GENERAL
Q1: What topics have been covered in the lecture on traffic dynamics and
simulation?
A1: data, models, applications (elaborate)
Q2: What are the main measuring methods to obtain traffic data?
A2: stationary detector cross-sections (e.g., single/double induction
loops), video, floating cars, mobile phones
Q3: Please list the main categories/types of traffic flow data. What
typical quantities of traffic flow are measured by each category?
A3: (i) Cross-section data:
(i1): Single vehicle:
Individual passage times, velocities, and lengths/occupancy times
(i2): Aggregated: Average velocity, flow, occupancy, truck percentage
(ii) FCD: travelling time through a section, velocity profile,
location profile for a few vehicles
(iii) Trajectory data: A complete set of trajectories {x_i(t),
lane_i(t)} for all vehicles in a given spatiotemporal region
(iv) Floating-phone data: approximate location from active cellular
phones
Q4: (I draw a trajectory diagram with a jam) How to determine density,
flow, velocity, and travelling
time? What about the lines ending/beginning in the middle of the
diagram?
A4:
Q5: What data capturing methods can be used to measure traffic flow:
(i) Single-loop detectors, (ii) double loop detectors, (iii) FCD, (iv)
FPD, (v) trajectory data?
A5: (i),(ii), (v)
Q6: What data capturing methods can be used to measure local velocity?
A6: (i), (iii), (v)
Q7: What data capturing methods can be used to measure traveling
times?
A7: (iii), (iv), (v)
Q8: Please state what is meant by data fusion in the traffic context
A8: Merge different data categories in a consistent way thereby
resolving problems due to contradicting traffic data channels and different
data types
MODELS
Q9: What are the main types of models used for modeling traffic flow?
A9: Micromodels (including CA), and macromodels
Q9a: What are the main differences of pedestrian and vehicular
traffic?
A9a: Dimensionality, 2D vs. 1D
Q10: What are typical dynamical variables in each model class?
A10: Micro: x_i(t), v_i(t), lane_i(t)[veh], y_i(t)[ped]
for each vehicle/pedestrian/moving agent
Macro: Density rho(x,t), vel V(x,t), flow Q(x,t), possibly
disaggregated for different lanes and vehicle classes;
flow density for pedestrian traffic
Q11: What are the main distinctions of the traffic models with respect
to the mathematical form? Please give an example for each mathematical
category, micro or macro?
PDE, ODE, coupled maps, CA
A11: PDE: d/dt rho(x,t)+d/dx Q(x,t)=0
ODE: dx_i/dt=v_i, dv_i/dt=a_i(s_i,v_i,Delta v_i)
CM: v(t+Delta t)=v(t)+a(s(t), v(t), Delta v(t)) Delta t,
s(t+Delta t)=s+v Delta t+1/2a 9Delta t)^2
CA: Iterated map of occupance of cells in {0,1}^n, and discrete
velocities of occupied cells
Q12: Which model type is better suited for applications (i) traffic-state
recognition and short-term forecast, (ii) simulate influence of ACC
vehicles in traffic
A12: (i) Macro, (ii) Micro
Q13: Please derive the continuity equation for vehicular traffic on a
homogeneous road from vehicle conservation/inflow-outflow balance
A13: dn/dt=dx*d/dt rho=Qin-Qout=Q(x)-Q(x+dx)=-dx*d/dx Q
=> d/dt rho+d/dx Q=0; Q=rho*V
Q14: Pleqase generalize the continuity equation to include onramps and
offramps
A14: Addtl. term (dn/dt)_rmp=Qrmp*dx/L => rhs term Qrmp/L
(Qrmp<0 for offramps)
A15a: LWR model
Q15: Please draw a fundamental diagram for traffic flow
A15: (Skizze)
Q16: (Punkt auf gestauter Seite) Please show graphically how to
determine the velocity of vehicles, and propagation velocity of small
perturbations for traffic characterized by this point.
A16
(Ursprungsgerade, Tangente)
Q16a: What is the road capacity in the LWR models?
Q17: The propagation velocity: Does it relate to a stationary or
moving reference frame?
Q18: (weiterer Punkt auf der freien Seite)
How to determine the propagation velocity of jam fronts: Transition
free-congested, congested/free
Q19: Queu behind red traffic light and its dissolution: Draw a
spatiotemporal diagram of density and draw some Trajectories into it
Q20: Drawbacks of first-order models?
A20: No growing jams, no hysteresis/metastability, no wide scattering
Q21: General form of macroscopic models with dynamic velocities?
Write it in a form such that the microscopic vehicle acceleration can
be seen (acceleration field A(x,t))
A21: dV/dt=(d/dt+v d/dx)V=A(x,t)
Q22: (The trajectory diagram from the data section, dissolution fromt
of jams) What is the sign of ablpart{V}{t} and \abltot{V}{t}?
A22: >0, <0
Q23: Please define metastability, linear instability, and convective
instability in the traffic context. At which density ranges these
instabilities typically show up? How does one derive linear
instability?
Q24: Micromodels: What are typical model parameters? Which human
factors can be modelled?
APPLICATIONS
Q25: Describe some applications of traffic flow simulations
A26: Traffic-state detection by stationary detectors or floating cars
(car navigation);
(1) traffic state forecast (e.g., by the shockwave
dynamics of the upstream fronts of LWR models)
(2) Generating the traffic background in research (traffic psychology) and
game driving simulators
(3) Learning/determining which driver's behaviour is safe, stable, and
efficient, and which is not (microscopic model parameters)
(4) Determining traffic related effects (safety,stability, efficiency) of
all the new vehicle innovations such as ACC, navigation, traffic-light
assistants, autonomous driving