Framework and Algorithms for Data Analytics, Semantic Querying and

Realistic Modelling of Trafﬁc

Sagar Pathrudkar

, Guido Schroeer

, Vijaya Sarathi Indla

and Saikat Mukherjee

Siemens Technology, India

Siemens Mobility, Germany

Keywords:

Trafﬁc Analytics, Semantic Data Models, Driving Behavior, Real2Sim, Simulation-Based Testing, State

Space Explosion.

Abstract:

Infrastructure elements would be crucial in enabling autonomous mobility at scale to provide centrally shared

insights and possibly planning and control. Infrastructure mounted multi-sensor perception systems observe

trafﬁc and generate data in object list format which typically consists of timestamped vehicle trajectories and

metadata about the vehicles, ie, their type, dimensions, etc. Such data is huge in volume and its analysis

is difﬁcult due to the spatiotemporal sequential nature of the data. In this work, we present framework and

algorithms to semantically model and analyze this data in the context of map geometry to gain statistics and

insights at an actionable level of abstraction. We start with algorithms to process common 2D-HDmap formats

to extract map features - roads, lanes, junctions, etc. We then present meaningful trafﬁc KPIs and statistics

that describe trafﬁc patterns. We ﬁnally describe methods to abstract the trafﬁc patterns and driving behaviors

into parametrized functions for various applications.

1 INTRODUCTION

Infrastructure mounted multi-sensor based trafﬁc per-

ception solutions observe trafﬁc over long periods of

time and gather huge amounts of data. This data is

rich given its multi-sensor nature and can provide ex-

tremely valuable insights wrt trafﬁc patterns, driving

behaviors and critical scenarios in the given map ge-

ometry. In this work we present framework and algo-

rithms to address following questions:

1. How to analyze this data to ﬁnd insights about

trafﬁc behavior in order to identify scenarios of

interest for a junction?

2. How to represent this data in a semantic fashion

and calculate trafﬁc KPIs and statistics to index

this data so that we can partition it based on a con-

dition of interest?

3. How to draw insights wrt microscopic KPIs which

describe the driving behavior of vehicles and

macroscopic KPIs which describe the statistical

simulation of trafﬁc?

4. How to semantically analyze this data so as to

gain insights at an actionable level of abstraction?

1.1 The Problem

The road-trafﬁc ecosystem is a complex system char-

acterized by high-dimensionality, nonlinearity, non-

stationarity and stochasticity. To develop miscella-

neous solutions that would work in open-loop/ closed-

loop, analysis and modelling of such a complex sys-

tem is a challenge. Any ﬁrst principles based analy-

sis/ modelling would essentially be only an approxi-

mation of such a complex system. Due to the high-

dimensionality (high number of inﬂuencing variables

involved), ﬁrst-principle based approaches are prone

to under-modelling. Due to the high nonlineari-

ties, it would be subject to simpliﬁcation and conse-

quently bias. Due to the stochasticities, model based

approaches would involve simplifying assumptions

about additive/multiplicative nature of the stochastic

component and may not estimate the random compo-

nent of the system as well as the deterministic com-

ponent. And due to the nonstationary nature, it may

not account for the evolving behavior of the system

over time, ie, the model’s parameters would need to

be updated dynamically adapting to the changes in the

subtle characteristics of the complex system.

Real world data captures all these complexities. If

there is nonlinearity, it is reﬂected in real world data.

240

Pathrudkar, S., Schroeer, G., Indla, V. and Mukherjee, S.

Framework and Algorithms for Data Analytics, Semantic Querying and Realistic Modelling of Trafﬁc.

DOI: 10.5220/0011838900003479

In Proceedings of the 9th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2023), pages 240-247

ISBN: 978-989-758-652-1; ISSN: 2184-495X

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

Any randomness is also captured by real world data.

When the system properties change or evolve over

time, it is also reﬂected by real world data. So it be-

comes necessary to use real world data to understand

and model the road-trafﬁc system.

1.2 Main Contributions

Given the absolutely huge volume and variety of traf-

ﬁc data that is observed, it becomes crucial to de-

velop efﬁcient and scalable algorithms to process,

condense, analyze and abstract this data. Multi-sensor

trafﬁc data that is observed typically consists of the

trajectories followed by different vehicles, ie, the

timestamped GPS coordinates, velocities of the vehi-

cles, their bounding boxes and orientations (heading/

yaw angles) at each timestamp, metadata such as the

vehicle type (car, bus, motorcycle, etc). This effec-

tively describes what kind of vehicle showcased what

sort of driving pattern/ maneuvers in that geolocation.

The conditioning on geolocation implies that another

feature of the trafﬁc data or another variable required

for complete description or representation of trafﬁc

data is the map geometry in which the driving or traf-

ﬁc maneuvers occurred. So vehicle trajectories data

make sense only when put in the context of map ge-

ometry - junctions, roads, lanes, etc - their locations

and boundaries.

The two major ways of describing the maps - Open-

Drive standards and Lanelet2 maps - encode the in-

formation regarding the map elements such as road

geometries, lane widths/lengths, junctions, elevation

proﬁles, etc. So the ﬁrst step to analyzing trafﬁc

data in the context of a map geometry is naturally

the extraction of this feature-level (roads, lanes, junc-

tions) information from the OpenDrive and/or Lanelet

maps.

Also to gain meaningful insights from such huge data,

it is important to condense data into meaningful or se-

mantic representation. Such semantic representation

should abstract all the discrete and independent enti-

ties in the real world road-trafﬁc ecosystem and model

their relationships and interactions accordingly. This

would enable description of trafﬁc patterns and driv-

ing behavior in a semantic fashion that allows in-

sights at actionable level of abstraction. We design

the schema of the semantic trafﬁc database to repre-

sent static entities of the map, ie, roads, lanes, junc-

tions and the dynamic entities of the map, ie, vehicles,

etc and their relationships. The resulting graph when

traversed for a vehicle essentially describes its entire

journey in the map or road network.

1.3 Related Work

Semantic trafﬁc models have been constructed us-

ing semantic and geographic information of trajec-

tory data happens along network infrastructure si-

multaneously (Haubrich et al., 2014). In (Mirboland

and Smarsly, 2018), a generative model of 3D ur-

ban scenes is proposed which is able to reason not

only about the geometry and objects present in the

scene, but also about the high-level semantics in the

form of trafﬁc patterns. An extendable model rep-

resenting road network logics (RNL) which allows

the integration of trafﬁc semantic information is pro-

posed in (L

ecu

e et al., 2012) for navigation and de-

cision making. Entity-entity and entity-environment

interactions with simple, feed-forward computations

in each timestep within an overall temporal model

of an agent’s behavior are demonstrated in (Buechel

et al., 2017). One of the key elements in the ADAS

system is to develop an algorithm to understand the

driver behaviors which can detect and analyze com-

mon driving maneuvers, such as making turns, on

an individual-by-individual basis – in (Bachmann,

2011), a position-based turn detection algorithm for

detecting turns from vehicle data and GPS coordi-

nates. A novel method of trajectory description is pro-

posed to establish the semantic model for automatic

trafﬁc violation events detection in (Wei et al., 2014).

In our previous work (Pathrudkar, 2021) we brieﬂy

described the semantic graph database for modelling

vehicle driving patterns in the context of road geom-

etry and motivate the problem of generating realistic

driving behavior for AV testing in simulation.

Section 2 describes the broad system overview

through the steps involved, database design, deter-

ministic and data-driven algorithms involved in devel-

oping the system. Section 3 describes the map pro-

cessing algorithms to extract the map features such

as road, lanes and junctions. Section 4 describes the

semantic graph database of trafﬁc and how it can be

used to describe the driving behavior of vehicles at

a semantic level along with a few graph data science

applications to draw insights from the database. Sec-

tion 5 describes how the data can statistically be used

to abstract the driving behavior of vehicles. Finally,

Section 6 provides concluding remarks and discusses

the next steps in this stream of work.

2 SYSTEM OVERVIEW

The Trafﬁc Analytics system (Figure 1) has two main

pillars. The ﬁrst being the high level framework to

process data from its object list stage into various lev-

Framework and Algorithms for Data Analytics, Semantic Querying and Realistic Modelling of Trafﬁc

241

els of analytics insights. And second being the al-

gorithms used to compute trafﬁc KPIs, perform se-

mantic analysis and also process the maps to contex-

tualize the trafﬁc data. The framework processes the

trafﬁc data in stages - ﬁrst it takes the object list data

from multi-sensor perception systems along with the

map geometry for that data either in OpenDrive or

Lanelet map format. It then extracts the map features

such as the boundaries of various roads and/or lanes

along with the geometries of various junctions - ap-

proach angles, junction radii, etc. It then describes

the semantic journey of the vehicle trajectory through

the network - at what time the vehicle was travelling

through which lane, at what time it crossed which

junction, taking what kind of turn (straight, left, right

or u-turn), what was the turning speed and the turn-

ing angle. This information is then represented in a

semantic graph database. Many trafﬁc KPIs that de-

scribe the trafﬁc behavior are also computed to de-

scribe the trafﬁc patterns and driving behaviors - time

headways, distance headways, accelerations, jerks,

throughput at a junction, network speed, density, ﬂow

rate from various entry nodes, etc.

We also process the semantic trafﬁc database using

multiple graph data science algorithms generating ad-

ditional insights. We use centrality algorithms to gen-

erate ranking insights such as which junctions are

more important wrt speciﬁc trafﬁc maneuvers for ex-

amples sharp higher speed turns making the junction

more dangerous than others. We use community al-

gorithms to generate clustering and grouping insights

such as which speciﬁc junctions and vehicles can be

sliced into sub-databases without losing much infor-

mation allowing additional insights such as particu-

lar types of vehicles travel through particular kinds of

junctions at particular times along with more efﬁcient

processing. We use similarity algorithms to generate

insights such as which types of vehicles exhibit simi-

lar behavior or which kinds of junctions create similar

kind of trafﬁc, etc. We ﬁnally use link prediction al-

gorithms to identify which vehicles and junctions are

likely to form a link, ie, which kind of vehicles are

likely to generate what kind of driving maneuver at

what kind of junction with what probability.

The trafﬁc analytics framework ﬁnally abstracts

the trafﬁc statistics and semantics into parameterized

functions or probability distributions. Such functions

realistically model the trafﬁc and driving behaviors

and can be used to represent these complex system

while developing and testing any products and solu-

tions that operate with real world trafﬁc.

3 ALGORITHMS TO EXTRACT

MAP FEATURES

Figure 2 demonstrates the vehicle trajectories from

an area shown in Figure 3. The trajectories make

sense only when put in the context of a map geom-

etry. Hence it is crucial to capture the various map

features such as junctions, roads, lanes and their con-

ﬁgurations and geometries.

3.1 OpenDrive Map Format

The geometry of the roads in OpenDrive (ASA, 2020)

is characterized by a central reference line. 3 differ-

ent coordinate systems used Figure 4. The s-t coordi-

nate system traverses the length and orientation of the

road curve, the u-v system indicates the starting ori-

entation of a road curve, and the inertial x-y system

that provides as a global reference for junctions and

road starting positions. The lane width is described

using the s-t system, while the shape of the reference

line is described in the u-v system. The shape can be

described in different ways such as linear, parameter-

ized cubic polynomial, arcs, spirals, etc Figure 6.

3.2 Road and Lane Boundaries

Extraction from OpenDrive Map

Format

To analyze the trajectories data in conjunction with

maps data, we need to convert the vehicle coordinate

to the s-t system. There is no direct way to do this,

so we ﬁrst convert it into the u-v system. The road

geometry is taken as mentioned in the curve type (pa-

rameterized cubic polynomial, linear, arc, spiral, etc)

. The road is a parametric (wrt parameter p) curve

(Figure 6) in the u-v system. From the transformed

vehicle u-v coordinates we ﬁnd the length of the nor-

mal to this curve and the point of intersection of this

curve. The length of the normal gives the t coordinate.

The length of the curve from starting point to point of

intersection gives the s coordinate. We ﬁnd the value

of the s coordinate by measuring the distance travelled

over its centerline from the starting point. We do this

by calcuating path integral over the centerline. We get

the value for the t coordinate using the perpendicular

distance to the curve from the point of interest. We

use this (s,t) coordinate to describe the (x,y) coordi-

nate’s road section and lane.

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Figure 1: System for Trafﬁc Statistics and Semantic Analytics.

Figure 2: Vehicle trajectories in a geographical area.

Figure 3: Map of the geographical area.

Figure 4: Coordinate systems in OpenDrive map format

(ASA, 2020).

Figure 5: Example of roads, lanes and sections in XODR

(ASA, 2020).

Figure 6: Parameterized descriptions of road format (ASA,

2020).

3.3 Junction Location and

Conﬁguration Identiﬁcation

A junction in OpenDRIVE (ASA, 2020) format is de-

ﬁned by the list of incoming and connecting roads.

Connecting roads are what form the junction neces-

sarily while the incoming roads are those that enter

and exit the junction at various directions. A refer-

ence line is provided for each of these roads in terms

of different geometries as mentioned in the previous

sections. A transformation is required between the in-

ertial x-y system and the coordinates of the local u-v

system that is headed along the direction of beginning

of the road geometry to retrieve the junction coordi-

nates in the x-y system. The steps of extraction are as

follows: 1. For each of the junction nodes, connect-

Framework and Algorithms for Data Analytics, Semantic Querying and Realistic Modelling of Trafﬁc

243

Figure 7: Junction as deﬁned the OpenDrive map format.

Figure 8: x-Y to u-v coordinate conversion in OpenDrive

HDmap format.

ing roads are identiﬁed. 2. The end geometries of the

connecting roads are chosen to be transformed. 3. For

each of the geometry, the u-v endpoint is transformed

to x-y frame as follows 1. A translation by (aU, aV)

2. A rotation by angle ‘hdg’ (The heading angle pro-

vided for a given u-v frame) 3. A translation by (x0,

y0) where (x0, y0) represents the start point of the ge-

ometry in the inertial x-y frame. 4. Once the critical

points are identiﬁed in the x-y plane, the centroid of

the convex hull of the points is used as a deﬁnition

of junction position (mean of the coordinates) and the

standard deviation is used as a measure of the radius

of the junction. (A scale factor of 1.5 is introduced to

allow for robustness)

4 SEMANTIC ANALYSIS OF

TRAFFIC DATA

In this section we present the semantic database de-

sign and algorithms to generate meaningful insights

and statistics from trafﬁc data.

4.1 Semantic Database of Trafﬁc

To analyze the road-trafﬁc ecosystem at a location

from the real-world data, all the entities which are

static such as junctions, roads and lanes and ones that

are dynamic such as vehicles need to be represented

at a common level of abstraction along with the kind

of interaction that happen between these entities. Se-

mantic data models are an excellent choice as they can

store the trafﬁc data in a way that captures the rela-

tionships or events and parameterizes an AV test sce-

nario in an intuitive, expandable and easily analyzable

manner. We deﬁne the schema for the database such

that the junctions, lanes and vehicles are represented

as nodes. The lane and junctions have attributes cor-

responding to their positions and boundaries. The

vehicles have attributes corresponding to their trajec-

tories which are timestamped paths followed by the

vehicles. The relationships between the vehicle and

junction are characterized by turn type, turning speed,

turning angle and turning time. The relationships be-

tween the lanes and vehicles are characterized by en-

try times and exit times of the vehicles into and out of

lanes.

Figure 9: Graphical visualization of a semantic trafﬁc

database of a ﬁve-junction area.

4.2 Example Trafﬁc Statistics and

Insights from the Semantic

Database

The trafﬁc database can then be statistically analyzed

to gain interesting insights such as below. The idea

is to use these insights to smartly design the exper-

imental scenarios of simulation-based testing of au-

tonomous vehicles. For example, in Figure 11, a scat-

ter plot shows the distribution of turning speed and

turning angle pairs. Such analysis can be used to

determine the more likely combinations or combina-

torial ranges of turning speed – turning angle pairs

as well as the anomalies and edge or corner cases.

In the below plot it can be seen that the turn angle-

speed pairs are mainly clustered in two areas which

cover only about half of the combinatorial state space.

Speed variability at an intersection can also be de-

scribed.

4.3 Graph Data Science Applications on

Trafﬁc Database

The semantic database of trafﬁc further opens up a

multitude of use cases in the form of graph algorithms

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244

Figure 10: Scatter plot showing the distribution of turning

speeds and turn angles.

Figure 11: Box plots of vehicle speed distributions in the

trafﬁc network.

and graph data science algorithms. The main themes

are community detection (group clustering or parti-

tions options), importance assignment or centrality

(creating hierarchy of the nodes in terms of a prede-

ﬁned parameter), similarity detection (evaluation of

likeliness of different nodes) and heuristic link pre-

diction (estimating the chance of two nodes forming

a link), etc.

4.3.1 Basic Statistics and Insights from

Semantic Trafﬁc Database

Through our framework, semantic queries can be used

for interesting insights on trafﬁc patterns. For exam-

ple as shown in Figure 12, we can query information

such as all the left turn events that happened at a par-

ticular junction, that were of a particular angle and

involved vehicles which also took a right turn at an-

other junction.

Figure 12: Basic Queries and corresponding Results from

Semantic trafﬁc database.

4.3.2 Centrality Algorithms - Node Importance

Through centrality algorithms, we can identify which

junctions or vehicles saw more activity as weighted

by composite properties that are for example, directly

proportional to turning speed and inversely propor-

tional to turning radius.

Table 1: Centrality – Ranking the junctions based on the

trafﬁc busy-ness.

name of junc-

tion

score

”3003000”

1.73347910

”3004000”

1.39484522

”3002000”

1.22697023

”3000000”

0.94313098

”3001000”

0.93407434

4.3.3 Community Algorithms - Slice Database

We can use the community set of algorithms from

graph data science to partition our database into

smaller chunks for more efﬁcient analysis. This can

also be used to cluster a group of junctions and vehi-

cles that have common interactions from other set(s).

Table 2: Community – Cluster the database of full map and

all vehicles into sub-map and subset of vehicles.

commmunity

names of nodes

”0”

[”3003000”, ”veh5”,

”veh6”, ”veh8”, ”veh9”,

”veh13”]

”1”

[”3004000”, ”veh10”,

”veh12”, ”veh15”,

”veh24”, ”veh31”]

”2”

[”3000000”, ”veh0”,

”veh3”, ”veh3”,

”veh11”, ”veh26”]

4.3.4 Similarity Algorithms - Node Similarity

Similarity algorithms can be used to identify which

pairs of vehicles and junctions exhibit similar behav-

ior to one another.

Framework and Algorithms for Data Analytics, Semantic Querying and Realistic Modelling of Trafﬁc

245

Table 3: Similarity – which pairs of vehicles or junction

exhibit similar behavior to each others.

name of ﬁrst

node

name of sec-

ond node

similarity

”veh4”

”veh19” 1.0

”veh5”

”veh6” 1.0

”veh3”

”veh0” 1.0

”veh5”

”veh8” 1.0

5 DRIVING BEHAVIOR

MODELLING AND

ABSTRACTION

In this section we show how real world trafﬁc data

can be used to model the driving behavior using pa-

rameterized functions. For the simple scenario of a

vehicle turning at an intersection, multiple factors in-

ﬂuence and multiple variables describe its behavior.

Main variables that can be attributed to a turn are the

turning speed, turning angle and general turn trajec-

tory. We abstract all three from captured real world

data into parameterized functions.

Figure 13: Histogram of (left) turning speed and angle at an

intersection.

The captured data can be visualized in histograms

to understand general descriptive statistics and empir-

ical distribution of the variable. It can then be ﬁt into

cumulative distribution functions based on the his-

togram as percentage of data before a speciﬁc value

to describe the cumulative probability at that value.

Many probability distribution functions can be used

based on general shape of the distribution.

Figure 14: Fitted empirical distributions describing turning

behavior wrt turning speed and angle.

Finally these distributions can be sampled from

and resulting samples can be used for many appli-

cations such as edge-case evaluation, scenario vari-

ations, scenario augmentation for simulation based

testing of AV stacks.

Figure 15: Trajectory Generation and Variation for Realistic

Scenarios in Simulation-based testing of AV stacks.

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246

6 CONCLUSIONS AND FUTURE

WORK

In this paper we have presented Trafﬁc Analytics Sys-

tem that analyses real world data and represents the

road-trafﬁc ecosystem in a semantic fashion. Our

framework produces trafﬁc analytics insights at ac-

tionable level of abstraction due to the semantic na-

ture of the database constructed and analyzed. We

also presented map-processing algorithms to extract

map features such as roads, lanes and junctions. We

also presented graph data science applications on the

semantic database of trafﬁc. Finally we presented

how real world trafﬁc data can be used to abstract

driving behavior which can in turn be used to gen-

erate realistic scenarios for simulation based testing

of AV stacks.

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