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Fig. 19.6 Congestion effects in AMoD systems [13]. Top left: Layout of the 9-station road net-
work. Each road segment has a capacity of 40 vehicles in each direction. Bottom left: The first pic-
ture shows the 9-station road network without rebalancing. The color on each road segment indi-
cates the level of congestion, where green is no congestion, and red is heavy congestion. The second
picture is the same road network with rebalancing vehicles. Right: The effects of rebalancing on
congestion. The x-axis is the ratio of rebalancing vehicles to passenger vehicles on the road. The
y-axis is the fractional increase in road utilization due to rebalancing.
19.4 Future research directions
linear program discussed in Section 19.2.2.1. The x-axis shows the ratio of rebalancing
vehicles to passenger vehicles on the road, which represents the inherent imbalance in the
system. The red data points represent the increase in average road utilization due to rebal-
ancing and the blue data points represent the utilization increase in the most congested road
segment due to rebalancing. It is no surprise that the average road utilization rate is a linear
function of the number of rebalancing vehicles. However, remarkably, the maximum con-
gestion increases are much lower than the average, and are in most cases zero. This means
that while rebalancing generally increases the number of vehicles on the road, rebalancing
vehicles mostly travel along less congested routes and rarely increase the maximum con-
gestion in the system. This can be seen in Figure 19.6 bottom left, where rebalancing clearly
increases the number of vehicles on many roads but not on the most congested road segment
(from station 6 to station 5).
The simple setup in Figure 19.6 suggests that AMoD systems would, in general, not lead
to an increase in congestion. A particularly interesting and intriguing research direction is
to devise routing algorithms for AMoD systems that indeed lead to a decrease in congestion
with current demand levels (or even higher). A promising strategy relies on the idea that if
AMoD systems are implemented such that passengers are given precise pickup times and
trips are staggered to avoid too many trips at the same time, congestion may be reduced.
Passengers may still spend the same amount of time between requesting a vehicle and
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