Future research directions

This chapter provided an overview of modeling and control techniques for AMoD systems, and a preliminary evaluation of their financial benefits. Future research on this topic should proceed along two main dimensions: efficient control algorithms for increasingly more realistic models and eventually for real-world test beds, and financial analyses for a larger number of deployment options and accounting for positive externalities (e.g., increased safety) in the economic assessment. Such research directions are discussed in some details next, with a particular emphasis on the inclusion of congestion effects and some related preliminary results.

Future research on modeling and control

A key direction for future research is the inclusion of congestion effects. In AMoD systems, congestion manifests itself as constraints on the road capacity, which in turn affect travel times throughout the system. To include congestion effects, a promising strategy is to study a modified lumped model whereby the infinite-server road queues are changed to queues with a finite number of servers, where the number of servers on each road represents the capacity of that road [13]. This approach is used in Figure 19.6 on a simple 9-station road network, where the aim is to illustrate the impact of autonomously rebalancing vehicles on congestion. Specifically, the stations are placed on a square grid, and joined by 2-way road segments, each of which is 0.5 km long. Each road consists of a single lane, with a critical density of 80 vehicles/km. Each vehicle travels at 30 km/hour in free flow, which means the travel time along each road segment is 1 minute in free flow. Figure 19.6 plots the vehicle and road utilization increases due to rebalancing for 500 randomly generated systems (where the arrival rates and routing distributions are randomly generated). The routing algorithm for the rebalancing vehicles is a simple open-loop strategy based on the linear program discussed in Section 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 rebalancing 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 congestion 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 congestion 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

Fig. 19.6 Congestion effects in AMoD systems [13]. Top left: Layout of the 9-station road network. Each road segment has a capacity of 40 vehicles in each direction. Bottom left: The first picture shows the 9-station road network without rebalancing. The color on each road segment indicates 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.

arrival at their destination, but the time spent waiting for the vehicle could be used for productive work as opposed to being stuck in traffic. Specifically, for highly congested systems, vehicle departures can be staggered to avoid excessive congestion, and the routing problem is similar to the simultaneous departure and routing problem [37].

Besides congestion, several additional directions are open for future research. As far as modeling is concerned, those include (i) analysis in a time-varying setup (e.g., with periodically time-varying arrival rates), (ii) inclusion of mesoscopic and microscopic effects into the models (e.g., increased throughput due to platooning or automated intersections), and (iii) more complex models for the transportation requests (e.g., time windows or priorities). On the control side, those include (i) inclusion of recharging constraints in the routing process, (ii) control of AMoD systems as part of a multi-modal transportation network, which should address synergies between AMoD and alternative transportation modes and interactions with human-driven vehicles, and (iii) deployment of control algorithms on real-world test beds.

Future research on AMoD evaluation

The AMoD evaluation presented in Section 19.3 already showed that AMoD systems might hold significant financial benefits. Remarkably, such financial benefits might be even larger when one also accounts for the positive externalities of an AMoD system, e.g., improved safety, freeing up urban land for other uses, and even creating a new economy based on infotainment systems onboard the self-driving vehicles. Such additional benefits, however, have not been thoroughly characterized yet and require additional analyses. Another research direction involves the evaluation of AMoD systems for more complex deployment options, e.g., as a last-mile solution within a multi-modal transportation system, or with a more sophisticated service structure, e.g., multiple priority classes.

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