Fluid and Diffusion Limits for Bike Sharing Systems

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.Comment: 34 pages, 1 figure

Computational complexity of maximum distance-(k, l) matchings in graphs

Секция 10. Теоретическая информатикаIn this paper, we introduce the concept of a distance-(k, l) matching of a graph, which is a subset of edges of this graph such that the number of intermediate edges in the shortest path between any two edges of this set lies between k and l. We prove that the problem MAXIMUM DISTANCE-(k, l) MATCHING, which asks whether a graph contains a distance-(k, l) matching of size exceeding a given number, is NP-complete for arbitrary given or variable k and l, and that the weighted variant of this problem is strongly NP-complete even for bipartite graphs. We also present several upper bounds on the size of a maximum distance-(k, l) matching

A Neural Network to Identify Driving Habits and Compute Car-Sharing Users’ Reputation

main question in urban environments is the continuous growth of private mobility with its negative effects such as traffic congestion and pollution. To mitigate them, it is important to promote different forms of mobility among the citizens. Car-sharing systems give users the same flexibility and comfort of private cars but at smaller costs. For this reason, car-sharing has continuously increased its market share although rather slowly. To boost such growth, car-sharing systems needs to increase vehicle fleet, improve company profits and, at the same time, make it more affordable for consumers. In this paper the promotion of car-sharing by reputation is proposed. Neural networks have been used to identify drivers’ habits in using car-sharing vehicles. To verify the effectiveness of the proposed approach, some experiments based on real and simulated data were carried out with promising results