Case Study II: AMoD in Singapore
This case study discusses an hypothetical deployment of an AMoD system to meet the personal mobility needs of the entire population of Singapore [18]. The study, which should be interpreted as a thought experiment to investigate the potential benefits of an AMoD solution, addresses three main dimensions: (i) minimum fleet size to ensure system stability (i.e., uniform boundedness of the number of outstanding customers), (ii) fleet size to provide acceptable quality of service at current customer demand levels, and (iii) financial estimates to assess economic feasibility. To support the analysis, three complementary data sources are used, namely the 2008 Household Interview Travel Survey – HITS – (a comprehensive survey about transportation patterns conducted by the Land Transport Authority in 2008 [34]), the Singapore Taxi Data – STD – database (a database of taxi records collected over the course of a week in Singapore in 2012) and the Singapore Road Network – SRD – (a graphbased representation of Singapore's road network).
19.3.2.1 Minimum fleet sizing
The minimum fleet size needed to ensure stability is computed by applying equation (19.1), which was derived within the distributed approach. The first step is to process the HITS, STD, and SRD data sources to estimate the arrival rate d, the average origin destination distance ErpO rpD [Y X ], the demand distributions rpO and rpD, and the average velocity v. Given such quantities, equation (19.1) yields that at least 92,693 selfdriving vehicles are required to ensure the transportation demand remains uniformly bounded. To gain an appreciation for the level of vehicle sharing possible in an AMoD system of this size, consider that at 1,144,400 households in Singapore, there would be roughly one shared car every 12.3 households. Note, however, that this should only be seen as a lower bound on the fleet size, since customer waiting times would be unacceptably high.
19.3.2.2 Fleet sizing for acceptable quality of service
To ensure acceptable quality of service, one needs to increase the fleet size. To characterize such increase, we use the same techniques outlined in Section 19.3.1, which rely on the lumped approach. Vehicle availability is analyzed in two representative cases. The first is chosen as the 2–3 pm bin, since it is the one that is the closest to the “average” traffic condition. The second case considers the 7–8 am rushhour peak. Results are summarized in Figure 19.5 (left). With about 200,000 vehicles, availability is about 90 percent on average, but drops to about 50 percent at peak times. With 300,000 vehicles in the fleet, availability is about 95 percent on average and about 72 percent at peak times. As in Section 19.3.1, waiting times are characterized through simulation. For 250,000 vehicles, the maximum wait time during peak hours is around 30 minutes, which is comparable with typical congestion delays during rush hour. With 300,000 vehicles, peak wait times are reduced to less than 15 minutes, see Figure 19.5 (right). To put these numbers into perspective, in 2011 there were 779,890 passenger vehicles operating in Singapore [35]. Hence, this case study suggests that an AMoD system can meet the personal mobility need of the entire population of Singapore with a number of robotic vehicles roughly equal to 1/3 of the current number of passenger vehicles.
Fig. 19.5 Case study of Singapore [18]. Left figure: Performance curve with 100 regions, showing the availability of vehicles vs. the size of the system for both average demand (2–3 pm) and peak demand (7–8 am). Right figure: Average wait times over the course of a day, for systems of different sizes.
19.3.2.3 Financial analysis of AMoD systems
This section provides a preliminary, yet rigorous economic evaluation of AMoD systems. Specifically, this section characterizes the total mobility cost (TMC) for users in two competing transportation models. In System 1 (referred to as traditional system), users access personal mobility by purchasing (or leasing) a private, humandriven vehicle. Conversely, in System 2 (the AMoD system), users access personal mobility by subscribing to a shared AMoD fleet of vehicles. For both systems, the analysis considers not only the explicit costs of access to mobility (referred to as cost of service COS), but also hidden costs attributed to the time invested in various mobilityrelated activities (referred to as cost of time – COT –). A subscript i = {1, 2} will denote the system under consideration (e.g., COS1 denotes the COS for System 1).
Cost of service: The cost of service is defined as the sum of all explicit costs associated
with accessing mobility. For example, in System 1, COS1 reflects the costs to individually purchase, service, park, insure, and fuel a private, humandriven vehicle, which, for the case of Singapore, are estimated for a midsize car at $18,162/year. For System 2, one needs to make an educated guess for the cost incurred in retrofitting production vehicles with the sensors, actuators, and computational power required for automated driving. Based upon the author's and his collaborators' experience on selfdriving vehicles, such cost (assuming some economies of scale for large fleets) is estimated as a onetime fee of $15,000. From the fleetsizing arguments of Section 19.3.2.2, one shared selfdriving vehicle in System 2 can effectively serve the role of about four private, humandriven vehicles in System 1, which implies an estimate of 2.5 years for the average lifespan of a selfdriving vehicle. Tallying the aforementioned costs on a fleetwide scale and distributing the sum evenly among the entire Singapore population gives a COS2 of $12,563/year (see [18] for further details about the cost breakdown). According to COS values, it is more affordable to access mobility in System 2 than System 1.
Cost of time: To monetize the hidden costs attributed to the time invested in mobilityrelated activities, the analysis leverages the Value of Travel Time Savings (VTTS) numbers laid out by the Department of Transportation for performing a costbenefit analysis of transportation scenarios in the US [36]. Applying the appropriate VTTS values based on actual driving patterns gives COT1 = $14,460/year (which considers an estimated 747 hours/year spent by vehicle owners in Singapore in mobilityrelated activities, see [18]). To compute COT2 , this analysis prices sitting comfortably in a shared selfdriving vehicle while being able to work, read, or simply relax at 20 percent of the median wage (as opposed to 50 percent of the median wage which is the cost of time for driving in freeflowing traffic). Coupling this figure with the fact that a user would spend no time parking, limited time walking to and from the vehicles, and roughly 5 minutes for a requested vehicle to show up (see Section 19.3.2.2), the end result is a COT2 equal to $4,959/year.
Total mobility cost: A summary of the COS, COT, and TMC for the traditional and
AMoD systems is provided in Table 19.1 (note that the average Singaporean drives 18,997 km in a year). Remarkably, combining COS and COT figures, the TMC for AMoD systems is roughly half of that for traditional systems. To put this into perspective, these savings
Table 19.1 Summary of the financial analysis of mobilityrelated cost for traditional and AMoD systems for a case study of Singapore [18].
Cost [USD/km] 
Yearly cost [USD/year] 

COS COT 
TMC 
COS COT TMC 

Traditional 
0.96 0.76 
1.72 
18,162 14,460 32,622 
AMoD 
0.66 0.26 
0.92 
12,563 4,959 17,522 
represent about one third of GDP per capita. Hence, this analysis suggests that it is much more affordable to access mobility in an AMoD system compared to traditional mobility systems based on private vehicle ownership.