Abstract

Bike sharing systems have rapidly developed around the world, and they are served as a promising strategy to improve urban traffic congestion and to decrease polluting gas emissions. So far performance analysis of bike sharing systems always exists many difficulties and challenges under some more general factors. In this paper, a more general large-scale bike sharing system is discussed by means of heavy traffic approximation of multiclass closed queueing networks with non-exponential factors. Based on this, the fluid scaled equations and the diffusion scaled equations are established by means of the numbers of bikes both at the stations and on the roads, respectively. Furthermore, the scaling processes for the numbers of bikes both at the stations and on the roads are proved to converge in distribution to a semimartingale reflecting Brownian motion (SRBM) in a $N^{2}$-dimensional box, and also the fluid and diffusion limit theorems are obtained. Furthermore, performance analysis of the bike sharing system is provided. Thus the results and methodology of this paper provide new highlight in the study of more general large-scale bike sharing systems.

Abstract

Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into account traffic congestion effects is the first topic, and it shows various links with Monge-Kantorovich theory and PDEs. Then, two models for urban planning are introduced. The last section is devoted to two problems from economics and their translation in the language of optimal transport.

Abstract

International audience; Urban transportation of next decade is expected to be disrupted by Autonomous Mobility on Demand (AMoD): AMoD providers will collect ride requests from users and will dispatch a fleet of autonomous vehicles to satisfy requests in the most efficient way. Differently from current ride sharing systems, in which driver behavior has a clear impact on the system, AMoD systems will be exclusively determined by the dispatching logic. As a consequence, a recent interest in the Operations Research and Computer Science communities has focused on this control logic. The new propositions and methodologies are generally evaluated via simulation. Unfortunately, there is no simulation platform that has emerged as reference, with the consequence that each author uses her own custom-made simulator, applicable only in her specific study, with no aim of generalization and without public release. This slows down the progress in the area as researchers cannot build on each other’s work and cannot share, reproduce and verify the results. The goal of this paper is to present AMoDSim, an open-source simulation platform aimed to fill this gap and accelerate research in future ride sharing system