5 research outputs found
Two-choice regulation in heterogeneous closed networks
A heterogeneous closed network with one-server queues with finite capacity
and one infinite-server queue is studied. A target application is bike-sharing
systems. Heterogeneity is taken into account through clusters whose queues have
the same parameters. Incentives to the customer to go to the least loaded
one-server queue among two chosen within a cluster are investigated. By
mean-field arguments, the limiting queue length stationary distribution as the
number of queues gets large is analytically tractable. Moreover, when all
customers follow incentives, the probability that a queue is empty or full is
approximated. Sizing the system to improve performance is reachable under this
policy.Comment: 19 pages, 4 figure
A Stochastic Model for Car-Sharing Systems
Vehicle-sharing systems are becoming important for urban transportation. In
these systems, users arrive at a station, pick up a vehicle, use it for a while
and then return it to another station of their choice. Depending on the type of
system, there might be a possibility to book vehicles before picking-up and/or
a parking space at the chosen arrival station. Each station has a finite
capacity and cannot host more vehicles and reserved parking spaces than its
capacity. We propose a stochastic model for an homogeneous car-sharing system
with possibility to reserve a parking space at the arrival station when
picking-up a car. We compute the performance of the system and the optimal
fleet size according to a specific metric. It differs from a similar model for
bike-sharing systems because of reservation that induces complexity, especially
when traffic increases
Modelling a vehicle-sharing station as a dual waiting system: stochastic framework and stationary analysis
19 pagesA waiting system with two kinds of resources, say the vehicles and the docks in a vehicle-sharing service, is considered. Two arrival flows of customers are assumed, access customers who require a vehicle versus egress customers that bring back their vehicle and require a dock at the station. The total number of docks sets a limit capacity for the service. A stochastic, markovian, state-transition model is defined, which constitutes a bi-sided capacitated queuing system. The balance equations are stated and solved, yielding a stationary distribution under two conditions of compatibility. Indicators of service quality and system performance are defined and formulated under steady state
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 -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