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Step 3: Randomization with probability p :
max( v n ( t + 3 ) 1 , 0) ,
with probability p ,
v n ( t +1):=
v n ( t + 3 ) ,
default.
Turn brake light on if appropriate:
if p = p b and v n ( t +1) <v n ( t + 2
3 ) , then b n ( t +1):=on .
Step 4: Move (drive):
x n ( t +1):= x n ( t )+ v n ( t +1) .
2.3 Free Lane Changes
Free lane changes are needed so that cars can overtake slower driving cars and
lorries. When designing rules for the free lane changes, one should take care of
that cars taking over do not disturb the tra c on the lane they use to overtake
to much, and one has to take account of German laws, which prohibit overtaking
a car to the left. Further, it is advantageous to prohibit lorries to drive on the
leftmost lane in the simulation, because a lorry overtaking another lorry forces
all cars on the left lane to reduce their velocity.
One more variable is needed for the free lane changes, l n ∈{ left , right ,
straight } notes if the car n should change the lane during the actual time-step
or not. This variable is not needed if the lane changes are executed sequentially,
but we prefer a parallel update of the lane changes for all cars and that renders
this variable necessary. For the left free lane changes the simulator executes the
following steps parallel for all cars n :
Overtake on the Lane to the Left:
Step 0: Initialization:
For car n find next car in front m on the same lane, next car in front s on
the lane left to car n , and the next car r behind car s . Set l n := straight.
Step 1: Check lane change:
if d e n,m ( t ) <v n ( t ) and d e n,m ( t ) <d e n,s ( t ) and d e r,n ( t ) >v r ( t ) , then set l n := left.
Step 2: Do lane change:
if l n = left, then change lane for car n to the left.
The definition of the gaps d e n,s ( t ) and d eff
r,n ( t ) is an obvious extensions of the
definition above, one simply considers a copy of the car n on its left side. These
overtake rules used by the simulator can verbally be summed up as follows:
First, a vehicle checks if it is hindered by the predecessor on its own lane. Then
it has to take into account the gap to the successor and to the predecessor on
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