A Hierarchical Approach to Integrated
Transit
Derek Edwards
Georgia Institute of Technology
Co

Authors:
Aarjav
Trivedi
,
Arun
Kumar
Elangovan
, and Steve Dickerson
IEEE Intelligent Transportation Systems Conference: October 6, 2011
•
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 Station
1
Empty Midtown Atlanta Bus Stop
1
http://gothamist.com/2008/05/13/confirmed_nyc_s.php
2
New York,
NY
Washington,
DC
Atlanta, GA
Population
Density
(people/mi
2
)
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.
3
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
4
5
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.
6
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.
7
http://www.gebweb.net/optimap/
•
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?
8
1
2
3
7
5
6
4
8
1
2
3
4
5
6
7
8
9
9
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.
•
2
!
2
𝑁
possible permutations.
•
NP

Hard
•
Solved heuristically for large
numbers of passengers.
9
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.
•
2
!
2
𝑁
possible permutations.
•
NP

Hard
•
Solved heuristically for large
numbers of passengers.
•
Solution
found using Ant
Colony Optimization:
•
Distance
16km
•
Travel Time
38:35
10
11
High Speed Data Trunk
Local Data Connection
Router/Gateway
Local Data Subnet
On

Demand
Transportation Subnet
Transit Station
Intra

City Transit
High Speed Commuter Rail
12
•
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.
13
The Network

Inspired Transportation System
•
Subnets
•
Static Transit System
•
Metro

Wide Transit System
𝜙
=
{
𝜎
𝜙
𝑖
,
𝜙
𝑖
}
𝑇
=
{
𝑣
,
}
Ψ
=
{
Φ
,
𝑇
,
}
𝜙
1
𝜙
2
𝜙
3
𝜙
4
𝑣
1
𝑣
2
𝑣
3
𝑣
4
A
B
C
A
B
C
Where,
Φ
is the set of all subnets, and
D
is the set of all on

demand vehicles
in
Ψ
.
14
Defining the Optimization Problem
•
Global Objective Function:
•
Operator’s Objective Function:
•
Passenger’s Objective Function:
𝐽
𝑜𝑡𝑎𝑙
=
𝐽
+
𝐽
𝐽
=
𝐷
𝐽
𝐷
+
𝐽
𝐽
=
𝑑
=
1
𝐽
=
𝑝
=
1
𝑱
𝑫
:
Total cost of operating the dynamic vehicles
𝑱
𝑺
:
Total cost of operating the static vehicles
𝑱
:
Total cost of routing the passengers
𝒑
: Cost of routing passenger
j
N
: Total number of passengers
𝑱
:
Total cost incurred by the operator
𝑱
𝑺
:
T
otal cost incurred by the passenger
𝒅
: Cost of operating dynamic vehicle
i
M
:
Total
number of dynamic vehicles
15
Street Network: Node 2 is a Transit Station.
EDWARDS, D., et.
a
l.,“The
Network

Inspired Transportation System:
A
Hierarchical Approach to Bi

Modal Transit”, 14
th
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.
16
EDWARDS, D., et.
a
l.,“The
Network

Inspired Transportation System:
A
Hierarchical Approach to Bi

Modal Transit”, 14
th
International IEEE Conference on Intelligent Transportation Systems, October, 2011.
Route of Static Bus.
𝐽
=
𝑙
+
2
+
1
=
1
(
𝑝
𝑤
,
+
𝑝
𝑟
,
)
=
1
N
= Number of Passengers
l
i
is the length of route segment
i
𝑝
𝑤
,
is the length of time passenger
j
waited
for the bus.
𝑝
𝑤
,
is the length of time passenger
j
rode
the bus
17
EDWARDS, D., et.
a
l.,“The
Network

Inspired Transportation System:
A
Hierarchical Approach to Bi

Modal Transit”, 14
th
International IEEE Conference on Intelligent Transportation Systems, October, 2011.
Route of Static Bus.
Results:
Objective: Minimize VMT
Objective: Minimize Passenger Wait
and Ride Time
18
19
Subnets
–
The on

demand regions where entire passenger trips
can be served by a single vehicle.
•
Size, Shape, Allocation (geographic versus functional)
20
•
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?
21
22
Derek Edwards
School of Electrical and Computer Engineering
Georgia Institute of Technology
dedwards@gatech.edu
Steve Dickerson
School of Mechanical Engineering
Georgia Institute of Technology
s
teve.dickerson@me.gatech.edu
Arun
Kumar
Elangovan
RideCell
, LLC
arunmib@ridecell.com
Aarjav
Trivedi
RideCell
, LLC
aarjav@ridecell.com
23
1.
E
ncode neighborhood as a graph. Using distances
between intersections as weights.
2.
Preprocessing: Using
Dijkstra’s
Algorithm, create a
complete distance graph of the neighborhood.
24
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.
25
Proof of Concept Objective Function
𝐽
𝑜𝑡𝑎𝑙
=
𝑙
+
2
−
1
=
1
[
𝜆
1
,
𝑝
1
,
+
=
1
𝜆
2
,
𝑝
2
,
+
𝜆
3
,
𝑝
3
,
]
𝜆
1
,
=
1
if
passenger
j
wishes
to
minimize
wait
time
0
else
𝜆
2
,
=
1
if
passenger
j
wishes
to
minimize
ride
time
0
else
𝜆
3
,
=
1
if
passenger
j
wishes
to
minimize
total
trip
time
0
else
p
1,j
the
wait
time for passenger
j
𝒍
:
length of the
i
th
segment traversed by the vehicle.
p
2
,j
the
ride
time for passenger
j
p
3
,j
the
total
trip time for passenger
j
26
Total Vehicle Mile
Traveled:
11.59
Minimize Wait (Green)
Minimize Ride (Blue)
Minimize Total
27
Total Vehicle Mile
Traveled:
4.25
Minimize Wait (Green)
Minimize Ride (Blue)
Minimize Total
28
Total Vehicle Mile
Traveled:
5.55
Minimize Wait (Green)
Minimize Ride (Blue)
Minimize Total
29
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