Carr, G. C., Erzberger, H., and Neuman, F., 1999, “Delay Exchanges in Arrival Sequencing and Scheduling,” J. Aircr., 36, pp. 785–791.

[CrossRef]Bayen, A., Tomlin, C., Ye, Y., and Zhang, J., 2003, “An Approximation Algorithm for Scheduling Aircraft with Holding Time,” IEEE Conference on Decision and Control (CDC).

Roy, K., Bayen, A., and Tomlin, C., 2005, “Polynomial Time Algorithms for Scheduling of Arrival Aircraft,” AIAA Guidance, Navigation, and Control Conference and Exhibit.

Bianco, L., Dell'Olmo, P., and Giordani, S., 2006, “Scheduling Models for Air Traffic Control in Terminal Areas,” J. Scheduling, 9(3), pp. 223–253.

[CrossRef]Balakrishnan, H., and Chandran, B., 2006, “Scheduling Aircraft Landings Under Constrained Position Shifting,” AIAA Guidance, Navigation, and Control Conference and Exhibit, Keystone, CO.

Lee, H., and Balakrishnan, H., 2008, “A Study of Tradeoffs in Scheduling Terminal-Area Operations,” Proc. IEEE, 96(12), pp. 2081–2095.

[CrossRef]Chipalkatty, R., Twu, P., Rahmani, A., and Egerstedt, M., 2010, “Distributed Scheduling for Air Traffic Throughput Maximization During the Terminal Phase of Flight,” 49th IEEE Conference on Decision and Control (CDC), pp. 1195–1200.

US Department of Transportation, 2010, “Order JO 7110.65T, Air Traffic Control,” Federal Aviation Administration, Washington, DC.

Bradley, S., Hax, A., and Magnanti, T., 1977, *Applied Mathematical Programming*, Addison Wesley.

Vazirani, V. V., 2004, *Approximation Algorithms*, Springer, New York.

Bayen, A. M., Zhang, J., Tomlin, C. J., and Ye, Y., 2003, “MILP Formulation and Polynomial Time Algorithm for an Aircraft Scheduling Problem,” Proc., 42nd IEEE Conference on Decision and Control, Dec. 9–12, Vol. 5, pp. 5003–5010.

[CrossRef]Sadovsky, A. V., Davis, D., and Isaacson, D. R., 2013, “Separation-Compliant, Optimal Routing and Control of Scheduled Arrivals in a Terminal Airspace,” Transport. Res. C: Emerging Tech. J., 37, pp. 157–176.

[CrossRef]Sussmann, H. J., 1999, “A Maximum Principle for Hybrid Optimal Control Problems,” 38th IEEE Conference on Decision and Control, pp. 425–430.

Sussmann, H. J., 1999, “A Nonsmooth Hybrid Maximum Principle,” The First European Community Nonlinear Control Network Workshop on Stability and Stabilization, pp. 325–354.

Tomlin, C., Mitchell, I., Bayen, A. M., and Oishi, M., 2003, “Computational Techniques for the Verification of Hybrid Systems,” Proc. IEEE, 91(7), pp. 986–1001.

[CrossRef]Branicky, M., 2005, “Introduction to Hybrid Systems,” *Handbook of Networked and Embedded Control Systems*, D.Hristu-Varsakelis and W. S.Levine (eds.), Birkhauser, Boston, pp. 91–116.

Simic, S., Johansson, H., Sastry, S., and Lygeros, J., 2000, “Towards a Geometric Theory of Hybrid Systems,” *Hybrid Systems: Computation and Control, Lecture Notes in Computer Science*, Vol. 1790, pp. 421–436.

Dmitruk, A., and Kaganovich, A., 2008, “The Hybrid Maximum Principle is a Consequence of Pontryagin Maximum Principle,” Syst. Control Lett., 57(11), pp. 964–970.

[CrossRef]Passenberg, B., Caines, P. E., Sobotka, M., Stursberg, O., and Buss, M., 2010, “The Minimum Principle for Hybrid Systems With Partitioned State Space and Unspecified Discrete State Sequence,” Proceedings of the 49th IEEE Conference on Decision and Control.

Sethian, J., and Vladimirsky, A., 2002, “Ordered Upwinds Methods for Hybrid Control,” Proceedings Fifth International Conference on Hybrid Systems and Control, LCNS 2289.

Isaacson, D. R., Robinson, J. E., III, and Swenson, H., and Denery, D., 2010, “A Concept for Robust, High Density Terminal Air Traffic Operations,” 10th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, Fort Worth, TX.

Swenson, H. N., Hoang, T., Engelland, S., Vincent, D., Sanders, T., Sanford, B., and Heere, K., 1997, “Design and Operational Evaluation of the Traffic Management Advisor at the Fort Worth,” 1st USA/Europe Air Traffic Management R&D Seminar, Saclay, France, pp. 17–19.

Love, D., Horn, W., and Fellman, L., 2002, “An Evaluation of the Use of the URET Prototype Tool at Indianapolis and Memphis Air Route Traffic Control Centers, Using Benefit Metrics,” Digital Avionics Systems Conference, 21st Proceedings, Vol. 1, pp. 1A1–1–1A1–12.

Neuman, F., and Erzberger, H., 1991, “Analysis of Delay Reducing and Fuel Saving: Sequencing and Spacing Algorithms for Arrival Traffic,” NASA TM-103880.

Sadovsky, A., Swenson, H., Haskell, W., and Rakas, J., 2011, “Optimal Time Advance in Terminal Area Arrivals: Throughput vs. Fuel Savings,” 30th Digital Avionics Systems Conference (DASC), Seattle, WA.

Isaacson, D. R., Sadovsky, A. V., and Davis, D., “Tactical Scheduling for Precision Air Traffic Operations: Past Research and Current Problems,” AIAA J. Aerosp. Info. Sys. (to appear).

Joint Planning and Development Office, 2007, “Concept of Operations for the Next Generation Air Transportation System,” Version 2.0.

Papadimitriou, C. H., and Steiglitz, K., 1998, *Combinatorial Optimization; Algorithms and Complexity*, Dover, New York.

Korn, G., and Korn, T., 1961, *Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review*, McGraw-Hill, New York.

Ghrist, R., O'Kane, J. M., and LaValle, S. M., 2005, “Computing Pareto Optimal Coordinations on Roadmaps,” Int. J. Rob. Res., 24(11), pp. 997–1010.

[CrossRef]Adams, C., and Franzosa, R., 2008, *Introduction to Topology: Pure and Applied*, Pearson, Upper Saddle River, NJ.

Arnol'd, V., 1997, *Mathematical Methods of Classical Mechanics*, 2nd ed., Springer, New York.

Jung, J. B., and Ghrist, R., 2008, “Pareto Optimal Multi-Robot Coordination With Acceleration Constraints,” IEEE International Conference on Robotics and Automation, ICRA 2008, pp. 1942–1947.

[CrossRef]Sadovsky, A., “Application of the Shortest-Path Problem to Routing Terminal Airspace Air Traffic,” AIAA J. Aerosp. Inf. Syst. (to be published).

Cormen, T., Leiserson, C., and Rivest, R., 1990, *Introduction to Algorithms*, MIT, Cambridge, MA.

Bryson, A. E., and Ho, Y. C., 1969, *Applied Optimal Control*, Blaisdell, New York.

ARINC, T. C. G., 2011, “424-20 Navigation System Database.”