Information Technology Reference
In-Depth Information
Typical values for the free parameters are
. The TOCA
generates more realistic fundamental diagrams than the original STCA, in particular
when used in conjunction with lane-changing rules on multi-lane streets.
(
p
ac
,p
dc
,τ
H
)=(0
.
9
,
0
.
9
,
1
.
1)
Dependence on the Velocity of the Car Ahead.
The above rules use gap alone as the
controlled variable. More sophisticated rules will use more variables, for example the
first derivative of the gap, which is the velocity difference. The idea is that if the car ahead
is faster, then this adds to one's effective gap and one may drive faster than without this.
In the CA context, the challenge is to retain a collision-free parallel update. Ref. [12]
achieved this by going through the velocity update twice, where in the second round
any major velocity changes of the vehicle ahead were included. Ref. [13] instead also
looked at the gap of the vehicle ahead. The idea here is that, if we know both the speed
and the gap of the vehicle ahead, and we make assumptions about the driver behavior of
the vehicle ahead, then we can compute bounds on the behavior of the vehicle ahead in
the next time step.
Traffic Breakdown.
An interesting topic is the transition from laminar to congested
traffic. For the deterministic model, things are clear: The laminar regime is when all
vehicles move at full speed; the congested regime is when at least one vehicle in the
system does not move at full speed. Deterministic models can also display bi-stability,
i.e. density ranges where both the laminar and the congested phase are stable. This is for
example the case with deterministic slow-to-start models [14]. This characterization is
the same as for deterministic fluid-dynamical models [15].
For stochastic models, things are less clear since even in the laminar regime there
may be slow vehicles, their slowness caused by random fluctuations. Often, the analogy
to a gas/liquid transition is used, meaning that traffic jams are droplets of the liquid phase
interdispersed in the gaseous phase of laminar traffic. However, the question of a phase
transition in stochastic models has not been completely settled [16,17,18]. The main
problem seems to be that questions of meta-stability and of phase separation are not
treated separately, although they should be, as our own recent investigations show [19].
Lane Changing.
Lane changing is implemented as an additional sub-timestep before
the velocity update. Lane changing consists of two parts: the reason to change lanes,
and the safety criterion. The first one can be caused by slow cars ahead, or by the desire
to be in the correct lane for a turn at the end of a link. The safety criterion means that
there should be enough empty space around a vehicle which changes lanes. A simple
symmetric implementation of these principles is:
-
Reason to change lanes (incentive criterion):
g ≤ v
.AND.
g
o
>g,
where
g
is the
is the gap ahead on the other lane. The rule means that a reason
to change lanes is given when the gap on the current lane inhibits speed and when
the gap on the other lane is larger. - This is a simple symmetric criterion based on
gaps, more complicated and/or asymmetric criteria are possible [20].
-
Safety criterion:
standard gap, and
g
o
refers to the vehicle
coming from from behind on the other lane. This safety criterion is fulfilled if the
gap on the other lane is larger than the current velocity, and the backwards gap on
the other lane is larger than the oncoming vehicle's velocity.
g
o
≥ v
.AND.
g
b,o
>v
b,o
,
where the index
b,o
