Random Waiting Research Articles

Fluid Reactive Anomalous Transport with Random Waiting Time Depending on the Preceding Jump Length

Anomalous (or non-Fickian) diffusion has been widely found in fluid reactive transport and the traditional advection–diffusion–reaction equation (ADRE) based on Fickian diffusion is proved to be inadequate to predict this anomalous transport of the reactive particle in flows. To capture the complex coupling effect among advection, diffusion and reaction, and the energy-dependent characteristics of fluid reactive anomalous transport, in the present paper we analyze $$A\rightarrow B$$ reaction under anomalous diffusion with waiting time depending on the preceding jump length in linear flows, and derive the corresponding generalized master equations in Fourier–Laplace space for the distribution of A and B particles in continuous time random walks scheme. As examples, the generalized ADREs for the jump length of Gaussian distribution and L $${\acute{\mathrm{e}}}$$ vy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived generalized master equations.

Reaction Subdiffusion with Random Waiting Time Depending on the Preceding Jump Length**Supported by the National Natural Science Foundation of China under Grant No 11626047, and the Foundation for Young Key Teachers of Chengdu University of Technology under Grant No KYGG201414.

To describe the energy-dependent characteristics of the reaction-subdiffusion process, we analyze the simple reaction under subdiffsion with waiting time depending on the preceding jump length, and derive the corresponding master equations in the Fourier–Laplace space for the distribution of A and B particles in a continuous time random walk scheme. Moreover, the generalizations of the reaction-diffusion equation for the Gaussian jump length with the probability density function of waiting time being quadratically dependent on the preceding jump length are obtained by applying the derived master equations.

Optimal Hospital Payment Rules Under Rationing by Random Waiting

We derive optimal rules for paying hospitals in a public health care system in which providers can choose quality and random patient demand is rationed by waiting time. Since waiting time imposes real costs on patients hospital payment rules should take account of their effect on waiting time as well as on quality and the number of patients treated. We develop a general stochastic model of rationing by waiting and use it to derive welfare maximising payment to hospitals linked to output, expected waiting times, quality, hospital capacity and length of stay. We show that, although prospective output pricing gives hospitals an incentive to attract patients by raising quality and reducing waiting times, it must be supplemented by prices attached to other hospital decisions and outcomes except under very strong assumptions about the welfare function, patient preferences, and whether patients lose income whilst waiting

Concentration Sensing by the Moving Nucleus in Cell Fate Determination: A Computational Analysis.

During development of the vertebrate neuroepithelium, the nucleus in neural progenitor cells (NPCs) moves from the apex toward the base and returns to the apex (called interkinetic nuclear migration) at which point the cell divides. The fate of the resulting daughter cells is thought to depend on the sampling by the moving nucleus of a spatial concentration profile of the cytoplasmic Notch intracellular domain (NICD). However, the nucleus executes complex stochastic motions including random waiting and back and forth motions, which can expose the nucleus to randomly varying levels of cytoplasmic NICD. How nuclear position can determine daughter cell fate despite the stochastic nature of nuclear migration is not clear. Here we derived a mathematical model for reaction, diffusion, and nuclear accumulation of NICD in NPCs during interkinetic nuclear migration (INM). Using experimentally measured trajectory-dependent probabilities of nuclear turning, nuclear waiting times and average nuclear speeds in NPCs in the developing zebrafish retina, we performed stochastic simulations to compute the nuclear trajectory-dependent probabilities of NPC differentiation. Comparison with experimentally measured nuclear NICD concentrations and trajectory-dependent probabilities of differentiation allowed estimation of the NICD cytoplasmic gradient. Spatially polarized production of NICD, rapid NICD cytoplasmic consumption and the time-averaging effect of nuclear import/export kinetics are sufficient to explain the experimentally observed differentiation probabilities. Our computational studies lend quantitative support to the feasibility of the nuclear concentration-sensing mechanism for NPC fate determination in zebrafish retina.

An Adaptive Spanning Tree-Based Data Collection Scheme in Wireless Sensor Networks

In-network data aggregation is a widely used method for collecting data efficiently in wireless sensor networks (WSNs). The authors focus on how to achieve high aggregation efficiency and prolonging networks’ lifetime. Firstly, this paper proposes an adaptive spanning tree algorithm (AST), which can adaptively build and adjust an aggregation spanning tree. Owing to the strategies of random waiting and alternative father nodes, AST can achieve a relatively balanced spanning tree and flexible tree adjustment. Then a redundant aggregation scheme (RAG) is illustrated. In RAG, interior nodes help to forward data for their sibling nodes and thus provide reliable data transmission for WSN. Finally, the simulations demonstrate that (1) AST can prolong the lifetime and (2) RAG makes a better trade-off between storage and aggregation ratio, comparing to other aggregation schemes.

Available Bandwidth Estimation Using Collision Probability, Idle Period Synchronization and Random Waiting Time in MANETs: Cognitive Agent Based Approach

In Mobile Ad hoc NETworks (MANETs), each node estimates available bandwidth (AB) before transmission of real-time multimedia data, as the channel is shared. The existing AB estimation techniques lack accuracy and add overhead. Accuracy of these AB estimation techniques could be enhanced by adopting some intelligent techniques. Intelligent software agents such as cognitive agent (CA) have significant potential to solve the challenges of estimating AB in MANETs. Intelligence is provided similar to the logical thinking like human for decision making in CA. The predominant CA architecture is belief desire intention model, which performs the task on behalf of human user as an assistant to him/her. In this paper, we propose CA-based available bandwidth estimation using collision probability, Idle period synchronization and random waiting time (BECIT) in MANETs. The proposed BECIT technique uses CA at each node to create mobile agents for collecting and distributing the statistics (such as idle period, packet loss, and AB, etc.) over the network. The collected network statistics are used by CA to estimate AB using our previous work distributed lagrange interpolation based AB estimation (DLI-ABE). The DLI-ABE comprises of statistical models for idle period synchronization by differentiating their states as BUSY, IDLE, and SENSE BUSY; collision probability using distributed Lagrange Interpolation polynomial; and random waiting time that consumes AB such as request-to-send, clear-to-send commands in IEEE 802.11 standard. Estimation of end-to-end AB on a multi-hop path uses each node AB. The simulation results show that BECIT performs approximately 30 % more accurate than the non-agent based AB estimation scheme. Memory overhead is essential to store knowledge base for agents whereas the computational overhead is due to Lagrange Interpolation polynomial at each node in the proposed scheme.

Kinetic lattice Monte Carlo simulation of viscoelastic subdiffusion

We propose a kinetic Monte Carlo method for the simulation of subdiffusive random walks on a cartesian lattice. The random walkers are subject to viscoelastic forces which we compute from their individual trajectories via the fractional Langevin equation. At every step the walkers move by one lattice unit, which makes them differ essentially from continuous time random walks, where the subdiffusive behavior is induced by random waiting. To enable computationally inexpensive simulations with n-step memories, we use an approximation of the memory and the memory kernel functions with a complexity O(log n). Eventual discretization and approximation artifacts are compensated with numerical adjustments of the memory kernel functions. We verify with a number of analyses that this new method provides binary fractional random walks that are fully consistent with the theory of fractional brownian motion.

Subdiffusive motion of a polymer composed of subdiffusive monomers

We use Brownian dynamics simulations and analytical theory to investigate the physical principles underlying subdiffusive motion of a polymer. Specifically, we examine the consequences of confinement, self-interaction, viscoelasticity, and random waiting on monomer motion, as these physical phenomena may be relevant to the behavior of biological macromolecules in vivo. We find that neither confinement nor self-interaction alter the fundamental Rouse mode relaxations of a polymer. However, viscoelasticity, modeled by fractional Langevin motion, and random waiting, modeled with a continuous time random walk, lead to significant and distinct deviations from the classic polymer-dynamics model. Our results provide diagnostic tools--the monomer mean square displacement scaling and the velocity autocorrelation function--that can be applied to experimental data to determine the underlying mechanism for subdiffusive motion of a polymer.

Asymptotic Analysis of the Waiting-Time Distribution for a Large Closed Processor-Sharing System

The service of an interactive computer system is characterized by the random waiting (or response) time perceived by users. The system consists of a bank of terminals, each of which asynchronously alternates between “thinking” and waiting for service from a central processing unit which operates under the processor-sharing discipline. It is assumed that there are $(N + 1)$ terminals, where N is large, and that $\rho = Np = O(1)$, where p is the ratio of the mean required service time to the mean think time. Asymptotic approximations to the equilibrium distribution of the waiting time are derived for: normal usage, $\rho < 1$; heavy usage, $\rho - 1 = O(N^{ - 1/2} )$; and very heavy usage, $\rho > 1$. Singular perturbation techniques are used, and the matching of the heavy-usage approximation with both the normal and very heavy-usage approximations is investigated. Numerical results are presented which indicate that the approximations are useful for $N\geqq 100$.

Moments of the conditioned waiting time in a large closed processor-sharing system

The service of an interactive computer system is characterized by the random waiting (or response) time perceived by users. The system consists of a bank of terminals, each of which asynchronously alternates between “thinking” and waiting for service from a central processing unit which operates under the processor-sharing discipline. It is assumed that there are (N+1) terminals, where N is large, and that , where p is ratio of the mean required service time to the mean think time. Asymptotic approximations to the mean and variance of the equilibrium waiting time, conditioned on the required service time τ, are derived, by means of singular perturbation techniques, for: normal usage, ρ>1; heavy usage and very heavy usage, ρ>1. Numerical results are presented

Asymptotic Expansions of Moments of the Waiting Time in a Shared-Processor of an Interactive System

An interactive computer system’ service is characterized by the random waiting (or response) time perceived by users. This paper presents a novel solution to the problem of efficiently computing the second moment of the waiting time of a class of large interactive systems. The physical system consists of a bank of terminals, each of which asynchronously alternates between “thinking” and waiting for service from a CPU which operates under the processor-sharing discipline. The problem of obtaining higher order waiting time moments is quite different from that of obtaining CPU queue statistics. Only the first moment of the waiting time is obtainable from the CPU queue statistics. The technique for arriving at the second moment of the waiting time consists of developing an asymptotic expansion in inverse powers of the number of terminals. Hence, as the system grows, quite fortuitously, fewer terms of the series require computation to achieve the desired accuracy. Beside its numerical advantages, the results give new insight since the leading terms of the series, which contain most of the information, are obtained explicitly. The novelty also rests on the fact that instead of solving matrix equations, the problem is turned into one of solving a second order differential equation. A simple two-dimensional recursion yields all the terms of the asymptotic expansion.