Related papers: Weighted Dyck paths for nonstationary queues

Using the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road…

This paper proposes a stochastic framework to evaluate the performance of public transit systems under short random service suspensions. We aim to derive closed-form formulations of the mean and variance of the queue length and waiting…

We consider random paths on a square lattice which take a left or a right turn at every vertex. The possible turns are taken with equal probability, except at a vertex which has been visited before. In such case the vertex is left via the…

Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by…

A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We…

Parallel real-time systems (e.g., autonomous driving systems) often contain functionalities with complex dependencies and execution uncertainties, leading to significant timing variability which can be represented as a probabilistic…

We consider Markovian multiserver retrial queues where a blocked customer has two opportunities for abandonment: at the moment of blocking or at the departure epoch from the orbit. In this queueing system, the number of customers in the…

This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks are characterized by the fact that the one-step transition probabilities are functions of the…

We study positive recurrence and transience of a two-station network in which the behavior of the server in each station is governed by a Markov chain with a finite number of server states; this service process can represent various service…

We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…

This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The…

Donsker Theorem is perhaps the most famous invariance principle result for Markov processes. It states that when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general…

We construct the conditional version of $k$ independent and identically distributed random walks on $\R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random…

We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…

We consider the processor sharing $M/M/1$-PS queue which also models balking. A customer that arrives and sees $n$ others in the system "balks" (i.e., decides not to enter) with probability $1-b_n$. If $b_n$ is inversely proportional to…

The inference of Markov models from data on stochastic dynamical trajectories over the large time-window $T$ is revisited via the Large Deviations at Level 2.5 for the time-empirical density and the time-empirical flows. The goal is to…

We study a one-dimensional Markov modulated random walk with jumps. It is assumed that amplitudes of jumps as well as a chosen velocity regime are random and depend on a time spent by the process at a previous state of the underlying Markov…

An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…

This article investigates discrete-time matrix-weighted consensus of multi-agent networks over undirected and connected graphs. We first present consensus protocols for the agents in common networks of symmetric matrix weights with possibly…

Let $X$ be the constrained random walk on ${\mathbb Z}_+^2$ having increments $(1,0)$, $(-1,1)$, $(0,-1)$ with jump probabilities $\lambda(M_k)$, $\mu_1(M_k)$, and $\mu_2(M_k)$ where $M$ is an irreducible aperiodic finite state Markov…