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Presentation

## 2. Introduction

### 2.2. ZDF: Zahlen Daten Fakten

2.2.1. 35 hours in traffic jam for German average commuter

2.2.2. 74 hours in traffic jam per year in Munich

2.2.3. 234 million hours in Traffic jams for all Germans

2.2.4. 3.5 billion € economic loss per year in Germany

2.2.5. 24 percent more traffic in rush hour

2.2.6. Potential of efficiency improvement (8 billion) and economic stimulus (2 billion) in Germany

### 2.3. "Next Generation"-communication

2.3.1. Technical Aspects

2.3.1.1. Wikipedia Logos Forschungspartner

2.3.1.2. Reducing CO2 emission by 2million tons per year

2.3.2. Regulatory Issues

2.3.2.1. Intelli drive programm bzw. Vehicle Infrastructure Integration (VII)

2.3.2.1.1. USDOT: official site

2.3.2.1.2. V2V mandatory in a "future year"

2.3.2.2. Japan: „Vehicle Information and Communication System“

2.3.2.2.1. Already integrated in all new cars

2.3.2.2.2. Common standard

2.3.2.2.3. State-run sensor network

## 3. Modelling

### 3.1. Basic Assumptions

3.1.1. Cars as point masses

3.1.2. Data exactly known

3.1.3. Straightforward driving

3.1.4. No other traffic participants

### 3.2. Deducing the optimization problem

3.2.1. Traffic light phases (u)

3.2.1.1. Optimization variables

3.2.1.2. Constraints

3.2.1.3. phase function u (0 = green / 1 = red)

3.2.2. Probability

3.2.2.1. Prediction of driving behavior

3.2.2.1.1. line-of-sight: Watching traffic light

3.2.2.1.2. Determination whether to stop

3.2.2.1.3. Probability distribution to handle yellow phase

3.2.2.1.4. u at line-of-sight corresponds to probibility p

3.2.2.2. Decision Tree

3.2.2.2.1. Alternative: Tikz

3.2.2.2.2. Powerpoint

3.2.2.3. Video: Probability Distribution

3.2.2.3.1. semi-transparent cars with probabilities

3.2.2.3.2. several graphics in a row

3.2.2.3.3. video mit "animate"-Package

3.2.3. Cost function

3.2.3.1. Evolution with one car

3.2.3.2. Sum over all cars

3.2.3.3. Convert into minimization problem

3.2.3.4. Transitions with "only" command

## 5. Implementation

### 5.1. IPOPT / CasADi

5.1.1. Integrator

5.1.2. Own integrator

### 5.2. Post-Processing

5.2.1. Avoiding Tailback

5.2.2. Data Validation (negative values,...)

## 6. Limitations

### 6.3. not scalable for many cars / many traffic lights

6.3.1. Warmstarting as solution