Vehicular Mobility Modeling for Flow Models Yaniv Zilberfeld Shai Malul Students: Date: May 7 th, 2012 VANET Course: Algorithms in computer networks

01/32 Introduction Almost since the advent of the automobile, scientists and engineers have been trying to understand and reproduce vehicular mobility patterns. The concept: proper vehicular mobility models must be defined in order to produce realistic mobility patterns. Vehicles Communication network VANET

1. Random Models 2. Flow Models 3. Traffic Models 4. Behavioral Models 5. Trace-based Models 02/32 Vehicular mobility models are considered in five categories as function of their scopes and characteristics: Speed, Heading and Destination are sampled from random processes. Limited interaction between vehicles Each car has an individual trip or path, or a flow of cars is assigned to trips or paths. Dynamically adapt to a particular situation by mimicking human behaviors – AI concepts. Another source of mobility information also comes from surveys human behaviors. Modeling the interactions between vehicles as flows. Flow theory MacroscopicMesoscopic Microscopic Single / Multi-lane Introduction

03/32 Flow Models Engineers were confronted very early on with a need for higher modeling details than simple random pattern. Problem: Vehicle-Vehicle Vehicle-Environment Solution: Modeling vehicular mobility as flows.

04/32 Flow Models Microscopic Modeling Macroscopic Modeling Mesoscopic Modeling 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. XY Describes the mobility parameters for number of cars, such as flow, speed, or density. Describes the mobility at intermediate level of details. Microscopic < Mesoscopic < Macroscopic Flow Models

Car following models (CFM)  The most popular class of driver model  Represent time, position, speed, and acceleration as continuous functions  Adapt a car’s mobility according to a set of rules in order to avoid any contact with the leading vehicle 05/32

General schema for car following models General schema for car following models Driver + Decision making Perception Vehicle dynamics Action Errors Lead vehicle state Following vehicle state 06/32 Car following models (CFM)

 This is done by controlling each individual car’s driving dynamics in order to maintain a safe inter-distance between vehicles, a safe time-headway or both. Model vehicular traffic avoiding accidents. 07/32 Car following models (CFM) Objective:

A good rule for following another vehicle at a safe distance is to allow yourself at least the length of a car between you and the vehicle ahead for every 16.1 km/hours (10 mph) of speed at which you are travelling (Pipe 1953). Pipe’s rule 08/32 Car following models (CFM)

L - the vehicle length T - reaction time (the safe time headway) - the breaking distance - the safe distance headway Collision Avoidance (CA) / Safety Distance 09/32 Car following models (CFM)

 Developed by a group of researchers at General Motors research (Gazis, Hermann and Rothery, Chandler and Montroll) response = sensitivity ∗ stimulus Gazis–Hermann–Rothery (GHR) model  Uses the Stimulus–Response approach  Also known as the General Motors (GM) model 10/32 Car following models (CFM)

Gazis–Hermann–Rothery (GHR) model  Proposed by Chandler in 1958 responsesensitivitystimulus γ – the driver’s sensitivity 11/32 Car following models (CFM)

c – a coefficient m - a speed exponent with values typically in [−2; 2] l - a distance exponent with values typically in [−4; 1] Gazis–Hermann–Rothery (GHR) model  Proposed by Gazis in /32 Car following models (CFM)

 The GHR model defines the acceleration of a vehicle at time t, as a function of the speed and distance differences between two vehicles at time t − T. Gazis–Hermann–Rothery (GHR) model By combining the equations, we get the GHR model: 13/32 Car following models (CFM)

 In 1999, Brackstone and McDonald presented typical values for c, l, and m as proposed by various studies: Gazis–Hermann–Rothery (GHR) model 14/32 Car following models (CFM)

Discrete formulation For an optimal discrete implementation:  ∆t ≤ T  the ratio T/∆t should result to an integer Gazis–Hermann–Rothery (GHR) model  Extra parameter ∆t - the update interval during which the acceleration is considered constant 15/32 Car following models (CFM)

Discrete formulation The discrete formulation of the GHR model: Gazis–Hermann–Rothery (GHR) model 16/32 Car following models (CFM)

17/32 Intelligent Driver Model (IDM) Objective: The IDM is also based on a stimulus-response approach which computes the instantaneous acceleration, consisting of:  Free acceleration:  Interaction deceleration: - Vehicle acceleration - Vehicle velocity - Vehicle desired velocity - Desired gap - Current gap - Vehicle acceleration

18/32  Free acceleration:  Interaction deceleration: The IDM may be expressed with the following equations: Intelligent Driver Model (IDM)

19/32 Let’s assume a ring road with 10 vehicles, initial velocity: 20 m/s. Example: Intelligent Driver Model (IDM) DescriptionValue Desired velocity30 m/s Safe time headway1.5 s Maximum acceleration1.00 m/s 2 Desired deceleration3.00 m/s 2 Jam distance2 m Vehicle length5 m

20/32 The Krauss Model Objective: The Krauss Model is based on a pure stimulus-response approach, which is discrete in time as it does not compute the instantaneous acceleration but the future speed at time step to be reached by vehicle. Notation: - Stochastic parameter, which model human sporadic and irrational reactions.

21/32 Krauss defines the following set of equations: Speed of vehicle required to maintain a safe inter-distance and avoid creating an accident with the preceding vehicle. Target speed to be reached by node which is a simple increment from the previous speed upper-bounded by and. The Krauss Model

22/32 Current speed for the next time step according to a stochastic variation around the target speed. Position of vehicle for the next time step. The Krauss Model

23/32 The Wiedemann Model The Wiedemann Model falls into the psycho-physical category: It is possible that different drivers will show different reactions in response to a same stimulus. Objective:

24/32 The Wiedemann Model identified four driving states that a driver may be in and that would control its reaction to a similar stimulus: 1. Free-driving The driver is far from any immediate preceding vehicle and is thus not influenced by any other vehicle. It freely accelerates to reach. Far 2. Approaching mode The driver is influenced by an approaching preceding vehicle and applies a normal deceleration rate to reach a safe inter-distance. Close – “Slow down” The Wiedemann Model

25/32 3. Following mode The driver is in a typical CFM with low acceleration or deceleration rate to guarantee a fine granularity of its reaction. Low acceleration – “Enough gap” 4. Breaking mode The driver is critically influenced by a preceding vehicle and applies a higher deceleration rate to avoid a crash. High deceleration: “Stop immediately” The Wiedemann Model

Cellular automata models (CA)  A different class of driver model  Discrete in space and time  Reduced computational complexity  Still being able to mimic drivers’ reaction in response to their environment  Describe a traffic system as a lattice of cells of equal size 26/32

 Without loss of generality, the velocity is defined as the number of cells a vehicle passes in a time step ∆t  A set of rules is provided to control the movement of vehicles moving from cell to cell  The cell size is chosen such that it can host a single vehicle that can move at least to the next cell in one time step ∆t 27/32 Cellular automata models (CA)

The Nagel and Schreckenberg (N-SCH) model  The most popular CA model  Defines the following rules: 28/32

Cellular automata models (CA) The Nagel and Schreckenberg (N-SCH) model t+1 t+2 t ii+1i+2i+3 x 29/32

Cellular automata models (CA) Conclusions:  The CA model can produce sudden and unrealistic breaks  This is a result of the synchronous movements at the next time step  Since all vehicles are making a decision at the same time, they can not know what action the vehicle in front of them will take  The domino effect  The action of the leading vehicle itself depends on its own leading vehicle  CA models have been shown to efficiently model vehicular traffic 30/32

31/32 Summary Microscopic models have high level of precision, which is being reflected by a similarly high computational complexity. Typical applications and traffic simulators are uses flow models, for example: “VanetMobiSim”, “VISSIM”, “SUMO”, etc… The common factor in each of these applications was the absolute requirement to avoid accidents. More recently, automated cruise control or even automated driving had also been investigated with these models. Yet, the ability to actually model accidents by drivers not respecting safety or regulatory rules is also crucial to the evaluation of VANET applications such as active safety, and depends on driver’s behavior.

Thank You! 32/32