Related papers: A Simple Network of Nodes Moving on the Circle
The problem Orienteering asks whether there exists a walk which visits a number of sites without exceeding some fuel budget. In the variant of the problem we consider, the cost of each edge in the walk is dependent on the time we depart one…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…
We consider a rumor model in which the network is divided into three classes of agents: ignorant, spreader, and stifler. A spreader transmits the rumor to each of its ignorant neighbors at rate one, and at the same rate, it becomes a…
We study the problem of patrolling the nodes of a network collaboratively by a team of mobile agents, such that each node of the network is visited by at least one agent once in every $I(n)$ time units, with the objective of minimizing the…
Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links…
A deterministic walk in a random environment can be understood as a general random process with finite-range dependence that starts repeating a loop once it reaches a site it has visited before. Such process lacks the Markov property. We…
In this two-part paper, we consider multicomponent systems in which each component can iteratively exchange information with other components in its neighborhood in order to compute, in a distributed fashion, the average of the components'…
Discrete-time discrete-state finite Markov chains are versatile mathematical models for a wide range of real-life stochastic processes. One of most common tasks in studies of Markov chains is computation of the stationary distribution.…
The difference between the speed of the actions of different processes is typically considered as an obstacle that makes the achievement of cooperative goals more difficult. In this work, we aim to highlight potential benefits of such…
We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains, that is, classical Markov chains with added memory. We show that these can simulate quantum walks, allowing us…
We extend the traditional problem of calculating the traveled distance of a fly that is moving with constant speed on a straight path between two trains that are approaching one another, we found two analytical solutions for the traditional…
A single queue incorporating a retransmission protocol is investigated, assuming that the sequence of per effort success probabilities in the Automatic Retransmission reQuest (ARQ) chain is a priori defined and no channel state information…
We show bounds on total variation and $L^{\infty}$ mixing times, spectral gap and magnitudes of the complex valued eigenvalues of a general (non-reversible non-lazy) Markov chain with a minor expansion property. This leads to the first…
The models studied in the steady state involve two queues which are served either by a single server whose speed depends on the number of jobs present, or by several parallel servers whose number may be controlled dynamically. Job service…
This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs. Using an auxiliary function of maximum representation type, conditions are given to…
In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…
In this paper we study the problem of tracking an object moving randomly through a network of wireless sensors. Our objective is to devise strategies for scheduling the sensors to optimize the tradeoff between tracking performance and…
The paper investigates efficient distributed computation in dynamic networks in which the network topology changes (arbitrarily) from round to round. Our first contribution is a rigorous framework for design and analysis of distributed…
We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spent by the process in the previous state of the underlying…