scholarly journals Queue Size Distribution on a New ND Policy Geo/G/1 Queue and Its Computation Designs

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Rongxiu Wang
Keyword(s):  
Steady State ◽  
Numerical Experiments ◽  
Probability Generating Function ◽  
Power Saving ◽  
Wireless Sensor ◽  
Size Distributions ◽  
Queue Size ◽  
Improve Model ◽  
Departure Time ◽  
Theoretical Results

This paper examines a new ND policy in the discrete-time Geo/G/1 queue. Under this ND policy, the idle server restarts its service when the N and D policies are simultaneously satisfied. By two classifications of the customers, the probability-generating function and the probabilistic analysis, the steady-state queue size distributions at a departure time and an arbitrary time t + are studied. Finally, the theoretical results are applied to the power-saving problem of a wireless sensor network. To improve model universality and numerical slowness, some computation designs are carried out. Under the N, D, and two ND policies, the numerical experiments are presented to obtain the optimal policy thresholds and the corresponding minimum power consumptions are compared.

scholarly journals An Intuitive Introduction to Fractional and Rough Volatilities

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 994
Author(s):  
Elisa Alòs ◽  
Jorge A. León
Keyword(s):  
Malliavin Calculus ◽  
Numerical Experiments ◽  
Implied Volatility ◽  
Natural Approach ◽  
Volatility Models ◽  
Implied Volatility Surface ◽  
Short Memory ◽  
White Type ◽  
Volatility Surface ◽  
Theoretical Results

Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.

scholarly journals Applications of matrix-geometric solutions for queueing performance evaluation of a hybrid switching system

1989 ◽  
Vol 31 (2) ◽  
pp. 219-239 ◽  
Author(s):  
Moshe Zukerman
Keyword(s):  
Steady State ◽  
Packet Delay ◽  
Arrival Process ◽  
Exact Results ◽  
Queue Size ◽  
Switching System ◽  
Hybrid Switching ◽  
Geometric Solutions ◽  
Best Fit ◽  
Queueing Performance

AbstractWe consider a hybrid switch which provides integrated packet (asynchronous) and circuit (isochronous) switching. Queue size and delay distribution of the packet switched traffic in the steady state are derived by modelling the packet queue as a queue in a Markovian environment. The arrival process of the packets as well as of the circuit allocation requests are both modelled by a Poisson process. The analysis is performed for several circuit allocation policies, namely repacking, first-fit (involving static or dynamic renumbering) and best-fit. Both exact results and approximations are discussed. Numerical results are presented to demonstrate the effect of increase in packet and circuit loading on the packet delay for each of the policies.

An Assessment of the Value of Theory in Predicting Gas-Bearing Performance

1961 ◽  
Vol 83 (2) ◽  
pp. 195-200 ◽  
Author(s):  
S. Cooper
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Experimental Methods ◽  
Experimental Results ◽  
Theoretical Investigations ◽  
Gas Bearing ◽  
Theoretical Results

The object of the paper is to indicate the value of theoretical investigations of hydrodynamic finite bearings under steady-state conditions. Methods of solution of Reynolds equation by both desk and digital computing, and methods of stabilizing the processes of solution, are described. The nondimensional data available from the solutions are stated. The outcome of an attempted solution of the energy equation is discussed. A comparison between some theoretical and experimental results is shown. Experimental methods employed and some difficulties encountered are discussed. Some theoretical results are given to indicate the effects of the inclusion of slip velocity, stabilizing slots, and a simple case of whirl.

scholarly journals Steady-State Size Distributions in Probabilistic Models of the Cell Division Cycle

1985 ◽  
Vol 45 (4) ◽  
pp. 523-540 ◽  
Author(s):  
Kenneth B. Hannsgen ◽  
John J. Tyson ◽  
Layne T. Watson
Keyword(s):  
Steady State ◽  
Cell Division ◽  
Probabilistic Models ◽  
Cell Division Cycle ◽  
Size Distributions ◽  
State Size

A Self-Adaptive Listen-Time Sleeping Algorithm Based on the Number of Neighbor Nodes for Wireless Mesh Sensor Networks

2012 ◽  
Vol 433-440 ◽  
pp. 5123-5128
Author(s):  
Jun Feng Hao ◽  
Jing Fan ◽  
Wen Yu Shi
Keyword(s):  
Wireless Sensor Network ◽  
Sensor Networks ◽  
Heavy Traffic ◽  
Power Saving ◽  
Critical Issue ◽  
Sensor Nodes ◽  
Wireless Sensor ◽  
Wireless Mesh ◽  
End To End Delay ◽  
Low Traffic

Power saving is a very critical issue in wireless sensor network. Many schemes for power saving can be found in the literature, but these schemes barely consider different topology of nodes. In this paper, based on S-MAC algorithm, NALS-MAC algorithm is designed and combined with the characters of application background of wireless mesh sensor networks. According to the number of neighbor nodes, sensor nodes self-adaptively generate the listen-time during a period respectively. The node with more neighbors will have longer listen-time, because more neighbors means higher probability of heavy traffic. The nodes need longer time to deal with information than nodes with low traffic. The results show that the sensor nodes adjusting the listen-time self-adaptively in proper way achieves the reduction of end-to-end delay and enhance throughout.

scholarly journals On the numerical solutions for nonlinear Volterra-Fredholm integral equations

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Parviz Darania ◽  
Saeed Pishbin
Keyword(s):  
Nonlinear System ◽  
Integral Equations ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Coefficient Matrix ◽  
Collocation Methods ◽  
Fredholm Integral Equations ◽  
Stability Estimates ◽  
Lower Triangular ◽  
Theoretical Results

In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an efficient implementation. Convergence analysis and linear stability estimates are investigated. Finally numerical experiments are given, which confirm our theoretical results.

Sign in / Sign up

Export Citation Format

Share Document