1. Traffic Models Alaa Hleihel 303156764 Daniel Mishne 304063845 1/32

2.  Introduction  Trip planning  Random trip  Stochastic turn  OD matrix  Path planning  Agent-centric  Flow-centric  Influence of time  Summary Agenda 2 / 32

3.  Previously we have learned how the flow models increases our safety during driving  But since flow models are mainly focused on safety related elements, they are not sufficient for planning the whole trip  Hence, the Traffic Models were introduced to provide the solution for planning a trip and dynamically change the route when necessary Introduction 3 / 32

4.  let us consider the motion dynamics approaching an intersection  How would each model behave? The differences between the flow and the traffic model classes 4 / 32

5.  Flow models will simply consider an intersection as a potential obstacle  A vehicle either reduces its speed to adjust to the turning angle or simply decelerates to come to a full stop  Yet no provision is included on what to do either at or after that intersection! Flow models behavior 5 / 32

6.  Traffic models will not consider an intersection as a potential obstacle  They will take into consideration the intersection policies (traffic light, stop sign, etc.)  The turning policy and the global path to be followed by a vehicle will also be taken into consideration Traffic models behavior 6 / 32

7.  Traffic models may be divided into two complementary motion patterns:  Trip planning  Path planning  Both influenced by a third parameter: time  A trip models the sequence of Origin–Destination (OD) points that vehicles visit  A path specifies the precise way followed by vehicles between an origin and a destination point Traffic models 7 / 32

8.  Trip planning has the responsibility for modeling vehicles moving from an origin to a destination point  Three major approaches may be found in the literature:  Random trip  Stochastic turn  OD matrix Trip planning 8 / 32

9.  The random trip is the simplest approach  Vehicles randomly select an origin and a destination point in the traffic environment  No correlation is either modeled between the different destinations or between vehicles Random trip 9 / 32

10.  In stochastic turn instead of choosing specific destination, we choose a new direction at each intersection  The new direction is chosen randomly according to a stochastic process Stochastic turn 10 / 32

11.  In this particular approach, a path planning is not required  The calibration of the stochastic turn process is usually performed by field measurements of turning flows at intersections Stochastic turn – cont. 11 / 32

12.  The OD (Origin–Destination) matrix approach selects Points of Interests (PoI) on the traffic environment and builds a transition matrix  This matrix is utilized to model the correlations between various trips  Example for POI of landmarks: http://www.mapmatters.org/keyword/landmarks http://www.mapmatters.org/keyword/landmarks OD matrix 12 / 32

13.  Despite the complexity of this approach, it significantly contributes to mimicking the strong non- uniform distribution of OD and the correlations found in various vehicular trips  Surveys are usually the primary source of information to identify the OD points and estimate the transition probabilities OD matrix cont. 13 / 32

14.  Similarly to flow modeling, trip planning may be considered with different degrees of precision.  Each vehicle may have a specific OD matrix with vehicle specific transition probabilities, or all vehicles may share a common OD Matrix.  Trip models are usually assigned to a flow of vehicles as it reduces the problem of modeling the large-scale mobility patterns to known physical properties OD matrix cont. 14 / 32

15.  Vertices are Points of Interest (PoI).  Transition probabilities are the tendency to move from one PoI to another. Example for OD matrix with transition probabilities 15 / 32

16.  Once the origin and destination points have been assigned, it is the role of the path planning to determine the sequence of directions to be followed by each vehicle to reach its destination. Path planning 16 / 32

17.  Path planning usually recomputes or dynamically recomputes the sequence of intersections to be followed based on a preferred optimization function:  shortest path  fastest path  less crowed path, etc. Path planning - cont. 17 / 32

18.  Path planning requires a scalable and dynamic algorithms as they typically have to build paths for a very large set of vehicles over a large area.  Moreover, as the best paths are usually based on dynamic weights that are altered by the paths’ usage itself, paths must often be recalculated or alternative paths be precomputed. Path planning - cont. 18 / 32

19.  Paths are mostly based on efficient Dijkstra-type graph algorithms  The link weights depend on different parameters (distance, speed, density, habits, etc.)  Efficient path planning is expected from inter- vehicular communications to provide path weights that would be more precise and more rapidly available Path planning - cont. 19 / 32

20.  When considering a large number of vehicles to be simulated over a large urban map consisting of thousands of vertices, a path planning algorithm may pace a scalability issue. Path planning scalability 20 / 32

21.  In order to deal with this as a function of the simulation environment, path planning may be seen from a microscopic or macroscopic point of view.  Microscopic - Describes the mobility parameters of a specific car. It usually commands the car’s acceleration/deceleration in order to maintain either a safe distance headway or to guarantee a safe time headway. Path planning scalability – cont. 21 / 32

22.  Macroscopic - Describes the mobility parameters for number of cars, such as flow, speed, or density.  The microscopic path planning called agent-centric  The macroscopic path planning called flow-centric Path planning scalability – cont. 22 / 32

23.  Agent-centric creates at least one distinct path per vehicle.  It controls each individual vehicle and any specific action to be conducted on the vehicle (drivers changing their mind, accident, traffic jam) is immediately applied by recomputing its optimal path. Agent-centric path planning 23 / 32

24.  The agent-centric approach is able to immediately model the impact of a traffic accident not only on immediate vehicles but also on other vehicles that could have heard the information by inter-vehicular communications.  The agent-centric approach is notably used by the traffic simulators MATSim (MATSim 2009), VanetMobiSim (2009), and Schroth et al. (2005). Agent-centric path planning – cont. 24 / 32

25.  The agent centric approach provides one path sequence for each vehicle Agent-centric path planning - Example 25 / 32

26.  Flow-centric only builds a subset of paths In order to increase scalability, and a flow of vehicles will be following the same path.  The major asset is its reduced computational complexity as the number of paths is usually significantly smaller than the number of vehicles.  Yet, it has the same limitations as any macroscopic approach as it models vehicles as flows and cannot control the reaction of an individual vehicle confronted by specific traffic situations. Flow-centric path planning 26 / 32

27.  In order to model vehicles being re-routed, a subset of alternative paths are precomputed.  This proactive computation is actually also a limitation as it is either not possible or too complex to optimize these alternative paths according to the dynamic evolution of traffic.  Yet, its high scalability made flow-centric models the first choice of popular traffic simulators, such as SUMO (2009), VISSIM (2009), Aimsun (2009), and CORSIM (2009). Flow-centric path planning – cont. 27 / 32

28.  The flow-centric approach provides one path sequence for each flow of vehicles (for example, a flow of 500 vehicles/hour follows a same path). Flow-centric path planning - Example 28 / 32

29.  By observing traffic over a single day, it is also easy to see that patterns are significantly different as a function of time.  During morning rush hours, we usually observe an inbound traffic stream while the evening rush hours show the opposite. Influence of time 29 / 32

30.  When planning trips or paths, it is therefore also crucial to include the influence of time in the equation.  For example, the OD matrix from the previous slides could be totally different or simply have different transition probabilities as a function of the time of day. Influence of time – cont. 30 / 32

31.  Also, the path departure times, per agent or per flow, must also be defined as function of time.  In order to estimate such time patterns and calibrate the trip or path planning, surveys or statistics from traffic traces are usually used. Influence of time – cont. 31 / 32

32.  WHY? Traffic Models provide the solution for planning a trip and dynamically change the route when necessary  HOW? Trip Planning with Path Planning  Another Example? Google Maps Summary 32 / 32