本論文應用高速公路的交通流量模型(LWR Model)，用以描述固定時間區段中的流量。不同於以往的交通流量模型，此模型將航道上的飛機轉化成流場中連續的流體，把飛機在航道上的存在，表示成飛機對於該空域安全產生的威脅。因此，以危險值分佈表示飛機的存在性。
在同樣時間內距離與速度成正比，飛機航行速度越快，經過的範圍越大。因此，飛機速度越快時，其對空域安全造成的危險涵蓋範圍越大。這樣的概念與空中防撞預警系統(TCAS or Traffic Alert and Collision Avoidance System)的防撞區域“protected volume”類似。
本文中提出的危險值分佈流量模型，利用飛機在航道上的速度計算出各航機所造成危險值的傳遞與擴散。同一航道上的各航機即使以不同速度飛行，各航機之間是否產生碰撞，則可由各自產生的危險值疊加，然後加以判斷。一但預測出可能發生碰撞，則須調整飛機之間的速度以保持飛航安全。此交通流量模型可以進一步作為協調交通、進而保持飛機之間適當時間隔離的工具。

This paper proposes a time-based flow model using the modified LWR highway model. This model treats each aircraft as a continuum in the flow. Instead of using density distribution, a distribution of air collision probability, the danger value distribution (DVD), is used to represent each aircraft. The closer the distance to the aircraft, the higher the danger value is. Since an aircraft passes through wider space under faster speed in a fixed time period, the faster the aircraft the wider the danger value distribution will be. This concept is the same as the protected volume in Traffic Alert and Collision Avoidance System (TCAS). Using the proposed flow model, danger value distribution propagates on the airway in coordination with the velocity profile of each aircraft while maintaining the characteristics of the danger level of collision. Collision can then be easily detected by the peak value of the overlap of each aircraft’s danger value distribution even if each aircraft has different velocity on the airway. Once the collision is predicted, the flow should be managed by adjusting the velocity of aircraft on the airway. Hence this model can be used as a tool to adjust the air traffic in the manner of time-based separation.

1. Elsa, F., Jean-Pierre, N., Antoine, V., and Peter, C. "Potential Benefits of A Time-Based Separation Procedure To Maintain The Arrival Capacity Of An Airport In Strong Head-Wind Conditions," ATM Seminar. Budapest, Hungary, June, 2003.
2. "Air Traffic Management Procedure (ATMP)." 2007.
3. Farley, T., Foster, J., D., Hoang, T., and Lee, K., K. "A Time-Based Approach to Metering Arrival Traffic to Philadelphia," First AIAA Aircraft Technology, Integration, and Operations Forum. Los Angeles, California, October 2001.
4. Milan, J. "Toward Time-Based Separation Rules for Landing Aircraft," Journal of the Transportation Research Board, 2008, pp. 79-89.
5. Daniel, J., Brudnicki, and Daniel, B., Kirk. "Trajectory Modeling for Automated En Route Air Traffic Control (AREA)," American Control Conference. Seattle, Washington, 1995.
6. P., K., Menon, G., D., Sweriduk, and K., D., Bilimoria. "New Approach for Modeling, Analysis, and Control of Air Traffic Flow," Journal of Guidance, Control, and Dynamics Vol. 27, 2004, pp. 737-744.
7. Banavar, S., and P., K., Menon. "Comparison of Linear Dynamic Models for Air Traffic Flow Management," IFAC. Vol. 16, Czech Republic, 2005.
8. Bayen, A. M., Raffard, R. L., and Tomlin, C. J. "Eulerian Network Model of Air Traffic Flow in Congested Areas," Proceedings of the American Control Conference. Vol. 6, Boston, Massachusetts, June 30 - July 2, 2004.
9. Alexandre, M., Bayen, Robin, L., Raffard, and Claire, J., Tomlin. "Adjoint-based control of a new eulerian network model of air traffic flow," IEEE Transactions on Control Systems Technology Vol. 14, 2006.
10. Alexandre, M., Bayen. "Computational Control of Networks of Dynamical System: Application to the National Airspace System," Department of Aeronautics and Astronautics. Stanford University, U.S., 2003, pp. 91-132.
11. Denfeng, S., Samuel, D., Yang, Issam, S., and Alexandre, M., Bayen. "Eulerian Trilogy," Proceedings of the AIAA Conference on Guidance, Control and Dynamics. AIAA, Keystone, CO, August 2006.
12. "Introduction to TCAS II V7 ". U.S. Department of Transprotation Federal Aviation Administration, November 2000.
13. Sander, L. "http://www.aircraftmech.com/pics/tcas.jpg."
14. John, C., Strikwerda. Finite Difference Schemes and Partial Differential Equations. 2nd ed., Siam, 2004.
15. K., W., Morton, and D., F., Mayers. Numerical Solution of Partial Differential Equations. 2nd ed., Cambridge University Press, 2005.
16. Corneluis, J., O'Connor, and David, K., Rutishauser. "Enhanced Capacity Through Reductions in Separation: NASA's AVOSS," Journal of Air Traffic Control, Dec. 2001.