Control of Robotic Mobility-On-Demand Systems: a Queueing-Theoretical Perspective

Abstract

Abstract-In this paper we present and analyze a queueingtheoretical model for autonomous mobility-on-demand (MOD) systems where robotic, self-driving vehicles transport customers within an urban environment and rebalance themselves to ensure acceptable quality of service throughout the entire network. We cast an autonomous MOD system within a closed Jackson network model with passenger loss. It is shown that an optimal rebalancing algorithm minimizing the number of (autonomously) rebalancing vehicles and keeping vehicles availabilities balanced throughout the network can be found by solving a linear program. The theoretical insights are used to design a robust, real-time rebalancing algorithm, which is applied to a case study of New York City. The case study shows that the current taxi demand in Manhattan can be met with about 8,000 robotic vehicles (roughly 60% of the size of the current taxi fleet). Finally, we extend our queueing-theoretical setup to include congestion effects, and we study the impact of autonomously rebalancing vehicles on overall congestion. Collectively, this paper provides a rigorous approach to the problem of system-wide coordination of autonomously driving vehicles, and provides one of the first characterizations of the sustainability benefits of robotic transportation networks.

Autonomous Mobility-on-Demand Systems for Future Urban Mobility

“…The results presented in this chapter build upon a number of previous works by the author and his collaborators, namely [13] for the lumped approach, [14,15,16,17] for the spatial queueing-theoretical framework and the distributed approach, and [13,18] for the case studies. The rest of this chapter is structured as follows.…”

“…Within the lumped approach [13], transportation requests are modeled by assuming that customers arrive at a set of stations located within a given environment 1 , similar to the hypercube model [19]. The arrival process at each station is Poisson with a rate i , where i {1, … , N} and N denotes the number of stations.…”

“…However, if the station is empty of vehicles, the customer immediately leaves the system. Under the assumptions of Poisson arrivals and exponentially-distributed travel times, an AMoD system is then translated into a Jackson network model through an abstraction procedure [13,29], whereby one identifies the stations with single-server queues and the roads with infinite-server queues. (Jackson networks are a class of queueing networks where the equilibrium distribution is particularly simple to compute as the network has a product-form solution [30,31]).…”

“…(Jackson networks are a class of queueing networks where the equilibrium distribution is particularly simple to compute as the network has a product-form solution [30,31]). With this identification, an AMoD system becomes a closed Jackson network with respect to the vehicles, which is amenable to analytical treatment [13] (Figure 19.3, left).…”

“…To control the network, for example, to (autonomously) rebalance the vehicles to ensure even vehicle availability, the strategy is to add virtual customer streams [13]. Specifically, one assumes that each station i generates "virtual customers" according to a Poisson process with rate i , and routes these virtual customers to station j with probability i j .…”