Kyle Treleaven

Toward a Systematic Approach to the Design and Evaluation of Automated Mobility-on-Demand Systems: A Case Study in Singapore

The objective of this work is to provide analytical guidelines and financial justification for the design of shared-vehicle mobility-on-demand systems. Specifically, we consider the fundamental issue of determining the appropriate number of vehicles to field in the fleet, and estimate the financial benefits of several models of car sharing. As a case study, we consider replacing all modes of personal transportation in a city such as Singapore with a fleet of shared automated vehicles, able to drive themselves, e.g., to move to a customer’s location. Using actual transportation data, our analysis suggests a shared-vehicle mobility solution can meet the personal mobility needs of the entire population with a fleet whose size is approximately 1/3 of the total number of passenger vehicles currently in operation.

Asymptotically Optimal Algorithms for One-to-One Pickup and Delivery Problems With Applications to Transportation Systems

Pickup and delivery problems (PDPs), in which objects or people have to be transported between specific locations, are among the most common combinatorial problems in real-world logistical operations. A widely-encountered type of PDP is the Stacker Crane Problem (SCP), where each commodity/customer is associated with a pickup location and a delivery location, and the objective is to find a minimum-length tour visiting all locations with the constraint that each pickup location and its associated delivery location are visited in immediate, consecutive order. The SCP is NP-Hard and the best known approximation algorithm only provides a 9/5 approximation ratio. In this paper, we examine an embedding of the SCP within a stochastic framework, and our objective is three-fold: First, we describe a large class of algorithms for the SCP, where every member is asymptotically optimal, i.e., it produces, almost surely, a solution approaching the optimal one as the number of pickups/deliveries goes to infinity; moreover, one can achieve computational complexity O(n2+ε) within the class, where n is the number of pickup/delivery pairs and ε is an arbitrarily small positive constant. Second, we characterize the length of the optimal SCP tour asymptotically. Finally, we study a dynamic version of the SCP, whereby pickup and delivery requests arrive according to a Poisson process, and which serves as a model for large-scale demand-responsive transport (DRT) systems. For such a dynamic counterpart of the SCP, we derive a necessary and sufficient condition for the existence of stable vehicle routing policies, which depends only on the workspace geometry, the distributions of pickup and delivery points, the arrival rate of requests, and the number of vehicles. Our results leverage a novel connection between the Euclidean Bipartite Matching Problem and the theory of random permutations, and, for the dynamic setting, exhibit novel features that are absent in traditional spatially-distributed queueing systems.

Conflict Resolution and Traffic Complexity of Multiple Intersecting Flows of Aircraft

This paper proposes a general framework to study the conflict resolution for multiple intersecting flows of aircraft in planar airspace. The conflict-resolution problem is decomposed into a sequence of subproblems, each involving only two intersecting flows of aircraft. The strategy for achieving the decomposition is to laterally displace the aircraft flows so that they intersect in pairs, and the resulting conflict zones have no overlap. A conflict zone is defined as a circular area that is centered at the intersection of a pair of flows, which allows aircraft approaching the intersection to resolve the conflict completely within the conflict zone without straying outside. An optimization problem is then formulated to minimize the lateral displacements of the aircraft flows. Although this optimization problem is difficult to solve in general due to its nonconvex nature, a closed-form solution can be obtained for three intersecting flows. The minimum requirement of lateral displacements of aircraft flows for conflict resolution can also be used as a metric of traffic complexity for multiple intersecting flows of aircraft. It is shown that the order of growth of this complexity metric is O(n 3) for symmetric configurations of n flows of aircraft.

Fundamental performance limits and efficient polices for Transportation-On-Demand systems

Transportation-On-Demand (TOD) systems, where users generate requests for transportation from a pick-up point to a delivery point, are already very popular and are expected to increase in usage dramatically as the inconvenience of privately-owned cars in metropolitan areas becomes excessive. Routing service vehicles through customers is usually accomplished with heuristic algorithms. In this paper we study TOD systems in a formal setting that allows us to characterize fundamental performance limits and devise dynamic routing policies with provable performance guarantees. Specifically, we study TOD systems in the form of a unit-capacity, multiple-vehicle dynamic pick-up and delivery problem, whereby pick-up requests arrive according to a Poisson process and are randomly located according to a general probability density. Corresponding delivery locations are also randomly distributed according to a general probability density, and a number of unit-capacity vehicles must transport demands from their pick-up locations to their delivery locations. We derive insightful fundamental bounds on the steady-state waiting times for the demands, and we devise constant-factor optimal dynamic routing policies. Simulation results are presented and discussed.

Computing Earth mover's distances on a road map with applications to one-way vehicle sharing

The Earth movers distance (EMD) is a measure of distance between probability distributions which is at the heart of mass transportation theory. Recent research has shown that the EMD plays a crucial role in studying the potential impact of one-way vehicle sharing paradigms like Mobility-on-Demand (MoD). While the ubiquitous physical transportation setting is the “road network”, characterized by systems of roads connected together by interchanges, most analytical works about vehicle sharing represent distances between points in a plane using the simple Euclidean metric. Instead, we consider the EMD when the ground metric is taken from a class of one-dimensional, continuous metric spaces, reminiscent of road networks. We produce an explicit formulation of the Earth movers distance given any finite road network R. The result generalizes the EMD with a Euclidean ℝ1 ground metric, which has remained one of the only known non-discrete cases with an explicit formula. Our formulation casts the EMD as the optimal value of a finite-dimensional, real-valued optimization problem, with a convex objective function and linear constraints. In the special case that the input distributions have piece-wise uniform (constant) density, the problem reduces to one whose objective function is convex quadratic. Both forms are amenable to modern mathematical programming techniques.

On the Nash equilibria of a timed asymmetric skirmish

In this work, we present a Nash equilibrium solution for a timed, asymmetric skirmish between two agents: an attacker, and a defender. We derive a solution by focusing on strategy profiles in which both the attacker and defender randomize their actions, which correspond to times, over a common atomic support. We show this class of strategies admits a unique mixed-strategy Nash equilibrium and give an algorithm for its computation. A numerical example highlights interesting features of a typical equilibrium strategy profile.