DEVELOPMENT OF ROUTING FOR CAR NAVIGATION SYSTEMS

Atsushi KOIKE Sokendai

Sept. 12, 2013

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Car navigation systems

Introduction

•  Devices that show us routes to our destinations •  Finding good routes is a key feature

http://gadgets.softpedia.com/gadgetsImage/The-AVIC-Z2-In-Dash-GPS-Navigation-System-and-Car-Multimedia-Center-1-13799.html

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I will explain the development of routing for the systems •  I will only talk about publicly-known technologies

Types of routing

Telematics

Routing in telematics

•  Navigation services using mobile communications •  With widespread smartphones, it is getting more important

※1 See also Wikipedia: Internavi http://en.wikipedia.org/wiki/Internavi Honda web site: インターナビ・ルート　http://www.honda.co.jp/internavi/service/internaviroute/ (in Japanese)

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Conventional routing Routing in telematics

Calculation •  Client-side •  Server-side

Memory •  Small amount •  Large amount Storage •  Small amount

•  Static data •  Large amount •  Real-time data※1

•  Traffic jams •  Blocked roads

Today’s topic

What is routing?

• Routing is a process to find good routes from a starting point to a destination

http://apptoi.com/archives/10102

What are good routes?

•  Save time •  Save money •  Save gasoline consumption etc.※1

※1 See also Honda web site: インターナビ・ルート　http://www.honda.co.jp/internavi/service/internaviroute/ (in Japanese)

Good routes save various costs

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Developing faster algorithms

Challenges for routing

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•  It reduces waiting time for users •  Applications can run more routing queries

Finding better routes

•  Users can save time and money on travel by getting better routes

•  Exact estimation of arrival time is sometimes crucial for users

High priority

Definition of cost

※1 See also　Wikipedia: Generalised cost,　http://en.wikipedia.org/wiki/Generalised_cost 竹内 健蔵, 交通経済学 (in Japanese)

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Generalized cost ※1

•  Generalized cost C := Monetary cost M + Non-monetary cost N

•  N ≈ WT

•  Indicates “how much each user pays to save unit time” •  Depends on users

T: travel time W: value of travel time saving (conversion factor from time to money)

def

Value of travel time saving

Basic formulation of routing

Input

•  Road network: directed Graph G = (V, E) •  Set of crossroads: V •  Set of roads: E

•  Edge cost function f : •  Vertex cost function h:

Query

•  Given a starting point s and a destination t, find a minimum cost path from s to t

{ }0≥ℜ∈→ xxE{ }0≥ℜ∈→ xxV

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5 1

2 3

Red: vertex generalized cost 6

6 3

5

4

9

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Blue: edge generalized cost

5 8 4

4 3 4 4

２

5 1

2 3

6

6 3

5

4

9

3 s t 5 8 4

4 3 4 4

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s t

Finding better routes

•  It is important to estimate generalized cost correctly

• Monetary cost M can be calculated correctly from the toll fare table

C =M +WTC: generalized cost M: monetary cost T: travel time W: value of travel time saving

Monetary cost

Non-monetary cost

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•  The challenge is to estimate travel time T and value of travel time saving W with high accuracy

Finding better routes: estimation of travel time

Why is the estimation difficult?

•  Driving speed depends on many parameters such as •  Traffic jams •  Road width/twist •  Traffic lights •  Average speed of each driver

How do we estimate travel time?

•  In telematics, we can use a variety of data※1 such as •  Road width/category •  Vehicle Information and Communication System (VICS):

a technology for delivering traffic information to drivers •  Vehicle’s GPS position data •  Congestion prediction data

※1 See also Aisin web site: Tell me about it! How does the car navigation system work? 　 http://www.aisin-aw.co.jp/en/products/information/structure/index.html Wikipedia: Internavi http://en.wikipedia.org/wiki/Internavi

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Honda Internavi ※1

An example of estimating travel time

※1 See also Honda web site: インターナビ・ルート　http://www.honda.co.jp/internavi/about/result/time/ (in Japanese)

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Error of estimated travel time

Without Internavi (conventional routing)

With Internavi (routing in telematics)

The error decreased by using telematics

30 min

7 min

Finding better routes: estimation of value of travel time saving

A method that exploits user choices※1

•  When a user asks for a route, car navigation systems suggest multiple routes •  The system can learn value of travel time saving W from the route the user

has chosen

※1 See also wikipedia: Discrete choice http://en.wikipedia.org/wiki/Discrete_choice 交通工学研究会, やさしい非集計分析 (in Japanese)

s t

Route 2 (min cost path at W=2500[yen/hour]) 40 min, 700 yen

Route 1 (min cost path at W=1500[yen/hour]) 60 min, 0 yen

Save money

Save time

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If a user chooses route 2, the choice indicates W >1500

Save time

Logit model ※1

Finding better routes: estimation of value of travel time saving (cont.)

※1 See also 交通工学研究会, やさしい非集計分析 (in Japanese)

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Each user has their own value of travel time

saving

He/she calculates the cost of each

route according to the value of travel

time saving

He/she chooses one route using

the function below

C1: cost of route 1 C2: cost of route 2

Probability of users choosing route 1

C2 – C1

If C1 is much less than C2, Users choose route 1 with high probability

If C2 is much less than C1, Users choose route 2 with high probability

We can estimate the value of travel time saving by maximum likelihood estimation

Predict the value of travel time saving from

the user choices

Developing faster algorithms

Conventional method

•  Dijkstra’s algorithm •  Widely used even today

Main idea for faster computation

•  Pre-computing supplementary data that accelerates routing queries

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Suitable for routing in telematics

Pre-computing

Developing faster algorithms (cont.) Recent studies

•  Contraction hierarchies [Geisberger et al. 2008]※1

•  Supplementary data •  Hierarchical networks

•  Advantages •  Small amount of supplementary data •  Features for commercial service

•  Hub labeling [Abraham et al. 2011]※2

•  Supplementary data •  A set of “hub” (important) vertices for each vertex •  Considerably large amount of supplementary data

⇒ Hub label compression [Delling et al. 2013]※3

•  Advantages •  Fastest

※1 R. Geisberger et al. Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks. (WEA’08) ※2 I.Abraham et al. A Hub-Based Labeling Algorithm for Shortest Paths on Road Networks. (SEA’11) ※3 Delling et al. Hub Label Compression. (SEA’13)

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Road network

Set of hub vertices

…

…

…

Contraction hierarchies

http://algo2.iti.kit.edu/download/geisberger_badherrenalb08.pdf

Developing faster algorithms (cont.)

Andrew V. Goldberg, Shortest Paths in Road Networks, Erice school "Graph Algorithms, Theory, and Applications http://research.microsoft.com/en-us/people/goldberg/erice.pdf

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Conclusion

•  The challenges for routing •  To estimate the cost correctly •  To calculate it quickly

•  Telematics is an effective means for both of them

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One reason is a lack of data

Issues

Future work

•  The error of estimated travel time is still large in some cases •  User preferences (including value of travel time saving) cannot be dealt with

enough.

•  Exploit more vehicle’s GPS position data and more user operation logs