TRAFFIC FLOW SIMULATION USING MESOSCOPIC APPROACH

Transcription

1 TRAFFIC FLOW SIMULATION USING MESOSCOPIC APPROACH 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

2 I am from Latvia 2

3 Aircraft Technician School (Kiev) 1919 Time line 3 Riga Institute for Civil Aviation Engineers (Riga) 1960 TSI University of applied sciences Higher Military School for Aviation Engineers (Riga) 1992 Riga Aviation University

4 Number of students: > 2900 Faculties: Key data Computer Science and Telecommunication Management and Economics Transport and Logistics Levels: Bachelor/Professional qualification Master PhD Staff: >160 teaching staff 4

5 Key research directions 5

6 6

7 Introduction Contents Fundamentals of mesoscopic discrete rate approach 7 Formulation of discrete rate traffic reference model Case-study: simulation of the two connected crossroads Case-study: Urban transport corridor mesoscopic simulation

8 Requirements to the modern transport system Transport key element of modern economics 8 Ecological requirements Safety Effectiveness

9 Sustainable development 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 on the base of doing strict impact analysis use of sound tax policy etc 9

10 Traffic analysis tools 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 10 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

11 Macro-, Mezo-, Micro- 11

12 Mesoscopic models 12 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) 2) Gilkerson G. et al Traffic Simulation

13 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) 13 FASTLANE (Gawron, C. 1998) DTASQ (Mahut, M. 2001) MEZZO (Burghout, W. 2004) Common disadvantages: Realised in proprietary software Defined only theoretically AMS (Y. C. Chiu, L. Zhou, and H. Song, 2010)

14 Fundamentals of discrete rate approach 14

15 Traditional simulation approaches 15 Discrete Rate

16 Level of detail VS simulation efforts 16

17 Microscopic View Mesoscopic View Macroscopic View General comparison of approaches 17 Performance Requirements Resources Performance Fulfillment Performance Results Stream Intensities Initial Inventories Aggregation Stream Intensities Initial Inventories Integration of Differential Equations Macroscopic Simulation Aggregated Throughputs Inventories Costs Quantities of Material and/or Orders Aggregation Quantities of Resources Mesoscopic Simulation Processing of Material and/or Order Portions Throughputs Cycle Times Inventories Utilizations Costs Decomposition Decomposition Microscopic Simulation Aggregation Individual Objects Objects as Resource Units Execution of individual Operations Event Streams

18 Flow process models 18

19 Characteristics of the mesoscopic discrete rate approach 19 Discrete Rate Event planning for continuous processes

20 Hybrid characteristics of a mesoscopic discrete rate approach 20

21 Concepts of discrete rate approach Formally mesoscopic models can be represented as funnel in ( t) arrival rate (cust/h) ( t) process rate (cust/h) B out cap ( t) interarrival rate(cust/h) funnel volume funnel 21 cap out B ( t) B and ( t) ( t) The idea of calculation current value of output flow can be presented : in 0, if 0 and B=0 out in in in, if 0 and and B=0, if B 0 B ( t t ) B ( t ) t in out j 1 j j 1 j ( t) - controlled parameter, can be set in any time point t t t j j 1 j 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 , 2010.

22 Formulation of DRTRM (discrete rate traffic reference model) 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 22 M O D E L F O R C O N G E S T E D N E T W O R K

23 Example of transport node 23 input flows turning flows output flows

24 Transport network in DRTRM notation

25 Mathematical Representation (1/4) 25 λ i input intensity of the flow from direction i=1..5 (used units: PCU per time unit); β i - output flow value from direction i=1..5 (used units: PCU per time unit); λ l i, λ s r i, λ i - intensity of the flow for the turns (l-left; s-straight; r-right) from direction i=1..5 (used units: PCU per time unit); b l i, b s i, b r i - queue length for the turns (l-left; s-straight; r-right) from direction i=1..5 (used units: PCU); µ l i, µ s i, µ r i -the processing rate for the turns (l-left; s-straight; r-right) from direction i=1..5 (used units: PCU per time unit); β l i, β s r i, β i output flow rate for the turns (l-left; s-straight; r-right) from direction i=1..5 (used units: PCU per time unit); β i total output flow to direction i=1..5 (used units: PCU per time unit); B cap 5 - the maximum value of queue length for direction 4 (used units: PCU);

26 Mathematical representation (2/4) The following equations could be written: 26 where: λ i r t = λ i t p i r λ i s t = λ i t p i s λ i l t = λ i t p i l p i r + p i s + p i l = 1 (5.1) p i r, p i s, p i l a probability of turns (l-left; s-straight; r-right) from direction i=1..5; t current time. β 1 t = β 1 s t + β 4 r t + β 3 l t β 2 t = β 2 s t + β 3 r t + β 4 l t β 3 t = β 3 s t + β 1 r t + β 2 l t β 4 t = β 4 s t + β 1 r t + β 2 l t β 5 t = β 5 s t + β 5 r t + β 5 l t (5.2)

27 Mathematical representation (3/4) 27 s β i (1,2,4,5) t = 0, λ i s t = 0 and b i s t = 0 λ i s t, λ i s t > 0 and λ i s t μ i s and b i s t = 0 μ i s, b i s t > 0 (5.4) r β i (2,3,4,5) t = 0, λ i r t = 0 and b i r t = 0 λ i r t, λ i r t > 0 and λ i r t μ i r and b i r t = 0 μ i r, b i r t > 0 (5.5)

28 Mathematical Representation (4/4) 28

29 Model for congested network 29 b tcur t0(1 a* sat ) if sat<sat crit b tcur t0(1 a* sat ) ( q qmax ) d if sat sat q sat q c sat crit max 1 r t = d b 2 t (5.10) crit

30 Compare micro-, meso-, macromodels parameters and characteristics 30 Microscopic 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 Mesoscopic models 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 Macroscopic models 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

31 Case-study: simulation of the two connected crossroads 31

32 Simulation object 32 1st Crossroad (left) 2nd Crossroad (right) 1st variant 2nd Crossroad (right) 2st variant 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 Incoming flow Distribution law Flow intensity Crossroad passing mean value (m/min) r Uniform 20 0,6 s Uniform 65 0,8 l Uniform 10 0,6 Source 1 1 Source 5 5 Queue 1 Queue 5 l3 s2 r4 Queue 4 l7 s6 r8 Source 8 Queue 8 r1 s4 l2 3 4 s3 r2 l1 7 r5 l6 s8 l5 s7 r6 8 Queue 3 Source 3 r3 s1 l4 Queue 7 r7 s5 l8 Queue 2 Queue 6 2 Source 2 6 Source 6

33 Crossroad 2 Crossroad 1 Structure of mesoscopic model 33 Flow control So1 So2 So3 Fu1 Fu2 Fu3 Fu4 r1 s1 l1 r2 s2 l2 r3 l3 r4 s4 l4 s3 So5 So6 So8 Fu5 Fu6 Fu7 Fu8 r5 s5 l5 r6 s6 l6 r7 s7 l7 r8 s8 l8 So Fu r1 Legend: source funnel material flow information flow control data type of product

34 PTV VISION VISSIM Microscopic model 34 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

35 Validation of mesoscopic model 35 Main hypothesis: no significant difference between output from microscopic and mesoscopic models Qualitative Animation Queue dynamics comparison Box-Whisker plots Quantitative Test for homogeneity Student t-test Mann-Whitney u-test Confidence interval test Naive test Novel test

36 Validation results (animation) 36

37 Validation results (queue dynamics comparison) 37

38 Validation results (Box-Whisker plots) 38

39 Validation results 39 Data set Qualitative validation (animation) Test for homogeneity Confidence interval test Naive 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

40 Case-study: Urban transport corridor mesoscopic simulation T A S K S I N F R A M E O F A P P R O B A T I O N O N R E A L D A T A : 40 1) D E T E R M I N E I N P U T D A T A 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 A T I O N O F L O S 4) C O M P A R E O U T P U T R E S U L T S W I T H M I C R O S C O P I C S I M U L A T I O N

41 Simulation Object m m. 127 m. 46m. 156 m. 138 m. 151 m. 180 m. 404 m. 155 m.

42 Input Data: Traffic light data and volume of traffic 42

43 quantity (m) Input Data: Passing function estimation More than 7 hours of video from two crossroads More than 400 observations q2 q1 Exemplary chart t1 t time (s)

44 ExtendSim simulation software 47

45 ExtendSim Discrete Rate library application 48

46 Model constructed in ExtendSim 49 General model Internal structure of node

47 Output results 50 Crossroad Number Microscopic model Mesoscopic model Average delay time (s) LOS Average delay time (s) LOS 1 B 14.5 B B 13.8 B A 1.6 A B 17.3 B * B 18.1 C B 11.2 B C 20.6 C * C 31.2 D A 2.1 A * D 41.5 E 55.6

48 Mesoscopic vs Microscopic (time resource) 51

49 Publications (1/2) Savrasovs M. "Traffic Flow Simulation on Discrete Rate Approach Base", Transport and Telecommunication, Vol. 13, April, 2012, pp Savrasovs M. Urban Transport Corridor Mesoscopic Simulation, the 25th European Conference on Modelling and Simulation (ECMS 2011), 2011, pp 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 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) pp Savrasovs M. Mesoscopic Simulation Concept for Transport Corridor, the 12th World Conference on Transport Research (WCTR 2010). Lisbon, Portugal, 2010.

50 Publications (2/2) Yatskiv, I., Savrasovs, M. Development of Riga-Minsk Transport Corridor Simulation Model. Transport and Telecommunication, 2010, Volume 11, No 1, pp Savrasovs, M. Overview of Traffic Mesoscopic Models, the 2nd International Magdeburg Logistics PhD Students Workshop, 2009, pp Savrasovs M. Flow Systems Analysis: Methods and Approaches Computer Modelling and New Technologies, 2008, Volume 12, No 4, pp 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 Savrasovs, M. Overview Of Flow Systems Investigation And Analysis Methods, the 8th International Conference, Reliability and Statistics in Transportation and Communication, 2008 pp Toluyew, Y., Savrasov, M. Mesoscopic Approach to Modelling a Traffic System, International Conference, Modelling of Business, Industrial and Transport Systems, 2008, pp 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