The Network-Inspired Transportation System

1. The Network-Inspired Transportation System Derek Edwards Georgia Institute of Technology Co-Authors: AarjavTrivedi, Arun Kumar Elangovan, and Steve Dickerson A Hierarchical Approach to Integrated Transit IEEE Intelligent Transportation Systems Conference: October 6, 2011

2. Motivation • Why is Atlanta’s mass transportation not as efficient and widely used as those in New York Cityand Washington DC? Crowded Manhattan and Washington Transit Stations Subway Station1 Empty Midtown Atlanta Bus Stop 1http://gothamist.com/2008/05/13/confirmed_nyc_s.php

3. Motivation U.S. Census Bureau, U.S. Census Bureau, County and City Data Book: 2000. U.S. Census Bureau, Annual Estimates of the Resident Population for Incorporated Places of 100,000: 2009. Rogoff, P.M. “Transit Profiles: The Top 50 Agencies national transit database 2009 report year”: 2010. Metropolitan Transportation Authority, MTA System Schedules, March 2011. Metropolitan Atlanta Rapid Transit Authority, Bus Routes and Schedules, March 2011. WMATA.com Bus Routes and Scheduled, 2011.

4. How can technology improve transportation in low-to-medium density areas? Enabling Technologies: Ubiquitous mobile networks, smart phones, GPS. • Remove inefficiencies from transportation • Optimize bus routes in real time. • Automate the car-pooling process • Leverage existing infrastructure

5. State-of-the-Art

6. The Dial-a-Ride Problem The dial-a-ride problem (DARP), is the problem of creating M dynamic vehicle routes to optimally service a set of N passengers curb-to-curb with a priori information of the passenger’s origins and destinations. CORDEAU, J.-F. and LAPORTE, G., “The dial-a-ride problem: models and algorithms,” Annals of Operations Research, vol. 153, no. 1, pp. 29–46, 2007.

7. Traveling Salesman Problem What is the best way for a salesman to visit N cities or locations? • For N passengers there are N! permutations. • NP-Hard • Solved heuristically for large numbers of cities. http://www.gebweb.net/optimap/

8. Traveling Salesman Problem What is the best way for a salesman to visit N cities or locations? • For N passengers there are N! permutations. • NP-Hard • Solved heuristically for large numbers of cities. • Solution found using Ant Colony Optimization: • Distance 14km • Travel Time 31:27 http://www.gebweb.net/optimap/

9. Dial-a-Ride Problem What is the best way for one or more vehicles to service N pickup and delivery requests? • For N passengers there are 2N locations that must be visited. • Additional Constraint: A passenger drop-off location cannot be visited before the pick-up location. • possible permutations. • NP-Hard • Solved heuristically for large numbers of passengers. 6 3 4 1 9 2 2 7 8 7 5 3 9 5 4 8 6 1

10. Dial-a-Ride Problem What is the best way for one or more vehicles to service N pickup and delivery requests? • For N passengers there are 2N locations that must be visited. • Additional Constraint: A passenger drop-off location cannot be visited before the pick-up location. • possible permutations. • NP-Hard • Solved heuristically for large numbers of passengers. • Solution found using Ant Colony Optimization: • Distance 16km • Travel Time 38:35

11. The Network-Inspired Transportation System

12. The Network Inspired Transportation System High Speed Data Trunk High Speed Commuter Rail Local Data Connection Intra-City Transit Router/Gateway Transit Station Local Data Subnet On-Demand Transportation Subnet

13. The Network Inspired Transportation System • Provides solution to the last mile problem. • Outperforms static transit options in low density areas. • Breaks up large DAR network into many small semi-independent networks.

14. The Network-Inspired Transportation System • Static Transit System A • Subnets } B • Metro-Wide Transit System A Where, is the set of all subnets, and D is the set of all on-demand vehicles in . C B C

15. Defining the Optimization Problem • Global Objective Function: Total cost incurred by the operator Total cost incurred by the passenger • Operator’s Objective Function: Total cost of operating the dynamic vehicles Total cost of operating the static vehicles : Cost of operating dynamic vehicle i M : Total number of dynamic vehicles • Passenger’s Objective Function: Total cost of routing the passengers : Cost of routing passenger j N : Total number of passengers

16. On-demand versus Static Routing for Getting Passengers to Transit Stations On-demand transit out performs static transit for solving the last mile problem. Street Network: Node 2 is a Transit Station. Route of Static Bus. EDWARDS, D., et. al.,“The Network-Inspired Transportation System: A Hierarchical Approach to Bi-Modal Transit”, 14th International IEEE Conference on Intelligent Transportation Systems, October, 2011.

17. On-demand versus Static Routing for Getting Passengers to Transit Stations N = Number of Passengers liis the length of route segment i is the length of time passengerj waited for the bus. is the length of time passenger j rode the bus Route of Static Bus. EDWARDS, D., et. al.,“The Network-Inspired Transportation System: A Hierarchical Approach to Bi-Modal Transit”, 14th International IEEE Conference on Intelligent Transportation Systems, October, 2011.

18. On-demand versus Static Routing for Getting Passengers to Transit Stations Results: Objective: Minimize VMT Objective: Minimize Passenger Wait and Ride Time Route of Static Bus. EDWARDS, D., et. al.,“The Network-Inspired Transportation System: A Hierarchical Approach to Bi-Modal Transit”, 14th International IEEE Conference on Intelligent Transportation Systems, October, 2011.

19. Current and Future Work

20. Determining the Size, Shape, and other Characteristics of On-Demand Subnets Subnets – The on-demand regions where entire passenger trips can be served by a single vehicle. • Size, Shape, Allocation (geographic versus functional)

21. Adapt the Van Assignment and Routing Algorithm for Ride-Share Option • The NITS should accommodate the ride-share option. • The ride-share option introduces semi-static routes. A driver with a car has a known origin and destination, but is willing to alter his trip to accommodate others. • How should these trips be integrated with static transit?

22. Thank You Derek Edwards School of Electrical and Computer Engineering Georgia Institute of Technology dedwards@gatech.edu AarjavTrivedi RideCell, LLC aarjav@ridecell.com Steve Dickerson School of Mechanical Engineering Georgia Institute of Technology steve.dickerson@me.gatech.edu Arun Kumar Elangovan RideCell, LLC arunmib@ridecell.com

23. Extra Slides - Home Park, Atlanta Implementation

24. Matlab Proof of Concept: Encode neighborhood as a graph. Using distances between intersections as weights. Preprocessing: Using Dijkstra’s Algorithm, create a complete distance graph of the neighborhood.

25. Matlab Proof of Concept: Identify location of passengers and destinations of passengers. Use a Genetic Algorithm to determine the optimal order in which to visit the passengers.

26. Proof of Concept Objective Function ] length of the ithsegment traversed by the vehicle. p1,j the wait time for passenger j p2,j the ride time for passenger j p3,j the total trip time for passenger j

27. Proof of Concept Results: Total Vehicle Mile Traveled: 11.59 Minimize Wait (Green) Minimize Ride (Blue) Minimize Total

28. Proof of Concept Results: Total Vehicle Mile Traveled: 4.25 Minimize Wait (Green) Minimize Ride (Blue) Minimize Total

29. Proof of Concept Results: Total Vehicle Mile Traveled: 5.55 Minimize Wait (Green) Minimize Ride (Blue) Minimize Total