1. Time Dependent Transportation Network Models Petko Bakalov, Erik Hoel, Wee-Liang Heng # Environmental Systems Research Institute (ESRI)

2. 1 Outline Review of network dataset model Time dependent data Time dependent analysis. Incorporating time data into the network model Internal representation Build process. Experimental Results

3. 2 Network Model: Definition A mechanism for defining and managing a connectivity information for features in a geodatabase. Feature is graphic representation of a real-world object Line (e.g. freeways and railways) Point (e.g. railway stations)

4. 3 The connectivity information is explicitly represented with network elements that are found in a single associated logical network (graph). Three types of network elements Junctions Edges Turns The Underlying Logical Network

5. 4 Line Feature * FID * Geometry Point Feature * FID * Geometry Edge * ID Junction * ID * Attributes Turn * ID * Attributes 1 1 0..n * 2 ** 1..n Conn. Graph Feature Space - stores features which have geometry Connectivity graph – contains connectivity information about the features in the feature space

6. 5 Network Attributes Network attributes are properties of the network elements that control traversability Cost. Certain attributes are used to measure and model impedances, such as travel time Descriptors. Those are attributes that describe characteristics of the network or its elements.

7. 6 Defining and Maintaining Building – a process of establishment of connectivity where the connectivity graph is derived from the features As edits are made to the features in a network model, the logical network becomes stale. Need to keep track of the modifications Employ the dirty area management concept. When a feature is modified it creates dirty area

8. 7 Build Algorithms Initial build of a logical network Simply a special case of a rebuild over a dirty region that encompasses the entire network Existing logical network is empty. Incremental Rebuilding Rebuilding region is a subset of the dirty region. When we rebuild the entire dirty region, the resulting logical network is completely correct.

9. 8 Build Algorithm First step: compute the set of connectivity nodes for the entire network. Extracted through connectivity analysis line endpoint interstate (indivisble) street (divisible) mid-span vertex interstate tunnel street bridge Interstate group: Street group: Interstate--Street interconnect: transition point streets connect streets connect interstates connect I1I2 S1 B1 T1 (0,0) I3 S2 S3 S4 P1 interstate connects to street Connectivity Nodes (X,Y)Point FCID, FIDLine FCIDs, FIDs, %'s along (0,0)T1I1/100%; I2/0% (0,0)B1S1/33% (1,0)P1I2/100%; S4/0% (2,0)S4/100% (-1,0)I1/0%; I3/100% (-1,1)I3/0% (0,1)S1/0% (-1,-1)S2/0% (0,-1)S2/50%; S1/67% (1,-1)S2/100% (-1,-2)S3/0% (0,-2)S3/50%; S1/100% (1,-2)S3/100%

10. 9 Step 1: Connectivity Analysis Extract the geometry of all features in the network dataset. Sort the vertex information in the table by coordinate values so that the coincident vertexes are grouped together Analyze each group of coincident vertexes according to the connectivity model

11. 10 Step 2: Junction creation Create junction elements and populate vertex information table from the extracted connectivity nodes 1. For each connectivity node 2. Create a logical junction element and set its x and y coordinate weight values 3. If there is a point feature participating in the connectivity node 4. Associate the junction element with the point feature 5. For each line vertex participating in the connectivity node 6. Add a record to the vertex information table, tagged with the junction element

12. 11 Example Connectivity Nodes (X,Y)Point FCID, FIDLine FCIDs, FIDs, %'s along (0,0)T1I1/100%; I2/0% (0,0)B1S1/33% (1,0)P1I2/100%; S4/0% (2,0)S4/100% (-1,0)I1/0%; I3/100% (-1,1)I3/0% (0,1)S1/0% (-1,-1)S2/0% (0,-1)S2/50%; S1/67% (1,-1)S2/100% (-1,-2)S3/0% (0,-2)S3/50%; S1/100% (1,-2)S3/100% j1j2 j3j6=P1j7 j8j9j10 j11j12j13 j4=T1 j5=B1 Streets S1 67% j3 Vertex Information Table Line FCIDLine FIDRelative PositionJunction EID Streets I3 0% j1Interstate I1 100% j9 Interstate I1 0% j2 StreetsS2 50% j4 StreetsS1 100% j10 Streets S4 100% j11 0% InterstateI3j3 Interstate I20%j4 33%j5 InterstateI2j6 0% StreetsS4100%j7 0%j8 S2 j9StreetsS1 StreetsS2100% StreetsS30% j12StreetsS350% StreetsS1100%j12 j13StreetsS3100%

13. 12 Create edge elements from vertex information table 1. Sort the vertex information table using the line FCID as primary key, line FID as secondary key, and relative position as tertiary key 2. For each adjacent pair of records in the sorted table 3. If the pair involves the same line feature 4. Create a logical edge element between the junction elements specified by the two records Step 3: Edge creation

14. 13 Example e11 e1 e9 e2 e10 e8 e4 e3 e5 e6e7 j1j2 j3j6=P1j7 j8j9 j10 j11j12 j13 j4=T1 j5=B1 Streets S1 67% j3 Sorted Vertex Information Table Line FCIDLine FIDRelative PositionJunction EID Streets I3 0% j1Interstate I1 100% j9 Interstate I1 0% j2 StreetsS2 50% j4 StreetsS1 100% j10 Streets S4 100% j11 0% InterstateI3j3 Interstate I20%j4 33%j5 InterstateI2j6 0% StreetsS4100%j7 0%j8 S2 j9StreetsS1 StreetsS2100% StreetsS30% j12StreetsS350% StreetsS1100%j12 j13StreetsS3100%

15. 14 Outline Review of network dataset model Time dependent data Time dependent analysis. Incorporating time data into the network model Internal representation Build process. Experimental Results

16. 15 Time Dependent Data Historical Speeds: based on the idea that travel speeds follow a week-long pattern. The traffic speeds are given to us in time slices e.g. 15 min durations. Current travel times can deviate considerably. Dynamic Traffic Speeds: The model client has to connect to the data providers over the Internet, download the live travel speeds Real Live Predictive

17. 16 Time Dependent Data Time-Dependent Turn Restrictions: Data vendors also provide addendums to their turn tables that specify the time of the day when turn restrictions are in effect Left turn is restricted from 4 to 6 pm Right turn is restricted on weekdays only.

18. 17 Outline Review of network dataset model Time dependent data Time dependent analysis. Incorporating time data into the network model Internal representation Build process. Experimental Results

19. 18 Time Dependent Analysis Clients query for the attribute value of a network element by specifying a current time, and the attribute implementation retrieve the appropriate value. To perform network analysis that is dependent on the time-of day, the historic and dynamic traffic speeds have to be converted to actual travel times. Obey the FIFO Principle for Time-Dependent Travel Times

20. 19 FIFO Principle For two departure times from the beginning of an edge, the earlier departure cannot arrive after the later departure.

21. 20 FIFO Principle Account for crossing time-slice boundaries while traversing an edge.

22. 21 Outline Review of network dataset model Time dependent data Time dependent analysis. Incorporating time data into the network model Internal representation Build process. Experimental Results

23. 22 Internal Representation Huge volume of data: For each applicable street, there is a set of speed values for various time-slices across the week, e.g., 672 values for a week. To resolve the data volume issue, we exploit the fact that the historic speeds are inherently imprecise, and can be well approximated by a small set of representative daily profiles. The values in the profiles are relative (ranging from 0.0 to 1.0).

24. 23 Example

25. 24 Build There are three additional data processing steps in the above network building example needed to support the population of traffic data. Extract free flow, weekday and weekend speeds from the data sources and map to profile. Create list of edge records. Resolve historic join. “Merge” the sorted list of regular edge tuples from step.

26. 25 System Architecture

27. 26 Outline Review of network dataset model Time dependent data Time dependent analysis. Incorporating time data into the network model Internal representation Build process. Experimental Results

28. 27 Experimental Results EdgesJunctionsSize North America 73.5 million27.2 million23.7 GB Europe 141.5 million55.5 million51.8 GB Latin America 25.1 million8.4 million6.9 GB Table 1 Test Datasets

29. 28 Experimental Results Table 2 Performance Results – North America Table 3 Performance Results- Europe Average90 th percentile Local 3 stop routes~680 ms~965 ms Nationwide 3 stops routes3.5 seconds5.5 seconds Average90 th percentile Local 3 stop routes~712 ms~1034 ms Nationwide 3 stops routes4.4 seconds6.7 seconds

30. 29 Questions ???