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The Network-Inspired Transportation System. Derek Edwards Georgia Institute of Technology Co-Authors: Aarjav Trivedi , Arun Kumar Elangovan , and Steve Dickerson . A Hierarchical Approach to Integrated Transit. IEEE Intelligent Transportation Systems Conference: October 6, 2011. - PowerPoint PPT Presentation
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The Network-Inspired Transportation SystemA Hierarchical Approach to Integrated Transit
Derek EdwardsGeorgia Institute of
Technology Co-Authors: Aarjav
Trivedi, Arun Kumar Elangovan, and Steve
Dickerson
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 City and 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
MotivationNew York,
NYWashingto
n, DCAtlanta,
GAPopulation Density(people/mi2) 27,532 9,800 4,018
Average Weekday Unlinked Transit Trips
10,303,095 1,460,125 504,420
Typical Headway Between Buses
5-15 minutes
8-20 minutes
20-45 minutesU.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
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The Dial-a-Ride ProblemThe 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.
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Traveling Salesman Problem
http://www.gebweb.net/optimap/
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.
8http://www.gebweb.net/optimap/
Traveling Salesman Problem
• 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
What is the best way for a salesman to visit N cities or locations?
9
1 2
37
5
6
4 8
1
2
34
5
6
78
9
9
Dial-a-Ride ProblemWhat 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.
10
Dial-a-Ride ProblemWhat 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
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The Network Inspired Transportation System
High Speed Data Trunk
Local Data Connection
Router/Gateway
Local Data SubnetOn-Demand Transportation Subnet
Transit Station
Intra-City Transit
High Speed Commuter Rail
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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.
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The Network-Inspired Transportation System
• Subnets
• Static Transit System
• Metro-Wide Transit System
}
𝑇={𝑣 ,𝐸 }
Ψ ={Φ,𝑇 ,𝐷 }
𝜙1
𝜙2
𝜙3
𝜙4
𝑣1
𝑣2
𝑣3
𝑣4
A
B
CA
B
C
Where, is the set of all subnets, and D is the set of all on-demand vehicles in .
15
Defining the Optimization Problem• Global Objective Function:
• Operator’s Objective Function:
• Passenger’s Objective Function:
𝐽𝑇𝑜𝑡𝑎𝑙=𝛼 𝐽𝑂+𝛽 𝐽 𝑃
𝐽𝑂=𝛼𝐷 𝐽𝐷+𝛼𝑆 𝐽𝑆
𝐽𝑂=∑𝑖=1
𝑀
𝑑𝑖
𝐽𝑃=∑𝑗=1
𝑁
𝑝 𝑗
Total cost of operating the dynamic vehicles Total cost of operating the static vehicles
Total cost of routing the passengers: Cost of routing passenger jN : Total number of passengers
Total cost incurred by the operator Total cost incurred by the passenger
: Cost of operating dynamic vehicle iM : Total number of dynamic vehicles
16
On-demand versus Static Routing for Getting Passengers to Transit Stations
Street Network: Node 2 is a Transit Station.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.
Route of Static Bus.
On-demand transit out performs static transit for solving the last mile problem.
17
On-demand versus Static Routing for Getting Passengers to Transit Stations
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.
Route of Static Bus.
𝐽=𝛼 ∑𝑖=1
2𝑁+1
𝑙𝑖+¿ 𝛽∑𝑗=1
𝑁
(𝑝𝑤 , 𝑗+𝑝𝑟 , 𝑗)¿
N = Number of Passengersli is the length of route segment i is the length of time passenger j waited for the bus. is the length of time passenger j rode the bus
18
On-demand versus Static Routing for Getting Passengers to Transit Stations
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.
Route of Static Bus.
Results:Objective: Minimize VMT
Objective: Minimize Passenger Wait and Ride Time
19
Current and Future Work
20
Determining the Size, Shape, and other Characteristics of On-Demand SubnetsSubnets – 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 YouDerek EdwardsSchool of Electrical and Computer EngineeringGeorgia Institute of [email protected] DickersonSchool of Mechanical EngineeringGeorgia Institute of [email protected]
Arun Kumar ElangovanRideCell, [email protected]
Aarjav TrivediRideCell, [email protected]
23
Extra Slides - Home Park, Atlanta Implementation
24
Matlab Proof of Concept:1. Encode neighborhood as a graph. Using
distances between intersections as weights.
2. Preprocessing: Using Dijkstra’s Algorithm, create a complete distance graph of the neighborhood.
25
Matlab Proof of Concept:3. Identify location of passengers and
destinations of passengers. 4. Use a Genetic Algorithm to determine the
optimal order in which to visit the passengers.
26
Proof of Concept Objective Function𝐽𝑇𝑜𝑡𝑎𝑙=𝛼 ∑
𝑖=1
2𝑁− 1
𝑙𝑖+¿¿𝛽∑𝑗=1
𝑁
¿ ¿]
𝜆1, 𝑗={1 if passenger j wishes to minimize wait time0 else
𝜆2 , 𝑗={1 if passenger j wishes to minimize ride time0 else
𝜆3 , 𝑗={1 if passenger j wishes to minimize total trip time0 else
p1,j the wait time for passenger j length of the ith segment traversed by the vehicle.
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:
11.59Minimize Wait (Green)Minimize Ride (Blue) Minimize Total
28
Proof of Concept Results:
Total Vehicle Mile Traveled:
4.25Minimize Wait (Green)Minimize Ride (Blue) Minimize Total
29
Proof of Concept Results:
Total Vehicle Mile Traveled:
5.55Minimize Wait (Green)Minimize Ride (Blue) Minimize Total