Related papers: A quantitative differential equation approximation…
In the setting of a recently developed cellular stochastic traffic flow model, it has shown that the joint per-cell vehicle densities, as a function of time, can be accurately approximated by a Gaussian process, which has the attractive…
We consider a single-server queue where interarrival and service times depend linearly and randomly on customer waiting times, and establish a sample-path moderate deviation principle (MDP) for the waiting time process. The waiting times…
In transportation and other types of facilities, various queues arise when the demands of service are higher than the supplies, and many point and fluid queue models have been proposed to study such queueing systems. However, there has been…
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…
In this article we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by…
This paper introduces a general model of a single-lane roundabout, represented as a circular lattice that consists of $L$ cells, with Markovian traffic dynamics. Vehicles enter the roundabout via on-ramp queues that have stochastic arrival…
Mean-field integro-differential equations are studied in an abstract framework, through couplings of the corresponding stochastic processes. In the perturbative regime, the equation is proven to admit a unique equilibrium, toward which the…
Using a microscopic model for stochastic transport through a single quantum dot that is modified by the Coulomb interaction of environmental (weakly coupled) quantum dots, we derive generic properties of the full counting statistics for…
The efficient management of large-scale queueing networks is critical for a variety of sectors, including healthcare, logistics, and customer service, where system performance has profound implications for operational effectiveness and cost…
This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have…
We consider Markov processes, which describe e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit…
Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…
We study aggregations for ordinary differential equations induced by fluid semantics for Markovian process algebra which can capture the dynamics of performance models and chemical reaction networks. Whilst previous work has required…
This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…
Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
An overview of the recursive equations based models and their applications in simulation based analysis and optimization of queueing systems is given. These models provide a variety of systems with a convenient and unified representation in…
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum…
This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density,…