Related papers: A Tandem Fluid Network with L\'evy Input in Heavy …
We introduce a traffic flow model that incorporates clustering and passing. We obtain analytically the steady state characteristics of the flow from a Boltzmann-like equation. A single dimensionless parameter, R=c_0v_0t_0 with c_0 the…
The result provided in this paper helps complete a unified picture of the scaling behavior in heavy-tailed stochastic models for transmission of packet traffic on high-speed communication links. Popular models include infinite source…
We investigate the behaviour of an original traffic model. The model considers a single multi-lane street, populated by autonomous vehicles directed from either end to the other. Lanes have no intrinsic directionality, and the vehicles are…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
We consider the problem of minimizing the delay of jobs moving through a directed graph of service nodes. In this problem, each node may have several links and is constrained to serve one link at a time. As jobs move through the network,…
In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…
In this paper, we study the stability of light traffic achieved by a scheduling algorithm which is suitable for heterogeneous traffic networks. Since analyzing a scheduling algorithm is intractable using the conventional mathematical tool,…
We introduce the totally asymmetric exclusion process with Langmuir kinetics (TASEP-LK) on a network as a microscopic model for active motor protein transport on the cytoskeleton, immersed in the diffusive cytoplasm. We discuss how the…
We study a simple rate control scheme for a multiclass queuing network for which customers are partitioned into distinct flows that are queued separately at each station. The control scheme discards customers that arrive to the network…
We study the rare event behavior of the workload process in a transitory queue, where the arrival epochs (or points) of a finite number of jobs are assumed to be the ordered statistics of independent and identically distributed (i.i.d.)…
Fluid queues are mathematical models frequently used in stochastic modelling. Their stationary distributions involve a key matrix recording the conditional probabilities of returning to an initial level from above, often known in the…
Mixture transition distribution time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary…
We propose a threshold detector for L\'evy distributed fluctuations based on a Josephson junction. The L\'evy noise current added to a linearly ramped bias current results in clear changes in the distribution of switching currents out of…
A novel model of transport is proposed to explain power law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Levy process of…
We show on- and off-diagonal upper estimates for the transition densities of symmetric Levy and Levy-type processes. To get the an-diagonal estimates we prove a Nash type inequality for the related Dirichlet form. For the off-diagonal…
We are interested in a large queue in a $GI/G/k$ queue with heterogeneous servers. For this, we consider tail asymptotics and weak limit approximations for the stationary distribution of its queue length process in continuous time under a…
This paper examines a continuous-time routing system with general interarrival and service time distributions, operating under the join-the-shortest-queue and power-of-two-choices policies. Under a weaker set of assumptions than those…
We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent deterministic routing between nodes. The random behavior of the network is constructed from…
We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…
Consider a network of $n$ single-server queues where tasks arrive independently at each server at rate $\lambda_n$. The servers are connected by a graph that is resampled at rate $\mu_n$ in a way that is symmetric with respect to the…