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23 Οκτ 2013 (πριν από 4 χρόνια και 16 μέρες)

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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