Probability Distribution Of Waiting Time Research Articles

Physical properties of phospholipids and integral proteins and their biofunctional roles in pulmonary surfactant from molecular dynamics simulation.

This work deals with a quantitative investigation of the physical properties of pulmonary surfactant near melting temperature. To this end, we make use of molecular dynamics simulations, using the MARTINI coarse-grained model, for determining the physical properties of the system, such as the potential energy, the specific heat, the microstructure, the diffusion laws, and the elastic properties of the surfactant. The microstructure is studied by computation of the radial-distribution-function upon varying the distance between constituents (lipid molecules or proteins). The diffusion phenomenon is investigated by determination of the mean-squared-displacement and the time dependent velocity-autocorrelation-function for various values of temperature. We show that the dynamics of lipids and proteins exhibit a subdiffusion regime (slow movement) due to the cage effect within pulmonary surfactant. From the obtained mean-squared-displacement, we get the values of the self-diffusion-coefficients and the anomalous exponents at different temperatures close to the melting temperature. For the mathematical description of the cage effect, we make use of the scale relations in terms of the waiting time probability distribution. The last study is concerned with determination of the dependence of the lateral stress upon the strain of pulmonary surfactant, which is found to be linear, and from which we deduce the lateral-elastic-modulus.

Anomalous transport in fluid field with random waiting time depending on the preceding jump length**Project supported by the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414) and the Opening Foundation of Geomathematics Key Laboratory of Sichuan Province, China (Grant No. scsxdz2013009).

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier–Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation.

Mesoscopic description of random walks on combs.

Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone. We analyze the overall diffusion properties along the backbone and find normal diffusion, anomalous diffusion, and stochastic localization (diffusion failure), respectively, depending on the characteristics of the continuous time random walk along the branches, and compare our analytical results with stochastic simulations.

Aging phenomena, probability distribution functions and numerical implementations for Lévy walks

Lévy walks are non-Markovian stochastic processes, whose explosion of space with time is faster than regular Brownian motion but slower than ballistic motion. More concretely, they correspond to a random walk process with jump distribution , where is a power law waiting-time distribution. In this paper, we first investigate the probability distribution functions of Lévy walks, then discuss their aging phenomena, forward waiting-time probability distribution and numerical implementations.

CONTINUOUS-TIME FINANCE AND THE WAITING TIME DISTRIBUTION: MULTIPLE CHARACTERISTIC TIMES

In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

Continuous-time random walk: Crossover from anomalous regime to normal regime

We consider decoupled continuous time random walk with finite characteristic waiting time and jump length variance. We take approximate jump length probability distribution and waiting time probability distribution given by a product of power-law and exponential function. Using this waiting time probability distribution we study diffusion behaviors for all the time. Due to the finite characteristic waiting time and jump length variance the model presents normal diffusive behavior in the long-time limit. However, the model can describe anomalous behavior at the short and intermediate times. In particular, the model can describe subdiffusive, normal, and superdiffusive behaviors at the short times. Moreover, exact solution for probability distribution of the system is also investigated.

Superdiffusive Heat Transport in a Class of Deterministic One-dimensional Many-Particle Lorentz Gases

We study heat transport in a one-dimensional chain of a finite number N of identical cells, coupled at its boundaries to stochastic particle reservoirs. At the center of each cell, tracer particles collide with fixed scatterers, exchanging momentum. In a recent paper (Collet and Eckmann in Commun. Math. Phys. 287:1015, 2009), a spatially continuous version of this model was derived in a scaling regime where the scattering probability of the tracers is γ∼1/N, corresponding to the Grad limit. A Boltzmann-like equation describing the transport of heat was obtained. In this paper, we show numerically that the Boltzmann description obtained in Collet and Eckmann (Commun. Math. Phys. 287:1015, 2009) is indeed a bona fide limit of the particle model. Furthermore, we study the heat transport of the model when the scattering probability is 1, corresponding to deterministic dynamics. Thought as a lattice model in which particles jump between different scatterers the motion is persistent, with a persistence probability determined by the mass ratio among particles and scatterers, and a waiting time probability distribution with algebraic tails. We find that the heat and particle currents scale slower than 1/N, implying that this model exhibits anomalous heat and particle transport.

A continuous model of human dynamics

Ideas and tools from statistical physics have recently been applied to the investigation of human dynamics. The timing of human activities, in particular, has been studied both experimentally and analytically. Empirical data show that, in many different situations, the time interval separating two consecutive tasks executed by an individual follows a heavy-tailed probability distribution rather than Poisson statistics. To account for this data, human behaviour has been viewed as a decision-based queuing system where individuals select and execute tasks belonging to a finite list of items as an increasing function of a task priority parameter. It is then possible to obtain analytically the empirical result P ( τ ) ∼ 1 / τ , where P ( τ ) is the waiting time probability distribution. Here a continuous model of human dynamics is introduced using instead an infinite queuing list. In contrast with the results obtained by other models in the finite case we find a waiting time distribution explicitly depending on the priority distribution density function ρ . The power-law scaling P ( τ ) ∼ 1 / τ is then recovered when ρ is exponentially distributed.

Random Walk Model with Waiting Times Depending on the Preceding Jump Length

In the present paper, the generalized continuous time random walk model with a coupled transition kernel is considered. The coupling occurs through the dependence of the waiting time probability distribution on the preceding jump length. For the description of this model, a method is suggested that includes the details of the microscopic distribution over the waiting times and arrival distances at a given point. A close analogy to the problem of a random walk with finite velocity is demonstrated for the particular case of coupling, when a waiting time is a simple function of a preceding jump length. With its help an analytical solution for the generalized random walk model is found, including both effects (finite velocity and jump dependent waiting times) simultaneously.

Analysis of fronts in reaction-dispersal processes

The existence of traveling wave front solutions with a minimum speed selected for reaction-dispersal processes is studied. We obtain a general existence condition in terms of the waiting time and dispersal distance probability distribution functions and we detail this result for situations of ecological interest. In particular, when particles disperse according to jumps of short length and any waiting time probability distribution function, we show that the minimum speed selection for traveling wave fronts is not always possible, so the waiting time and the dispersal distance distributions cannot be arbitrarily chosen.

NONPARAMETRIC STATISTICAL ANALYSIS OF DISCRETE-TIME QUEUES, WITH APPLICATIONS TO ATM TELETRAFFIC DATA

In this paper nonparametric statistical analysis of a discrete-time queueing system is considered. Estimation of performance measures of the system is studied. The attention is first focused on the estimation of the waiting time probability distribution, as well as of functionals of interest (mean waiting time, variance of the waiting time, etc.). The approach is based on the estimation of the corresponding generating function. Attention is paid to the estimation of the probability of a “long delay”, in view of its importance for applications. Results for possibly unstable models are also obtained. Finally, an application to ATM teletraffic data is provided.

D/G/1 Queues with Vacations

Many data switching systems have processors with arrival streams of regularly spaced tasks (e.g., individual bytes) requiring attention (e.g., directing the bytes to the appropriate outgoing line). In many of these systems the processor might also be required to handle other jobs (small maintenance routines or secondary tasks that await service in one or more other queues) as well. From the point of view of the primary queue of tasks, the processor ceases its service and takes a vacation. The performance of such a system is determined in part by the processor service schedule. In this paper, we define and analyze a model for investigating the waiting time probability distribution at the primary queue in terms of the primary task arrival rate, the service time distribution for the primary tasks, the probability distribution of the vacation duration, and the processor's service schedule. In addition, we discuss two characteristics of systems of this type that may have important design implications: (i) the steady-state waiting time probability distribution might be dependent upon the initial state of the system; and (ii) the waiting time might not decrease if the service time of the system decreases.

The GI/Geom/N Queue In Discrete Time

AbstractThe paper is concerned with the investigation of the GI/Geom/N queue in discrete time using the method of the imbedded Markov chain. The queueing system under consideration has a general independent input, of which the interarrival times are assumed to be identically distributed positive independent random variables with a general probability distribution {an}, first-come first-served queue discipline, geometric service-time distribution and iVservers. The limiting state probability distribution, the waiting-time probability distribution and the delay probability are determined analytically. The problem is also solved for the case when the queue length is bounded by the number of servers. Of special importance is the probability oi customer loss. Erlang's delay and loss formulae are obtained using a limiting process.