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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…
Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic…
We consider large fluctuations, namely overload of servers, in a network with dynamic routing of messages. The servers form a circle. The number of input flows is equal to the number of servers, the messages of any flow are distributed…
This paper purpose is to investigate exponential behavior conditions for the infinite servers queue with Poisson arrivals busy period length distribution. It is presented a general theoretical result that is the basis of this work. The…
This paper studies the diffusion limit for a network of infinite-server queues operating under Markov modulation (meaning that the system's parameters depend on an autonomously evolving background process). In previous papers on (primarily…
In this note, we apply Stein's method to analyze the performance of general load balancing schemes in the many-server heavy-traffic regime. In particular, consider a load balancing system of $N$ servers and the distance of arrival rate to…
Recently research on bubble and its burst attract much interest of researchers in various field such as economics and physics. Economists have been regarding bubble as a disorder in prices. However, this research strategy has overlooked an…
We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…
In this paper, we investigate the number of customers that overlap or coincide with a virtual customer in an Erlang-A queue. Our study provides a novel approach that exploits fluid and diffusion limits for the queue to approximate the mean…
In the finite element analysis with fast decoupled time integration scheme for viscoelastic fluid (the Leonov model) flow, we investigate strong nonlinear behavior in 2D creeping contraction flow. The algorithm is applicable in the whole…
Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting…
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…
Two important aspects of the Internet, namely the properties of its topology and the characteristics of its data traffic, have attracted growing attention of the physics community. My thesis has considered problems of both aspects. First I…
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…
This work considers a server that processes $J$ classes using the generalized processor sharing discipline with base weight vector $\alpha=(\alpha _1,...,\alpha_J)$ and redistribution weight vector $\beta=(\beta_1,...,\beta_J)$. The…
Rayleigh--Taylor fluid turbulence through a bed of rigid, finite-size, spheres is investigated by means of high-resolution Direct Numerical Simulations (DNS), fully coupling the fluid and the solid phase via a state-of-the art Immersed…
We propose a minimal model for the emergence of a directed flow in autonomous Hamiltonian systems. It is shown that internal breaking of the spatio-temporal symmetries, via localised initial conditions, that are unbiased with respect to the…
We study infinite server queues driven by Cox processes in a fast oscillatory random environment. While exact performance analysis is difficult, we establish diffusion approximations to the (re-scaled) number-in-system process by proving…
We report numerical simulations of a strongly biased diffusion process on a one-dimensional substrate with directed shortcuts between randomly chosen sites, i.e. with a small-world-like structure. We find that, unlike many other dynamical…
The limit order book mechanism has been the core trading mechanism of the modern financial market. In the cryptocurrency market, centralized exchanges also adopt this limit order book mechanism and a centralized matching engine dynamically…