11/$26.00 ©2011 IEEE
FAA Model
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Fig. 1 Research structure of the proposed method
Because the basic data is the influenced by all constraints, such as runway’s layout, airspace limitation, the terminal, the time table, etc, the result is the whole-constraints capacity of runway. A. Basic Data TABLE II lists each hour’s number of flight in airport W one day, there are some 0 flight in some hours because the airport is closed from midnight to early morning and those data will be abandoned. The first column is the time period, the “ARRIVAL” column is the number of landing flight, and the “DEPARTURE” column is the number of take-off flight.
Fig. 2 The arrival/departure capacity curve
From the Fig. 2, the conclusion which the maximal peak quality is 30 flights is drawn and the total number 30 composed of 13 landing flights and 17 departure flights, or 19 landing flights and 11 departure flights. But there is one question; is the result the actual maximal capacity in the airport W? Or the quality is just the occasional capacity and the actual capacity is not this number when there are more than 30 flights, the air traffic controller will be tired of operating the flights and the safety pressure will increase exponentially. Meanwhile, there is another possibility that the maximal capacity is larger than 30, but this real number cannot be calculated for the reason of irrational sampling. So the method to evaluate the actual capacity from the history flights’ data is the essential. The traditional method is to get rid of some special points; the remaining points will construct a convex set which frontier is the theoretical capacity. There are a lot of methods such as abandon the apparent unseasonal point; get rid of 5% of all data and use the remaining 95% points, which are discussed in some paper[3]. The prior method has 2 disadvantages; the first is the proportion of abandoned data is decided randomly which is not based on the same standard with the various airport; the second is that if some data is erased, the result will never exceed the history level which means less flexibility. In order to overcome these disadvantages, the paper proposes to use statistical distribution as the analysing method. Firstly verify the distribution principle of landing and take-off flights, and then calculate the descriptive parameter, such as mean value and variance for Gaussian distribution, the degree of freedom for T-distribution, then the reasonable and actual capacity is computed C. Distribution and Parameter Of Flights Firstly, the distribution of flights will be verified, and the Gaussian distribution is supposed. The process is described as following: 1)check the histogram of the number of landing and take-off flights and confirm whether this distribution fits. The histogram is a usual method to describe the data’s distribution. The data is grouped into many sections which have the same covering length. The height of a rectangle stands for the frequency density of the interval, And the width
TABLE II THE DATE: EACH HOUR’S NUMBER OF FLIGHT IN AIRPORT W
Time Period 00-01 01-02 02-03 03-04 04-05 05-06 06-07 07-08 08-09 09-10 10-11 11-12
Arrival 3 7 8 16 9 10 12 13 6 19 6 15
Departure 11 18 14 4 6 8 9 17 8 11 14 11
Time Period 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22 22-23 23-24
Arrival 8 10 7 3 4 4 3 0 0 0 0 3
Departure 10 9 9 4 1 0 0 0 0 0 0 0
B. Arrival/Departure Capacity Curve The arrival/departure capacity curve is a curve whose vertexes is composed of the outer collection of data representing the arrival and departure number of flight in some period (such as 15 minutes, half hour, or one hour). Fig. 2 is the capacity curve calculate from TABLE II, here the vertical axis is the number of departure flight per hour and the horizontal axis Is the number of arrival flight per hour. And the total time is 24 hours, if there are more data, such as monthly, or even yearly, the result will be more precise.
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is the class interval. The total area equals to the number of data. In the paper, the class interval is 2 flights per hour. The histogram is showed in Fig. 3.
If every distance is short, the conclusion that the empirical distribution fits the actual distribution can be drawn[5]. The empirical distribution is Gaussian and the significance level is 0.1 in the paper. TABLE III THE RESULT OF K-S TEST
Arrival flight per hour 20
N Normal Parameters
Mean
Std. Deviation Kolmogorov-Smirnov Z Asymp. Sig. (2-tailed)
Fig. 3 The histogram of arrival/departure flights
It cannot be drawn that the distribution of flights fits the Gaussian distribution, so more detailed analysis is required. 2)Q-Q plot The histogram is usually to verify the data’s distribution, but it is not general correct and it’s hard to check the detailed distribution. If the particular distribution is needed, the Q-Q plot will be used to help recognize the approximate distribution [5]. Suppose the Gaussian distribution is N(μ,σ2), for the sample x1,x2,…xn, the sequenced list is x(1),x(2),…,x(n). set Φ(x) as the standard Gaussian distribution, and Φ-1(x) as inverse function, the Gaussian Q-Q plot is made of the following points. , i=1,2,…,n If the sample fits the Gaussian distribution, the points in the Q-Q plot will be near to the line:
Departure flight per hour 17
8.3000
9.6471
4.72507
4.51305
.586
.606
.882
.857
Because 0.882 and 0.857 is larger than 0.1, the number of landing and take-off flights both fit the Gaussian distribution, and mean value is 8.30 and 9.64 and the variance is 4.72 and 4.51 separately. 4) Evaluation policy After the distribution is determined, the method covering arbitrary area will be provided. For example, the 3σ can cover 99.7% of sampling space, and 6σ in quality control can cover 99.99955% of data. This phenomenon reflects the relationship between expectation and mean value, variance. Because the paper is based on the sampling method, the result should show the difference between evaluation policies, and then the various policies here are proposed: conservative, normal and positive policy, which represents the busy, normal and not busy runway and cover 85%, 90% and 95% of expected data separately. The more percentage is, the over evaluation is. The Fig. 5 shows the result.
Because the slope is variance and the offset is the mean value, the Q-Q plot can be used to check whether the dada is from Gaussian distribution if the most points position the area around the line.
Fig. 4 The Q-Q plot
It can been drawn that the data fits Gaussian distribution because Fig. 4 shows the point is very close to the line. 3) Kolmogorov–Smirnov test (K–S test) K–S test calculates the distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution and can be used to compare a sample with a reference probability distribution. Suppose the empirical distribution function Fn(x) is the estimate of actual distribution F(x), the distance is defined as:
Fig. 5 Expected capacity under different policy
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It can be seen that the corresponding variance rate is 1.04, 1.3 and 1.6 separately. 5) Result From Fig. 5, the capacity under different estimation policy can been calculated, the result is showed in TABLE IV.
month, or even a year, and more precise time period, such as 15 minutes, the result will be more accurate. REFERENCES [1] Massound Bazargan, Kenneth Fleming, and Parakash Subramania, “A simulation study to investigate runway capacity using TAAM,” Proceedings of the 2002 Winter Simulation Conference, pp. 1-9. 2002. [2] Federal Aviation Administration, FAA Airport Capacity and Delay Models, 1977. [3] E. P. Gilbo, “Airport capacity: representation, estimation, optimization,” IEEE Transactions on Control Systems Technology, vol.1, no.3, pp.144153,1993. [4] TAAM Reference Manual, Jeppesen Company, 2007. [5] Xue Yi and Chen Liping, Statistical Model and R Software, Tsinghua University Press, 2007, pp.122-129.
TABLE IV THE RESULT OF DIFFERENT POLICY
Evaluation Policy Conservative(85%) Normal(90%) Positive(95%)
Landing (Flights Per Hour) 13.22 14.45 15.87
Take-Off (Flights Per Hour) 14.34 15.51 16.87
Capacity (Flights Per Hour) 27.56 29.96 32.73
Then Fig. 2 will be updated to Fig. 6.
Fig. 6 Final result of evaluating capacity
Fig. 6 is the compassion between statistical data and evaluation. When conservative policy is applied, the result will less than the capacity in Fig. 2, that means the runway now is a little busy and require enlarge or new construction to satisfy the insufficient capacity 2.44 flights per hour (=3027.56); when normal policy is available, the result is equal to the curve in Fig. 2, which means the current method can cover the old method; when positive policy is used, the result is more than previous result, which means the method can jump the history and evaluate the actual capacity. According to the discussion, when evaluating the runway’s capacity, the choice of evaluation policy is essential to correct and accurate result. III. CONCLUSION In the practice, when the runway’s capacity is insufficient, the controller will feel hard to conduct the air traffic, and the traditional method can get the precise difference between the actual and theoretical capacity. The paper proposes a fast method to evaluate the runway capacity based on arrival/departure curve. The method is also based on statical sampling and can calculate the capacity shortage by choosing different evaluation policy. The process is very simple, lowcost and suitable to fast evolution and makes a balance between the precision and implementing difficulty comparing with the traditional methods.. If there are more data, such as a
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