Time Dependent Transportation Network Models Petko Bakalov Erik

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

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

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

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

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

Network Attributes l Network attributes are properties of the network elements that control traversability l l 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. 5

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

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

Build Algorithm First step: compute the set of connectivity nodes for the entire network. Extracted through connectivity analysis l l line endpoint mid-span vertex I 3 P 1 B 1 I 1 (0, 0) interstates connect I 2 T 1 interstate connects to street S 1 S 2 streets connect S 4 Interstate group: interstate (indivisble) interstate tunnel Street group: street (divisible) street bridge S 3 streets connect Interstate--Street interconnect: transition point Connectivity Nodes (X, Y) Point FCID, FID (-1, 1) (0, 1) (-1, 0) (0, 0) T 1 (0, 0) B 1 (1, 0) P 1 (2, 0) (-1, -1) (0, -1) (1, -1) (-1, -2) (0, -2) (1, -2) Line FCIDs, FIDs, %'s along I 3/0% S 1/0% I 1/0%; I 3/100% I 1/100%; I 2/0% S 1/33% I 2/100%; S 4/0% S 4/100% S 2/50%; S 1/67% S 2/100% S 3/50%; S 1/100% S 3/100% 8

Step 1: Connectivity Analysis l l l 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 9

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

Example j 1 j 2 j 4=T 1 Connectivity Nodes (X, Y) Point FCID, FID (-1, 1) (0, 1) (-1, 0) (0, 0) T 1 (0, 0) B 1 (1, 0) P 1 (2, 0) (-1, -1) (0, -1) (1, -1) (-1, -2) (0, -2) (1, -2) j 3 j 6=P 1 j 7 j 5=B 1 Line FCIDs, FIDs, %'s along I 3/0% S 1/0% I 1/0%; I 3/100% I 1/100%; I 2/0% S 1/33% I 2/100%; S 4/0% S 4/100% S 2/50%; S 1/67% S 2/100% S 3/50%; S 1/100% S 3/100% j 8 j 11 j 9 j 12 Vertex Information Table Line FCID Line FID Relative Position Interstate I 3 0% Streets S 1 0% Interstate I 3 100% Interstate I 1 100% Interstate I 2 0% Streets S 1 33% Interstate I 2 100% Streets S 4 100% Streets S 2 50% Streets S 1 67% Streets S 2 100% Streets S 3 50% Streets S 1 100% Streets S 3 100% j 10 j 13 Junction EID j 1 j 2 j 3 j 4 j 5 j 6 j 7 j 8 j 9 j 10 j 11 j 12 j 13 11

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

Example j 1 j 3 e 1 j 4=T 1 e 10 e 9 j 6=P 1 e 8 j 7 j 5=B 1 e 2 j 8 e 4 j 9 e 5 j 10 e 3 Junction EID j 2 j 5 j 9 j 12 j 8 j 9 j 10 j 11 j 12 j 13 j 6 j 7 j 3 j 4 j 6 j 1 j 3 e 11 Sorted Vertex Information Table Line FCID Line FID Relative Position Streets S 1 0% Streets S 1 33% Streets S 1 67% Streets S 1 100% Streets S 2 50% Streets S 2 100% Streets S 3 50% Streets S 3 100% Streets S 4 100% Interstate I 1 100% Interstate I 2 100% Interstate I 3 100% j 2 j 11 e 6 j 12 e 7 j 13 13

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

Time Dependent Data l Historical Speeds: based on the idea that travel speeds follow a week-long pattern. l l l 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 l l Real Live Predictive 15

Time Dependent Data l 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 l l Left turn is restricted from 4 to 6 pm Right turn is restricted on weekdays only. 16

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

Time Dependent Analysis l l l 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 18

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

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

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

Internal Representation l l l 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). 22

Example 23

Build l There are three additional data processing steps in the above network building example needed to support the population of traffic data. l l l 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. 24

System Architecture 25

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

Experimental Results Table 1 Test Datasets North America Europe Latin America Edges Junctions Size 73. 5 million 27. 2 million 23. 7 GB 141. 5 million 55. 5 million 51. 8 GB 25. 1 million 8. 4 million 6. 9 GB 27

Experimental Results Table 2 Performance Results – North America Average 90 th percentile Local 3 stop routes Nationwide 3 stops routes ~712 ms 4. 4 seconds ~1034 ms 6. 7 seconds Table 3 Performance Results- Europe Average 90 th percentile Local 3 stop routes ~680 ms ~965 ms Nationwide 3 stops routes 3. 5 seconds 5. 5 seconds 28

Questions ? ? ? 29