Traffic Flows Mesoscopic Simulation...
Transcript of Traffic Flows Mesoscopic Simulation...
D R . S C . I N G . M I H A I L S S AV R A S O V S
T R A N S P O R T A N D T E L E C O M M U N I C AT I O N I N S T I T U T E
R I G A , L AT V I A
TRAFFIC FLOW SIMULATION USING
MESOSCOPIC APPROACH
Time line3
Higher Military
School for Aviation
Engineers (Riga)
1946
Riga Institute for
Civil Aviation
Engineers (Riga)
1960
1992
Riga Aviation
University
TSI
University of
applied
sciences
1999
Aircraft Technician
School (Kiev)
1919
Key data4
Number of students: > 2900
Faculties:
Computer Science and Telecommunication
Management and Economics
Transport and Logistics
Levels:
Bachelor/Professional qualification
Master
PhD
Staff: >160 teaching staff
Contents7
Introduction
Fundamentals of mesoscopic discrete rate
approach
Formulation of discrete rate traffic reference model
Case-study: simulation of the two connected
crossroads
Case-study: Urban transport corridor mesoscopic
simulation
Requirements to the modern transport system8
Transport – key element of modern economics
Ecological requirements
EffectivenessSafety
Sustainable development9
Sustainable development is a development that meets the needs of the present without compromising the ability of future generations to meet their own needs
Transport sustainable development tools: use of ITS (Intelligent Transportation Systems)
use of P&R (Park and Ride)
optimization of existing transport infrastructure
development of intermodality
implementation of new transport infrastructure elements onthe base of doing strict impact analysis
use of sound tax policy
etc
Traffic analysis tools10
A traffic analysis tools is a collective term used to describe a variety of
software-based analytical procedures and methodologies that support
different aspects of traffic and transportation analyses
Traffic analysis tools:
• Sketch –planning tools
• Travel demand models
• Analytical deterministic tools (HCM, ICU…)
• Traffic signal optimization tools
• Macroscopic simulation models
• Mesoscopic simulation models
• Microscopic simulation models
Mesoscopic models12
Mesoscopic models combine the properties of both microscopic and macroscopic simulation models. These models simulate individual vehicles, but describe their activities and interactions based on aggregate (macroscopic) relationships 1
Mesoscopic models of traffic flow are based on estimation macroscopic indices on microscopic level 2
Mesoscopic models combine the properties of both microscopic and macroscopic simulation models. These models simulate individual vehicles or group of vehicles, but describe their activities and interactions based on aggregate (macroscopic) relationships
1) http://www.dot.ca.gov
2) Gilkerson G. et al. 2005. Traffic Simulation
Some mesoscopic models
СONTRAM (Leonard, D.R. et al. 1989)
Cellular Automata (Nagel K. and Schreckenberg M. , 1992)
DYNASMART (Jayakrishnan, R. et al. 1994)
DYNAMIT (Ben-Akiva, M. 1996)
FASTLANE (Gawron, C. 1998)
DTASQ (Mahut, M. 2001)
MEZZO (Burghout, W. 2004)
AMS (Y. C. Chiu, L. Zhou, and H. Song, 2010)
13
Common disadvantages:
• Realised in proprietary software
• Defined only theoretically
General comparison of approaches17
Performance
RequirementsResources
Performance
Fulfillment
Performance
Results
Quantities of Materi-
al and/or Orders Quantities of
Resources
Processing of
Material and/or
Order Portions
Throughputs
Cycle Times
Inventories
Utilizations
Costs
Individual Objects Objects as
Resource
Units
Execution of
individual
Operations
Event Streams
Decomposition Decomposition
Mes
osco
pic
Vie
w
Mic
rosc
opic
Vie
w
Aggregation
Mesoscopic
Simulation
Microscopic
Simulation
Aggregation
Stream Intensities
Initial Inventories
Integration of
Differential
Equations
Aggregated
Throughputs
Inventories
CostsMacroscopic
Simulation
Aggregation
Stream Intensities
Initial Inventories
Mac
rosc
opic
Vie
w
Performance
RequirementsResources
Performance
Fulfillment
Performance
Results
Quantities of Materi-
al and/or Orders Quantities of
Resources
Processing of
Material and/or
Order Portions
Throughputs
Cycle Times
Inventories
Utilizations
Costs
Individual Objects Objects as
Resource
Units
Execution of
individual
Operations
Event Streams
Decomposition Decomposition
Mes
osco
pic
Vie
w
Mic
rosc
opic
Vie
w
Aggregation
Mesoscopic
Simulation
Microscopic
Simulation
Aggregation
Stream Intensities
Initial Inventories
Integration of
Differential
Equations
Aggregated
Throughputs
Inventories
CostsMacroscopic
Simulation
Aggregation
Stream Intensities
Initial Inventories
Mac
rosc
opic
Vie
w
Characteristics of the mesoscopic
discrete rate approach19
Discrete Rate
Event planning for continuous processes
Concepts of discrete rate approach
Formally mesoscopic models can be represented as funnel
funnel
( ) arrival rate (cust/h)
( ) process rate (cust/h)
( ) interarrival rate(cust/h)
funnel volume
( ) and ( ) ( )
The idea of calculation current value of output flow c
in
out
cap
cap out
t
t
t
B
B t B t t
1 1
1
an be presented :
0, if 0 and B=0
, if 0 and and B=0
, if 0
( ) ( )
( ) - controlled parameter, can be set in any time point
in
out in in in
in out
j j j j
j j j
B
B t t B t t
t t t t
21
M. Schenk, Y. Tolujew, and T. Reggelin, "A Mesoscopic Approach to the Simulation of Logistics Systems," Advanced Manufactoring and Suistainable Logistics Lecture Notes in Business Information Processing, vol. 46, no. 1, pp. 15-25, 2010.
M O D E L F O R U N C O N G E S T E D N E T W O R K
M O D E L F O R C O N G E S T E D N E T W O R K
22
Formulation of DRTRM
(discrete rate traffic reference model)
Mathematical Representation (1/4)25
• 𝜆𝑖 – input intensity of the flow from direction i=1..5 (used units: PCU per time unit);
• 𝛽𝑖- output flow value from direction i=1..5 (used units: PCU per time unit);
• 𝜆𝑖𝑙 , 𝜆𝑖
𝑠 , 𝜆𝑖𝑟 - intensity of the flow for the turns (l-left; s-straight; r-right) from direction
i=1..5 (used units: PCU per time unit);
• 𝑏𝑖𝑙 , 𝑏𝑖
𝑠 , 𝑏𝑖𝑟 - queue length for the turns (l-left; s-straight; r-right) from direction i=1..5
(used units: PCU);
• µ𝑖𝑙 , µ𝑖
𝑠 , µ𝑖𝑟 -the processing rate for the turns (l-left; s-straight; r-right) from direction
i=1..5 (used units: PCU per time unit);
• 𝛽𝑖𝑙 , 𝛽𝑖
𝑠 , 𝛽𝑖𝑟 – output flow rate for the turns (l-left; s-straight; r-right) from direction
i=1..5 (used units: PCU per time unit);
• 𝛽𝑖 – total output flow to direction i=1..5 (used units: PCU per time unit);
• 𝐵5𝑐𝑎𝑝
- the maximum value of queue length for direction 4 (used units: PCU);
Mathematical representation (2/4)26
The following equations could be written:
𝜆𝑖
𝑟 𝑡 = 𝜆𝑖 𝑡 𝑝𝑖𝑟
𝜆𝑖𝑠 𝑡 = 𝜆𝑖 𝑡 𝑝𝑖
𝑠
𝜆𝑖𝑙 𝑡 = 𝜆𝑖 𝑡 𝑝𝑖
𝑙
𝑝𝑖𝑟 + 𝑝𝑖
𝑠 + 𝑝𝑖𝑙 = 1
(5.1)
where:
• 𝑝𝑖𝑟 , 𝑝𝑖
𝑠 , 𝑝𝑖𝑙 – a probability of turns (l-left; s-straight; r-right) from direction i=1..5;
• 𝑡 – current time.
𝛽1 𝑡 = 𝛽1
𝑠 𝑡 + 𝛽4𝑟 𝑡 + 𝛽3
𝑙 𝑡
𝛽2 𝑡 = 𝛽2𝑠 𝑡 + 𝛽3
𝑟 𝑡 + 𝛽4𝑙 𝑡
𝛽3 𝑡 = 𝛽3𝑠 𝑡 + 𝛽1
𝑟 𝑡 + 𝛽2𝑙 𝑡
𝛽4 𝑡 = 𝛽4𝑠 𝑡 + 𝛽1
𝑟 𝑡 + 𝛽2𝑙 𝑡
𝛽5 𝑡 = 𝛽5𝑠 𝑡 + 𝛽5
𝑟 𝑡 + 𝛽5𝑙 𝑡
(5.2)
Mathematical representation (3/4)27
𝛽𝑖∈(1,2,4,5)𝑠 𝑡 =
0, 𝜆𝑖𝑠 𝑡 = 0 𝑎𝑛𝑑 𝑏𝑖
𝑠 𝑡 = 0
𝜆𝑖𝑠 𝑡 ,𝜆𝑖
𝑠 𝑡 > 0 𝑎𝑛𝑑 𝜆𝑖𝑠 𝑡 ≤ 𝜇𝑖
𝑠 𝑎𝑛𝑑 𝑏𝑖𝑠 𝑡 = 0
𝜇𝑖𝑠 , 𝑏𝑖
𝑠 𝑡 > 0
(5.4)
𝛽𝑖∈(2,3,4,5)𝑟 𝑡 =
0, 𝜆𝑖𝑟 𝑡 = 0 𝑎𝑛𝑑 𝑏𝑖
𝑟 𝑡 = 0
𝜆𝑖𝑟 𝑡 ,𝜆𝑖
𝑟 𝑡 > 0 𝑎𝑛𝑑 𝜆𝑖𝑟 𝑡 ≤ 𝜇𝑖
𝑟 𝑎𝑛𝑑 𝑏𝑖𝑟 𝑡 = 0
𝜇𝑖𝑟 , 𝑏𝑖
𝑟 𝑡 > 0
(5.5)
Model for congested network29
𝑟 𝑡 = 𝑑 − 𝑏2 𝑡 (5.10)
0
0 max
max
(1 * ) if sat<sat
(1 * ) ( ) if sat sat
1
b
cur crit
b
cur crit
crit
t t a sat
t t a sat q q d
qsat
q c
sat
Compare micro-, meso-, macromodels parameters and
characteristics 30
Microscopic models Macroscopic models
Traffic flow
• Intensity of the flows
• Different types of vehicles with
different characteristics
• Interaction between vehicles
• Queuing is possible
• Influence on speed from other
vehicles
Infrastructure
• Real sizes of the road (including
lane number)
• Geometry of the road
• Topology of the crossroads
• Traffic lights data
• Priority rules
Traffic flow
• Volume of traffic
• Homogeneous flow
• No interaction between flows
• Queues are not taken into account
• Influence on speed in form of VDF
Infrastructure
• Link-node notation
• Length of the links
• Traffic lights are not taken into
account
• No priority rules
Traffic flow
• Volume of traffic
• Homogeneous flow
• Interaction between flows
• Queuing is possible
• Influence on speed in form of VDF
Infrastructure
• Link-node notation
• Length of the links
• Traffic lights data
• Priority rules
Mesoscopic models
Simulation object32
Source 1
Source 2
r1
s1
l1
r2
s2
l2
r3
s3
l3 r4
s4
l4
Source 5
Source 6
r5
s5
l5
r6
s6
l6
r7
s7
l7 r8
s8
l8Source 3
1
2
3 4
Queue 4
Queue 7
7
Queue 2
Queue 3
Queue 1 Queue 5
Queue 6
Queue 8
Source 8
5
6
8
Source 1
Source 2
r1
s1
l1
r2
s2
l2
r3
s3
l3 r4
s4
l4
Source 5
Source 6
r5
s5
l5
r6
s6
l6
r7
s7
l7 r8
s8
l8Source 3
1
2
3 4
Queue 4
Queue 7
7
Queue 2
Queue 3
Queue 1 Queue 5
Queue 6
Queue 8
Source 8
5
6
8
Cycle time
25 s 5 s 25 s 5 s 60 s
Cycle time
30 s 5 s 30 s 5 s 70 s
Cycle time
40 s 5 s 40 s 5 s 90 s
1st Crossroad (left)
2nd Crossroad (right)
1st variant2nd Crossroad (right)
2st variant
Incoming
flow
Distribution
law
Flow intensity
mean value (m/min)
Crossroad
passing
r Uniform 20 0,6
s Uniform 65 0,8
l Uniform 10 0,6
Structure of mesoscopic model33
So1
r1 s1 l1
So2 So3
Flow control
r2 s2 l2 r3
s3
l3 r4 s4 l4
Fu1 Fu2 Fu3 Fu4
Legend:
source
funnel
material f low
information flow
control data
type of productr1
So
Fu
So5
r5 s5 l5
So6 So8
r6 s6 l6 r7 s7 l7 r8
s8
l8
Fu5 Fu6 Fu7 Fu8
Cro
ss
road
1C
ross
road
2
So1So1
r1 s1 l1
So2So2 So3So3
Flow control
r2 s2 l2 r3
s3
l3 r4 s4 l4
Fu1 Fu2 Fu3 Fu4
Legend:
source
funnel
material f low
information flow
control data
type of productr1
So
Fu
Legend:
source
funnel
material f low
information flow
control data
type of productr1
So
Fu
So5So5
r5 s5 l5
So6So6 So8So8
r6 s6 l6 r7 s7 l7 r8
s8
l8
Fu5 Fu6 Fu7 Fu8
Cro
ss
road
1C
ross
road
2
Microscopic model
PTV VISION VISSIM
Number of links and connectors – 66
Number of vehicle inputs – 18
Number of routes – 24
Number of conflict areas – 8
Number of traffic lights – 24
Data collection points – 24
34
Validation of mesoscopic model
Qualitative
Animation
Queue dynamics comparison
Box-Whisker plots
35
Main hypothesis:
no significant difference between output from microscopic and
mesoscopic models
Quantitative
Test for homogeneity
Student t-test
Mann-Whitney u-test
Confidence interval test
Naive test
Novel test
Validation results
Data set
Qualitative
validation
(animation)
Test for
homogeneity
Confidence
interval testNaive test Novel test
Queue 1 Valid Valid Valid Valid Valid
Queue 2 Valid Valid Valid Valid Not valid
Queue 3 Valid Valid Valid Valid Valid
Queue 4 Valid Valid Valid Not valid Not valid
Queue 5 Valid Valid Valid Valid Valid
Queue 6 Valid Valid Valid Valid Not valid
Queue 7 Valid Valid Valid Not valid Not valid
Queue 8 Valid Valid Valid Valid Not valid
39
TA S K S I N F R A M E O F A P P R O B AT I O N O N R E A L D ATA :
1 ) D E T E R M I N E I N P U T D ATA F O R M E S O S C O P I C M O D E L
2 ) M O D E L D E V E L O P M E N T
3 ) E S T I M AT I O N O F L O S
4 ) C O M PA R E O U T P U T R E S U LT S W I T H M I C R O S C O P I C S I M U L AT I O N
40
Case-study: Urban transport corridor
mesoscopic simulation
Simulation Object41
1496 m.
139 m. 127 m. 46m. 156 m. 138 m. 151 m. 180 m. 404 m. 155 m.
1 2
3
4 5 6 7 8
9
10
Input Data: Passing function estimation
More than 7 hours of video from two crossroads
More than 400 observations
43
Exemplary chart
0
50
100
150
200
250
300
350
400
450
0 10 20 30 40 50 60
time (s)
qu
an
tity
(m
)
t1 t2q1
q2
Exemplary chart
0
50
100
150
200
250
300
350
400
450
0 10 20 30 40 50 60
time (s)
qu
an
tity
(m
)
t1 t2q1
q2
Output results50
Crossroad
Number
Microscopic model Mesoscopic
model
LOS Average
delay time (s) LOS
Average
delay time (s)
1 B 14.5 B 18.6
2 B 13.8 B 17.5
3 A 1.6 A 1.2
4 B 17.3 B 17.6
5 B 18.1 C 21.6
6 B 11.2 B 14.3
7 C 20.6 C 30.8
8 C 31.2 D 45.5
9 A 2.1 A 1.2
10 D 41.5 E 55.6
*
*
*
Publications (1/2)
Savrasovs M. "Traffic Flow Simulation on Discrete Rate Approach Base", Transport and
Telecommunication, Vol. 13, April, 2012, pp. 167-173.
Savrasovs M. “Urban Transport Corridor Mesoscopic Simulation”, the 25th European
Conference on Modelling and Simulation (ECMS’2011) , 2011, pp. 587-593.
Savrasovs M. “The Application of a Discrete Rate Approach to Traffic Flow Simulation”,
the 10th International Conference, Reliability and Statistics in Transportation and
Communication, 2010, pp. 433-439.
M. Savrasov, I. Yatskiv, A. Medvedev and E. Yurshevich. "Simulation as a Tool of
Decision Support Process: Latvia-based Case Study". In Proceedings of 1-st
International Conference on Road and Rail Infrastructure (CETRA 2010). 2010. pp.
217-222.
Savrasovs M. “Mesoscopic Simulation Concept for Transport Corridor”, the 12th World
Conference on Transport Research (WCTR 2010). Lisbon, Portugal, 2010.
52
Publications (2/2)53
Yatskiv, I., Savrasovs, M. “Development of Riga-Minsk Transport Corridor Simulation Model”.
Transport and Telecommunication, 2010, Volume 11, No 1, pp. 38-47.
Savrasovs, M. “Overview of Traffic Mesoscopic Models”, the 2nd International Magdeburg
Logistics PhD Students’ Workshop, 2009, pp. 71-79.
Savrasovs M. “Flow Systems Analysis: Methods and Approaches” Computer Modelling and New
Technologies, 2008, Volume 12, No 4, pp. 7-15.
Savrasovs, M., Toluyew, Y. “Transport System’s Mesoscopic Model Validation Using Simulation
on Microlevel”, the 8th International Conference, Reliability and Statistics in Transportation and
Communication, 2008, pp. 297-304.
Savrasovs, M. “Overview Of Flow Systems Investigation And Analysis Methods”, the 8th
International Conference, Reliability and Statistics in Transportation and Communication, 2008
pp. 273-280.
Toluyew, Y., Savrasov, M. “Mesoscopic Approach to Modelling a Traffic System”, International
Conference, Modelling of Business, Industrial and Transport Systems, 2008, pp. 147-151.
Savrasov, M., Toluyew, Y. “Application of Mesoscopic Modelling for Queuing Systems Research”,
the 7th International Conference, Reliability and Statistics in Transportation and Communication,
2007, pp. 94-99.