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We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level…
Flowgraph models provide an alternative approach in modeling a multi-state stochastic process. One of the most widely used stochastic processes that have many real-world applications especially in actuarial models is the Markov jump process…
We use coupling to study the time taken until the distribution of a statistic on a Markov chain is close to its stationary distribution. Coupling is a common technique used to obtain upper bounds on mixing times of Markov chains, and we…
Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds.…
In transportation systems (e.g. highways, railways, airports), traffic flows with distinct origin-destination pairs usually share common facilities and interact extensively. Such interaction is typically stochastic due to natural…
Stochastic processes on complex networks, where each node is in one of several compartments, and neighboring nodes interact with each other, can be used to describe a variety of real-world spreading phenomena. However, computational…
We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
Flow and bridge matching are a novel class of processes which encompass diffusion models. One of the main aspect of their increased flexibility is that these models can interpolate between arbitrary data distributions i.e. they generalize…
This paper addresses the problem of steering an initial probability distribution to a target probability distribution through a deterministic or stochastic linear control system. Our proposed approach is inspired by the flow matching…
Stochastic network calculus is an evolving theory which accounts for statistical multiplexing and uses an envelope approach for probabilistic delay and backlog analysis of networks. One of the key ideas of stochastic network calculus is the…
Fundamental to many transportation network studies, traffic flow models can be used to describe traffic dynamics determined by drivers' car-following, lane-changing, merging, and diverging behaviors. In this study, we develop a…
We consider the queuing networks, which are made from servers, exchanging their positions. The customers, using the network, try to reach their destinations, which is complicated by the movements of the servers, taking their customers with…
We consider a stochastic, dynamic job scheduling problem, formulated as a queueing control problem, in which a single server processes jobs of different types that arrive according to independent Poisson processes. The problem is defined on…
Optimal sensor scheduling with applications to networked estimation and control systems is considered. We model sensor measurement and transmission instances using jumps between states of a continuous-time Markov chain. We introduce a cost…
Machine learning and computational intelligence technologies gain more and more popularity as possible solution for issues related to the power grid. One of these issues, the power flow calculation, is an iterative method to compute the…
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…
The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has $x$ requests to transmit, then it receives a fraction of the capacity proportional to $\log(1+x)$,…
Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…