• Journal of Information Processing Systems
• /
• v.11 no.4
• /
• pp.583-600
• /
• 2015

Generally, the wireless network provides priority to handover calls instead of new calls to maintain its quality of service (QoS). Because of this QoS provisioning, a call admission control (CAC) scheme is essential for the suitable management of limited radio resources of wireless networks to uphold different factors, such as new call blocking probability, handover call dropping probability, channel utilization, etc. Designing an optimal CAC scheme is still a challenging task due to having a number of considerable factors, such as new call blocking probability, handover call dropping probability, channel utilization, traffic rate, etc. Among existing CAC schemes such as, fixed guard band (FGB), fractional guard channel (FGC), limited fractional channel (LFC), and Uniform Fractional Channel (UFC), the LFC scheme is optimal considering the new call blocking and handover call dropping probability. However, this scheme does not consider channel utilization. In this paper, a CAC scheme, which is termed by a uniform fractional band (UFB) to overcome the limitations of existing schemes, is proposed. This scheme is oriented by priority and non-priority guard channels with a set of fractional channels instead of fractionizing the total channels like FGC and UFC schemes. These fractional channels in the UFB scheme accept new calls with a predefined uniform acceptance factor and assist the network in utilizing more channels. The mathematical models, operational benefits, and the limitations of existing CAC schemes are also discussed. Subsequently, we prepared a comparative study between the existing and proposed scheme in terms of the aforementioned QoS related factors. The numerical results we have obtained so far show that the proposed UFB scheme is an optimal CAC scheme in terms of QoS and resource utilization as compared to the existing schemes.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1225-1234
• /
• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• Journal of the Korean Mathematical Society
• /
• v.61 no.4
• /
• pp.621-657
• /
• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• Education of Primary School Mathematics
• /
• v.14 no.3
• /
• pp.261-275
• /
• 2011

We observed the process for solving linear equations of two 5th grade elementary students, who do not have any pre-knowledge about solving linear equation. The way of students' usage of fractional schemes and manipulations are closely observed. The change of their scheme adaptation are carefully analyzed while the coefficients and constants become complicated. The results showed that they used various fractional scheme and manipulations according to the coefficients and constants. Noticeably, they used repeating fractional schemes to establish the equivalence relation between unknowns and the given quantities. After establishing the relationship, equivalent fractions played important role. We expect the results of this study would help shorten the gap between the arithmetic and the algebraic thinking.

• Proceedings of the KSME Conference
• /
• 2002.08a
• /
• pp.27-30
• /
• 2002

As computer capacity has been progressed continuously, the studies of the flow characteristics have been performing by the numerical methods actively. In this study, 3-dimensional unsteady incompressible Wavier-Stokes equation was solved by numerical method using the fractional step method with the fourth order compact pade' scheme to achieve high accuracy To validate the present code and algorithm, 3D flow-field around a cylinder was simulated. The drag coefficient and lift coefficient were computed and, then, compared with experiment. The present code will be tailored to LES simulation for more accurate turbulent flow analysis.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1241-1261
• /
• 2018

We derive discrete time model of the geometric fractional Brownian motion. It provides numerical pricing scheme of financial derivatives when the market is driven by geometric fractional Brownian motion. With the convergence analysis, we guarantee the convergence of Monte Carlo simulations. The strong convergence rate of our scheme has order H which is Hurst parameter. To obtain our model we need to convert Wick product term of stochastic differential equation into Wick free discrete equation through Malliavin calculus but ours does not include Malliavin derivative term. Finally, we include several numerical experiments for the option pricing.

• Journal of the Korean Statistical Society
• /
• v.33 no.4
• /
• pp.459-470
• /
• 2004

We study the approximation of the solution of linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter H > 1/2 through discretization of space and time. The rate of convergence of an approximation for Euler scheme is established.

• Communications of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.281-298
• /
• 2023

A class of systems of Caputo fractional differential equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a uniform mesh is proposed. Supremum norm is used to derive an error estimate which is of order κ − 1, 1 < κ < 2. Numerical examples are given which validate our theoretical results.

• Journal of applied mathematics & informatics
• /
• v.31 no.1_2
• /
• pp.299-309
• /
• 2013

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

• Journal of the Korean Statistical Society
• /
• v.34 no.3
• /
• pp.197-208
• /
• 2005

We consider the problem for approximate solution of linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter $H\;\in$ (0,1/2). The error of the approximate solution for the explicit Euler scheme is investigated.