lagrangian xgraphs: a logical data-model for spatio-temporal network data acknowledgement: venkata...
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Lagrangian Xgraphs: A logical data-model for Spatio-temporal Network Data
Acknowledgement:
Venkata Gunturi, Shashi Shekhar
University of Minnesota, Minneapolis
Outline of the Talk
What is Spatio-temporal Network (STN) data?
Value addition potential of STN data
Problem Definition
Challenges
Limitations of Related Work
Proposed Lagrangian Xgraphs
Concluding Remarks
What is Spatial-temporal Network (STN) Data?
STN data is result of interactions (across time) of entity(s) with a network embedded in space.
Large number of urban sensors produce a variety of datasets. E.g., GPS navigation devices, Loop detector data, Social media etc.
Some are mobile, some are stationary, All of them capture diverse characteristics of a network in a urban
scenario
Sample STN datasets over Transportation Network Temporally detailed roadmaps. Traffic signal and coordination data. GPS tracks annotated with engine measurement data.
Motivation: Collective wisdom from these datasets could support valuable use-cases, e.g., eco-routing
From Traditional Roadmaps
Source: Google Maps
Dinky town RoadmapCorresponding Digital Representation
Intersection between 5th Ave SE and 4th St
Intersection between 5th Ave SE and 5th St
5th Ave SE edge
Attributes of 5th Ave SE road segment between N4 and N7
N7 N4
To Temporally Detailed (TD) Roadmaps
Contains typical travel-time under traffic equilibrium conditions
Per minute speed/travel time values 100 million road segments in US NAVTEQ’s highly compressed
weekly speed profile data
Source: ESRI and NAVTEQ
GPS traces
Sources: Mobile devices
Smart phones, in car/truck GPS devices, GPS collars Coupled with engine measurements
VGI Commuter preferred routes under non-equilibrium conditions
Estimate traffic signal delays? Ramp meters Coordinated signals Left turn delays
Waiting at signals
Outline of the Talk
What is Spatio-temporal Network (STN) data?
Value addition potential of STN data
Problem Definition
Challenges
Limitations of Related Work
Proposed Lagrangian Xgraphs
Concluding Remarks
McKinsey Conjecture and Preliminary Evidence
U.P.S. Embraces High-Tech Delivery Methods (July 12, 2007) By “The research at U.P.S. is paying off. ……..— saving roughly three million gallons of fuel in good part by mapping routes that minimize left turns.”
Outline of the Talk
What is Spatio-temporal Network (STN) data?
Value addition potential of STN data
Problem Definition
Challenges
Limitations of Related Work
Proposed Lagrangian Xgraphs
Concluding Remarks
Input– A collection of Spatio-temporal Network datasets– Use case queries (e.g. compare candidate routes)
Output– A unified logical model across these datasets
Objective– Travel related concepts are expressed upfront – Suitable for common routing algorithms e.g. Dijsktra’s, A*
PROBLEM DEFINITION
PROBLEM ILLUSTRATION: AT CONCEPTUAL LEVEL
Logical Model for STN datasets over Transportation Network Usually entities like Roads, Signals, Streets are modeled using lines
strings and polygons. Queried through OGIS operators
Not suitable for comparing candidate routes.
Modeling as Spatial/Spatio-temporal networks?
GPS DATA Delay DataTD roadmaps
Outline of the Talk
What is Spatio-temporal Network (STN) data?
Value addition potential of STN data
Problem Definition
Challenges
Limitations of Related Work
Proposed Lagrangian Xgraphs
Concluding Remarks
CHALLENGES OF “SEQUENCE OF” RELATION
Logical Model for STN datasets over Transportation Network Current spatial/spatio-temporal models work for M=2 What if M>2? e.g. GPS traces and Traffic signal coordination
What if M >2?
Outline of the Talk
What is Spatio-temporal Network (STN) data?
Value addition potential of STN data
Problem Definition
Challenges
Limitations of Related Work
Proposed Lagrangian Xgraphs
Concluding Remarks
After waiting at SG1, SG2 and SG3 become wait-free! Non-local interactions (SG1 not a neighbor of SG2)Typical delay measured over S-B-C-E-D will have wait only at SG1Not true for journeys starting after intersection B or intersection C
Limitations of Related Work: Non-decomposable Properties of N-ary relations
Holistic Property: Properties measured over a larger instance loose their semantic meaning
when broken down into properties of small instances
Sample N-ary relation: Typical delay experienced in series of coordination signals
Typical Representational model used by current network databases, e.g., Oracle spatial, ArcGIS etc.
Query: What is the typical travel-time experienced on Hiawatha Ave (between S and D)?Result: Between 21mins – 25mins 30secs
Current related work not suitable for representing holistic properties which cannot be decomposed
Cannot represent signal coordination upfront!
Limitations of Related Work: Non-decomposable Properties of N-ary Relations
Outline of the Talk
What is Spatio-temporal Network (STN) data?
Value addition potential of STN data
Problem Definition
Challenges
Limitations of Related Work
Proposed Lagrangian Xgraphs
Concluding Remarks
Proposed Approach: Lagrangian Xgraphs
Summary of proposed approach
Holistic properties are modeled as series of overlapping “sub-journeys”
Each “sub-journey” is contains one non-local interaction
Suitable for non-decomposable properties of N-ary relations.
3mins
8mins
5mins
5mins
Travel Related Concepts: Lagrangian vs Eulerian frame of reference
Eulerian Frame: Perspective of a fixed observe, e.g., traffic observatory
What is cost of following routes at 5:00pm• I-35W• Hiawatha Route
Legend: A-I-D: UMN-I35W-Airport A-H-D: UMN-Hiawatha-Airport
Digital Road Map
Path Cost from Traveler Pers.
Cost at 5:00pmFixed Obs.
A-I-D 27 mins 20 minsA-H-D 25 mins 25 mins
Legend: A-I-D: UMN-I35W-Airport A-H-D: UMN-Hiawatha-Airport
Digital Road Map
Travel Related Concepts: Lagrangian vs Eulerian frame of reference
Lagrangian Frame: Perspective of a traveler travelling through the network
What is cost of following routes at 5:00pm• I-35W• Hiawatha Route
Path Cost from Traveler Pers.
Cost at 5:00pmFixed Obs.
A-I-D 11+ 20 minsA-H-D ?? 25 mins
Legend: A-I-D: UMN-I35W-Airport A-H-D: UMN-Hiawatha-Airport
Digital Road Map
Lagrangian Frame: Perspective of a traveler travelling through the network
Travel Related Concepts: Lagrangian & Eulerian frame of reference
What is cost of following routes at 5:00pm• I-35W• Hiawatha Route
Path Cost from Traveler Pers.
Cost at 5:00pmFixed Obs.
A-I-D 11+16 =27 20 minsA-H-D ?? 25 mins
Legend: A-I-D: UMN-I35W-Airport A-H-D: UMN-Hiawatha-Airport
Digital Road Map
Path Cost from Traveler Pers.
5:00PM Snapshot
A-I-D 27 mins 20 minsA-H-D 25 mins 25 mins
What is cost of following routes at 5:00pm• I-35W• Hiawatha Route
Travel Related Concepts: Lagrangian & Eulerian frame of reference
Distance inferred from a GPS track can be decomposed into distances along individual road segments
Travel Related Concepts: Decomposable vs Holistic Properties
Decomposable: Property measured over a larger instance can be broken down into properties of small instances
Travel Related Concepts: Decomposable vs Holistic Properties
What about travel-time inferred from a GPS track?
Time spent on a segment depends on the initial velocity attained before entering the segment!
Holistic Property: Properties measured over a larger instance loose their semantic meaning when broken down into properties of small instances
Taxonomy of Travel Related Concepts Captured in STN Datasets
All STN datasets capture data along two dimensions.
TD roadmaps
Signal Delay Data
GPS DATA
Traveler’s Frame of Reference For Comparing Candidate Routes
Candidate routes are evaluated from the perspective of a person moving through the transportation network.
What is shortest path between A and D for t=1 ? A-B-D or A-C-D
A-C-D is shorter for t=1 : Lagrangian Frame needs to be upfront
Langrangian Xgraph: Formal Definition Lagrangian Xgraph: {Xnodes, Xedges}
Xnodes: Underlying entities at specific space-time coordinates.
– Xv1, Xv2, Xv3…
Xedges: Express a Lagrangian relation (i.e.,’as-traveled’ or ‘typical- experience-in-travel’) relationship among a group a Xnodes
– Xei = {Xvs, Xv1, Xv2, Xv3…, Xvk, Xvd1, Xvd2,..,Xvdj}
First and Last set of Xnodes in an Xedge are marked separately
Xedges are classified based on these TD roadmaps Shoot Xedges
GPS Traces Shoot and Stem Xedges
Trafffic Signal Delays Bush and Flower
Xedges
Get, Set and Join operators (only Xedges) For Xndoes and Xedges
Sample Langrangian Xgraph for Signal Coordination (1/2)
Xnodes: Underlying road segments between two road intersections at specific departure-times.
Xedges: Express a ‘as-traveled’ or ‘typical-experience-in-travel’ relationship among a group a Xnodes
3mins
8mins
5mins
Xnode ED6:Road segment ED for departure-time 7:03am at E
Xedge SB0 and (ED32, ED33, ED34, ED 35) as first and last Xnodes: – An Xedge representing: “If one leaves at S at 7:00am he/she can start
traversing segment E-D at times 7:16, 7:16:30, 7:17, or 7:17:30”
Sample Langrangian Xgraph for Signal Coordination (2/2)
Outline of the Talk
What is Spatio-temporal Network (STN) data?
Value addition potential of STN data
Problem Definition
Challenges
Limitations of Related Work
Proposed Lagrangian Xgraphs
Concluding Remarks
Conclusion
Increased proliferation of sensors
– Spatio-temporal datasets capturing diverse phenomena on a transportation network
Collectively they can add significant value to societal use-cases.
However, they pose modeling challenges due to holistic nature of properties captured in these datasets.
Proposed Lagrangian Xgraphs
– can model both decomposable and holistic properties