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Autonomous Mobility-on-Demand Systems for Future Urban
Mobility406
can be cast as a linear program (hence, this approach extends well to large transportation
networks). This method encourages coordination but does not enforce it, which is the key
to maintaining tractability of the model [13]. The rates {ȥi} and probabilities {Įi j} are then
used as feedforward reference signals in a receding horizon control scheme to control in
real-time an entire AMoD system [13], as done for case studies of New York City and
Singapore presented in Section 19.3.
19.2.2.2 Distributed approach
The key idea behind the distributed approach [14, 15, 16, 17] is that the number of stations
represents a continuum (i.e., N ĺ VLPLODU WR WKH '\QDPLF 7UDYHOLQJ 5HSDLUPDQ SUREOHP
[20, 21, 22, 23]. In other words, customers arrive at any point in a given bounded environ-
ment [15, 16], or at any point along the segments of a road map [15]. In the simplest sce-
nario, a dynamical process generates spatially-localized origin-destination pairs (represent-
ing the transportation requests) in a geographical region Q R2 . The process that generates
origin-destination pairs is modeled as a spatio-temporal Poisson process, namely, (i) the
time between consecutive generation instants has an exponential distribution with intensity
Ȝ , and (ii) origins and destinations are random variables with probability density functions,
respectively, ijO and ijD , supported over Q, see Figure 19.3 (right). The objective is to
design a routing policy that minimizes the average steady-state time delay between the
generation of an origin-destination pair and the time the trip is completed. By removing
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in an environment, one transforms the problem of controlling N different queues into one
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and control, and allows one to derive analytical expressions for important design parame-
Fig. 19.3 Left figure: In the lumped model, an AMoD system is modeled as a Jackson network,
where stations are identified with single-server queues and roads are identified with infinite-server
queues. (Customers are denoted with yellow dots and servicing vehicles are represented by small car
icons.) Some vehicles travel without passengers to rebalance the fleet. Right figure: In a distributed
model of an AMoD system, a stochastic process with rate Ȝ generates origin-destination pairs, dis-
tributed over a continuous domain Q.
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