1. How to get a smoother ride on BART Pamela Williams pwillia@sandia.gov Susanna Gordon spgordo@sandia.gov Sandia National Laboratories, CA

2. How to get a smoother ride on BART Pamela Williams pwillia@sandia.gov Susanna Gordon spgordo@sandia.gov Sandia National Laboratories, CA

3. Outline l Advanced Automatic Train Control (AATC) l Enhanced Control Objectives »Interference Management »Delay Recovery l Concluding Remarks

4. The transit system connects San Francisco to East Bay communities l Approx. 67 trains l 39 stations/ 5 lines l 95 miles of double track l Train Capacity: 700 comfortably,1500 crush load l Approx. 750 ft long l Avg. speed = 36mph l 92% on-time performance For more information, go to http://www.bart.org

5. Numerous optimization problems arise in the area of advanced automatic train control l On a daily basis, the control system experiences approximately 20 delays of 5 or more minutes l Short Term - improve passenger comfort for the Bay Area Rapid Transit (BART) District l Long Term - minimize energy consumption

6. Modern radio-based train control systems provide a new domain for applying optimization techniques

7. Description of the Control Simulator »Primary Command - Acceleration »Multiple Control Zones »Unidirectional Travel »Flat Terrain »Jerk Limit On-board Trains »No Drag Forces »Simplified Safe Following Distance Equation The simulator contains both a safety critical and enhanced controller.

8. A train experiences interference during acceleration Situation »Two trains are travelling close together in the midst of frequent station stops Problem »The following train repeatedly accelerates and brakes

9. Enhanced train control objectives for a more reliable system l Avoid low train voltage l Smooth interfered headway operation »Interference during acceleration »Interference near station stops »Interference during delay recovery l Coordinate starts and stops

10. Our enhanced control objective is to smooth interference during acceleration l while »adhering to the schedule, »maintaining the worst case stopping distance, »making required station stops, »travelling at safe speeds, and »braking into a station at a controlled rate.

11. We apply interior-point algorithms to determine an acceleration trajectory Can be viewed as damped, perturbed Newton’s method on the first order optimality conditions of the original problem. Generate a sequence of iterates that travel through the interior of the feasible region and, under the proper assumptions, converge to the solution set.

12. We use O3D to solve the quadratic program in the enhanced controller l Large-scale quadratic programming algorithm (Boggs, Domich, and Rogers, Annals of Operations Research, 1996) l A primal interior-point method l Optimizes over a sequence of 3-Dimensional spaces

13. Simulation Conditions l Command cycle=.5 sec l Dispatch headway = 70 sec l “Optimized” headway = 75 sec l Simulation time = 360 sec l Max acceleration= 4.4 f/s/s (3.0mph/s) l Station brake rate= 3.2 f/s/s (2.2mph/s) l Number of trains = 3 l Number of stations= 4 l Station stops = {2000, 4000, 6500, 10200}

14. Comparing the solvers O3D l JAVA l Slow (> 7 seconds per train) l Enhanced controller relinquishes control last 3-5 seconds of trip PCX l Fortran and C l Fast(~.2 seconds per train) l Vital controller takes over for station stops

15. Summary l Modern radio-based train control systems provide a new domain for application of optimization techniques l Heuristic control algorithms provide improved performance for limited situations l Optimization techniques will more broadly address the need for control enhancement l Initial results demonstrate great promise for the applicability of interior-point methods

16. References l E. Nishinaga, J. A. Evans, G. L. Mayhew. Wireless Advanced Automatic Train Control. IEEE Vehicular Technology News, 41, p.13, 1994. l S. P. Gordon and D. G. Lehrer. Coordinated Train Control and Energy Management Control Strategies. 1998 ASME/IEEE Joint Railroad Conference (IEEE, 1998), p. 166-176. l S. P. Gordon and D. G. Lehrer. Service- and Energy- Related Optimization of AATC. 1998 Rapid Transit Conference (APTA, 1998). l S. P. Gordon and P. J. Williams. Train Control Optimization. SIAG/OPT Views-and-News,10:1, p.1-6, 1999.