Calculation of Roundabouts (eBook)

Calculation of Roundabouts 2
Preface 8
Acknowledgments 10
Contents 12
1 Calculation of Roundabouts: Problem Definition 14
1.1 Statistical Equilibrium and Steady-State Conditions 15
1.1.1 A Worked Example on Traffic Demand at a Roundabout 17
1.2 Capacity and Capacity Indices 20
1.3 Delays and Queue Lengths 22
References 26
2 Capacity Evaluation 27
2.1 Capacity Calculation at Steady-State Conditions 27
2.1.1 Brilon-Bondzio Formula (Germany) 29
2.1.2 Bovy et al. Formula (Switzerland) 31
2.1.3 TRRL Formula (United Kingdom) 34
2.1.4 GIRABASE Formula (France) 39
2.1.5 Brilon-Wu Formula (Germany) 44
2.1.6 HCM 2000 Formula (USA) 46
2.2 Exit and Circle Capacities 47
2.3 Consideration of Pedestrian Crosswalks 48
2.3.1 Entry Capacities in Presence of Pedestrian Crosswalks 49
2.3.1.1 Marlow and Maycock Formula 49
2.3.1.2 Brilon, Stuwe and Drews Formula 53
2.3.1.3 CETE de l'Ouest Formula 53
2.3.2 Exit Capacities in Presence of Pedestrian Crosswalks 56
2.4 Some Concluding Remarks on Capacity Formulations 56
2.5 Capacity Calculation at Saturation or Oversaturation Conditions of Entries 58
2.5.1 A Worked Example 59
2.6 Calculation Procedures for Simple Capacity and Total Capacity 64
2.6.1 A Worked Example 66
2.6.1.1 Simple Capacity Calculation 66
2.6.1.2 Total Capacity Calculation 67
References 68
3 Waiting Phenomena at Steady State and Non-steadyState Conditions 70
3.1 Some Results of Probabilistic Analysis of Queues 71
3.1.1 Some Remarkable Results 72
3.1.1.1 Poissonian Arrivals and Exponential Service Times 75
3.1.1.2 Poissonian Arrivals and Deterministic Service Times 75
3.1.2 Concluding Remarks 76
3.2 Deterministic Analysis of Queues 78
3.2.1 A Worked Example 81
3.2.2 Some Remarkable Results 85
3.2.2.1 First Remarkable Case and a Worked Example 85
3.2.2.2 Second Remarkable Case and Worked Examples 89
3.2.3 Further Expressions of the Average Waiting Times 97
3.2.4 Concluding Remarks 98
3.3 Time-Dependent Solutions and Waiting Phenomena 99
3.3.1 Time-Dependent Solutions for the Number of Users in the System and in the Queue. A Worked Example 102
3.3.2 Time-Dependent Solutions for the Average Time Spent in the System and in the Queue. A Worked Example 105
3.3.3 Generalized Time-Dependent Solutions 108
3.3.4 Time-Dependent Solutions for Traffic Peaks Between Two Periods at Steady-State Conditions 109
3.3.5 Concluding Remarks 115
References 116
4 Calculation of Waiting Times, Queue Lengths,and Levels of Service 117
4.1 State Evolutions with Undersaturated Entries 117
4.1.1 First Worked Example 121
4.1.2 Second Worked Example 126
4.2 State Evolution with Saturated or Oversaturated Entries 131
4.2.1 First Worked Example 133
4.2.2 Second Worked Example 142
4.3 Evaluation of Levels of Service 142
References 147
5 Evaluation of Roundabout Reliability 148
5.1 Reliability and Performance Functions 148
5.2 General Calculation Procedure of Reliability 152
5.2.1 A Worked Example 154
5.3 Approximated Calculation Procedure of Reliability 159
5.3.1 A Worked Example 162
5.4 Some Remarks 163
References 165
Index 166