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One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…
We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
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…
Many molecular junctions display stochastic telegraphic switching between two distinct current values, which is therefore an important source of fluctuations in nanoscale quantum transport. We investigate electronic fluctuations arising via…
We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…
We obtain a complete description of anisotropic scaling limits of random grain model on the plane with heavy tailed grain area distribution. The scaling limits have either independent or completely dependent increments along one or both…
By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear…
This is the transcript of a talk given at the 1992 Complex Systems Summer School. The theory of large fluctuations of stochastically perturbed continuous-time dynamical systems is reviewed, and the large fluctuations of two stochastic…
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 study binary state contagion dynamics on a social network where nodes act in response to the average state of their neighborhood. We model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into…
In a circuit-switched network, traffic can be characterized by several factors that define how communication resources are allocated and utilized during a connection. The amount of traffic basically determines how frequently connection…
A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…
This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…
In "On Coding for Reliable Communication over Packet Networks" (Lun, Medard, and Effros, Proc. 42nd Annu. Allerton Conf. Communication, Control, and Computing, 2004), a capacity-achieving coding scheme for unicast or multicast over lossy…
The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained…
We define a new mass transport model on a one-dimensional lattice of size $N$ with continuous masses at each site. The lattice is connected to mass reservoirs of different `chemical potentials' at the two ends. The mass transfer dynamics in…
In the mid-90's, it was shown that the statistics of aggregated time series from Internet traffic departed from those of traditional short range dependent models, and were instead characterized by asymptotic self-similarity. Following this…
In order to maintain consistent quality of service, computer network engineers face the task of monitoring the traffic fluctuations on the individual links making up the network. However, due to resource constraints and limited access, it…