a hierarchical approach to integrated transit derek edwards georgia institute of technology...

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

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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

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Motivation

New York, NY

Washington, DC

Atlanta, GA

Population 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 minutes

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.

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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

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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?

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4 8

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2

3

4

5

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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.

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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

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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

C

A

B

C

Where, is the set of all subnets, and D is the set of all on-demand vehicles in .

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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

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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.

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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

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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

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Current and Future Work

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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)

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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?

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Thank You

Derek EdwardsSchool of Electrical and Computer EngineeringGeorgia Institute of Technologydedwards@gatech.edu

Steve DickersonSchool of Mechanical EngineeringGeorgia Institute of Technologysteve.dickerson@me.gatech.edu

Arun Kumar ElangovanRideCell, LLCarunmib@ridecell.com

Aarjav TrivediRideCell, LLCaarjav@ridecell.com

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Extra Slides - Home Park, Atlanta Implementation

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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.

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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.

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Proof of Concept Objective Function

𝐽𝑇𝑜𝑡𝑎𝑙=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

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Proof of Concept Results:

Total Vehicle Mile Traveled:

11.59

Minimize Wait (Green)Minimize Ride (Blue) Minimize Total

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Proof of Concept Results:

Total Vehicle Mile Traveled:

4.25

Minimize Wait (Green)Minimize Ride (Blue) Minimize Total

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Proof of Concept Results:

Total Vehicle Mile Traveled:

5.55

Minimize Wait (Green)Minimize Ride (Blue) Minimize Total