Related papers: Weighted Dyck paths for nonstationary queues
The shortest-path, commute time, and diffusion distances on undirected graphs have been widely employed in applications such as dimensionality reduction, link prediction, and trip planning. Increasingly, there is interest in using…
Let $G$ be a directed graph on finitely many vertices and edges, and assign a positive weight to each edge on $G$. Fix vertices $u$ and $v$ and consider the set of paths that start at $u$ and end at $v$, self-intersecting in any number of…
This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…
The rotor-router model is a deterministic process analogous to a simple random walk on a graph. This paper is concerned with a generalized model, functional-router model, which imitates a Markov chain possibly containing irrational…
We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays $\xi_{i}$. The standard deviation $\sigma$ of the delay is finite, but its value is much larger than the deterministic unit service time.…
We extend the notion of nonbacktracking walks from unweighted graphs to graphs whose edges have a nonnegative weight. Here the weight associated with a walk is taken to be the product over the weights along the individual edges. We give two…
We revisit a single-server retrial queue with two independent Poisson streams (corresponding to two types of customers) and two orbits. The size of each orbit is infinite. The exponential server (with a rate independent of the type of…
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…
Longitudinal binary relational data can be better understood by implementing a latent space model for dynamic networks. This approach can be broadly extended to many types of weighted edges by using a link function to model the mean of the…
We develop a path-based approach to continuous-time random walks on networks with arbitrarily weighted edges. We describe an efficient numerical algorithm for calculating statistical properties of the stochastic path ensemble. After…
The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…
Demand for studying queueing systems with multiple servers providing correlated services was created about 60 years ago, motivated by various applications. In recent years, the importance of such studies has been significantly increased,…
We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…
We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the $\Delta_{(i)}/G/1$ queue, the customers decide…
In this paper we study the Poisson Hypothesis, which is a device to analyze approximately the behavior of large queueing networks. We prove it in some simple limiting cases. We show in particular that the corresponding dynamical system,…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We consider the down/up crossing property of weighted Markov branching processes. The joint probability distribution of multi crossing numbers of such processes are obtained. In particular, for Markov branching processes, the probability…
We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $Z$. The construction can be interpreted in terms of "multi-line diagrams" or…