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19.3 Evaluating AMoD systems

Leveraging models and methods from Section 19.2, this section studies hypothetical deployments of AMoD systems in two major cities, namely New York City and Singapore.

Collectively, the results presented in this section provide a preliminary, yet rigorous evaluation of the benefits of AMoD systems based on real-world data. We mention that both case studies do not consider congestion effects – a preliminary discussion about these effects is presented in Section 19.4.

19.3.1 Case Study I: AMoD in New York City

This case study applies the lumped approach to characterize how many self-driving vehicles in an AMoD system would be required to replace the current fleet of taxis in Manhattan while providing quality service at current customer demand levels [13]. In 2012, over 13,300 taxis in New York City made over 15 million trips a month or 500,000 trips a day, with around 85 percent of trips within Manhattan. The study uses taxi trip data collected on March 1, 2012 (the data is courtesy of the New York City Taxi & Limousine Commission) consisting of 439,950 trips within Manhattan. First, trip origins and destinations are clustered into N = 100 stations, so that a customer is on average less than 300 m from the nearest station, or approximately a 3-minute walk. The system parameters such as arrival rates {di}, destination preferences {pi j} and travel times {Ti j} are estimated for each hour of the day using trip data between each pair of stations.

Vehicle availability (i.e., probability of finding a vehicle when walking to a station) is calculated for three cases – peak demand (29,485 demands/hour, 7–8 pm), low demand (1,982 demands/hour, 4–5 am), and average demand (16,930 demands/hour, 4–5 pm). For each case, vehicle availability is calculated by solving the linear program discussed in Section and then applying mean value analysis [29] techniques to recover vehicle availabilities. (The interested reader is referred to [13] for further details). The results are summarized in Figure 19.4.

Fig. 19.4 Case study of New York City [13]. Left figure: Vehicle availability as a function of system size for 100 stations in Manhattan. Availability is calculated for peak demand (7–8 pm), low demand (4–5 am), and average demand (4–5 pm). Right figure: Average customer wait times over the course of a day, for systems of different sizes.

For high vehicle availability (say, 95 percent), one would need around 8,000 vehicles (~70 percent of the current fleet size operating in Manhattan, which, based on taxi trip data, we approximate as 85 percent of the total taxi fleet) at peak demand and 6,000 vehicles at average demand. This suggests that an AMoD system with 8,000 vehicles would be able to meet 95 percent of the taxi demand in Manhattan, assuming 5 percent of customers are impatient and leave the system when a vehicle is not immediately available. However, in a real system, customers would wait in line for the next vehicle rather than leave the system, thus it is important to determine how vehicle availability relates to customer waiting times. Customer waiting times are characterized through simulation, using the receding horizon control scheme mentioned in Section The time-varying system parameters di, pi j, and average speed are piecewise constant, and change each hour based on values estimated from the taxi data. Travel times Ti j are based on average speed and Manhattan distance between stations i and j, and self-driving vehicle rebalancing is performed every 15 minutes. Three sets of simulations are performed for 6,000, 7,000, and 8,000 vehicles, and the resulting average waiting times are shown in Figure 19.4 (right). Specifically, Figure 19.4 (right) shows that for a 7,000 vehicle fleet the peak averaged wait time is less than 5 minutes (9–10 am) and, for 8,000 vehicles, the average wait time is only 2.5 minutes. The simulation results show that high availability (90–95 percent) does indeed correspond to low customer wait time and that an AMoD system with 7,000 to 8,000 vehicles (roughly 70 percent of the size of the current taxi fleet) can provide adequate service with current taxi demand levels in Manhattan.

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