Related papers: Fluid and Diffusion Limits for Bike Sharing System…
Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial…
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…
Bike sharing systems often suffer from poor capacity management as a result of variable demand. These bike sharing systems would benefit from models to predict demand in order to moderate the number of bikes stored at each station. In this…
We develop a heavy traffic diffusion limit theorem under nonstandard spatial scaling for the queue length process in a single server queue employing shortest remaining processing time (SRPT). For processing time distributions with unbounded…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…
The paper develops a method that quantifies the effect of weather conditions on the prediction of bike station counts in the San Francisco Bay Area Bike Share System. The Random Forest technique was used to rank the predictors that were…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
This paper models the availability of bikes at San Francisco Bay Area Bike Share stations using machine learning algorithms. Random Forest (RF) and Least-Squares Boosting (LSBoost) were used as univariate regression algorithms, and Partial…
Mobility systems featuring shared vehicles are often unable to serve all potential customers, as the distribution of demand does not coincide with the positions of vehicles at any given time. System operators often choose to reposition…
In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
We recover the so-called field-road diffusion model as the hydrodynamic limit of an interacting particle system. The former consists of two parabolic PDEs posed on two sets of different dimensions (a "field" and a "road" in a population…
Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well-understood…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different…
Bicycle-sharing systems (BSS) have become a daily reality for many citizens of larger, wealthier cities in developed regions. However, planning the layout of bicycle-sharing stations usually requires expensive data gathering, surveying…
Mixing a passive scalar field by stirring can be measured in a variety of ways including tracer particle dispersion, via the flux-gradient relationship, or by suppression of scalar concentration variations in the presence of inhomogeneous…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
An excessive demand of vehicles to a motorway bottleneck leads to traffic jams. Motorbikes are narrow and can drive next to each other in a lane, or in-between lanes in low speeds. This paper analyses the resulting traffic characteristics…
The efficiency of flow-based networking mechanisms strongly depends on traffic characteristics and should thus be assessed using accurate flow models. For example, in the case of algorithms based on the distinction between elephant and mice…