Related papers: A Note on Many-server Fluid Models with Time-varyi…
A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment…
We introduce a multiclass single-server queueing system in which the arrival rates depend on the current job in service. The system is characterized by a matrix of arrival rates in lieu of a vector of arrival rates. Our proposed model…
In this paper, we study the lifespan and continuation criteria of several two-dimensional incompressible fluid models. Motivated by a novel energy-vorticity formulation, combining linear transport estimate and a bootstrap argument, we are…
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…
We consider a dynamic model of traffic that has received a lot of attention in the past few years. Users control infinitesimal flow particles aiming to travel from an origin to a destination as quickly as possible. Flow patterns vary over…
In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction $p$ of an available resource is deployed in a centralized manner…
Service platforms must determine rules for matching heterogeneous demand (customers) and supply (workers) that arrive randomly over time and may be lost if forced to wait too long for a match. Our objective is to maximize the cumulative…
We study a single server queue under a processor-sharing type of scheduling policy, where the weights for determining the sharing are given by functions of each job's remaining service(processing) amount, and obtain a fluid limit for the…
Forecasting traffic flows is a central task in intelligent transportation system management. Graph structures have shown promise as a modeling framework, with recent advances in spatio-temporal modeling via graph convolution neural…
When considering a general system of equations describing the space-time evolution (flow) of one or several variables, the problem of the optimization over a finite period of time of a measure of the state variable at the final time is a…
Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting…
The definitions of temporal instability and of spatial instability in a flow system are comparatively surveyed. The simple model of one-dimensional Burgers' flow is taken as the scenario where such different conceptions of instability are…
Extending the famous Model B for the time evolution of a liquid mixture, we derive an approximate expression for the mobility matrix that couples the different mixture components. This approach is based on a single component fluid with…
Motivated by the ongoing COVID-19 pandemic, this paper investigates customers' infection risk by evaluating the overlapping time of a virtual customer with others in queueing systems. Most of the current methodologies focus on…
We derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance…
We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its…
We use multidimensional diffusion processes to approximate the dynamics of a queue served by many parallel servers. The queue is served in the first-in-first-out (FIFO) order and the customers waiting in queue may abandon the system without…
We consider the velocity fluctuations of a system of particles described by the Inelastic Maxwell Model. The present work extends the methods, previously employed to obtain the one-particle velocity distribution function, to the study of…
This paper presents a framework to incorporate ride-pooling from a mesoscopic point of view, within time-invariant network flow models of Mobility-on-Demand systems. The resulting problem structure remains identical to a standard network…
We apply supervised machine learning techniques to a number of regression problems in fluid dynamics. Four machine learning architectures are examined in terms of their characteristics, accuracy, computational cost, and robustness for…