Quantitative Examination of Internet Traffic Dynamics at Ghana Communication Technology University | Chapter 5 | Research Updates in Mathematics and Computer Science Vol. 7

We seek to unearth which distribution best describes traffic behaviour to help solve the problem of congestion on campus from a mathematical point of view. Telecommunications traffic engineering (i.e. Tele -traffic engineering) is the application of traffic engineering theory to telecommunications. Tele-traffic engineers use their cognition of statistics including queuing theory, the nature of traffic, their practical fashion model, and their mensuration and computer simulation to make predictions and to program telecommunication networks such as a telephone network or the Internet. Internet traffic is a flow of data across the internet. This flow exhibits certain behaviour in accordance with a Probability distribution.  Statistical analysis was performed to understand the characteristics of the traffic population. The empirical cumulative distribution process (CDF) together with essential statistical parameters were benchmarked. The goodness of Fit (GOF) test using the Anderson-Darling (AD) estimation method was applied to establish the best probability distribution model which describes the situation alongside with Probability plot. Deep-down opinion or analysis hints that if the period of time (or space) of grouping is increased well enough, the degree of data relationships will eventually become unimportant by scaling. The N-Flow traffic model was used to determine the burstiness of internet traffic in finite sessions. The Empirical and Theoretical CDF graph was used to determine the discrepancies between them. In the end, it was discovered that the data best fit normal distribution. From experimental and theoretical analysis, it is clear that the internet traffic behaviour in Ghana Technology University College is normally distributed.

 

 

Author(s) Details

Emmanuel Kwame Mensah

Department of Computer and Telecommunication Engineering, Faculty of Engineering, Ghana Communication Technology, PMB 100 Accra-North, Ghana.

 

Please see the book here:- https://doi.org/10.9734/bpi/rumcs/v7/2039G

 

Quantitative Examination of Internet Traffic Dynamics at Ghana Communication Technology University | Chapter 6 | Research Updates in Mathematics and Computer Science Vol. 7

 

We seek to unearth which distribution best describes traffic behaviour to help solve the problem of congestion on campus from a mathematical point of view. Telecommunications traffic engineering (i.e. Tele -traffic engineering) is the application of traffic engineering theory to telecommunications. Tele-traffic engineers use their cognition of statistics including queuing theory, the nature of traffic, their practical fashion model, and their mensuration and computer simulation to make predictions and to program telecommunication networks such as a telephone network or the Internet. Internet traffic is a flow of data across the internet. This flow exhibits certain behaviour in accordance with a Probability distribution.  Statistical analysis was performed to understand the characteristics of the traffic population. The empirical cumulative distribution process (CDF) together with essential statistical parameters were benchmarked. The goodness of Fit (GOF) test using the Anderson-Darling (AD) estimation method was applied to establish the best probability distribution model which describes the situation alongside with Probability plot. Deep-down opinion or analysis hints that if the period of time (or space) of grouping is increased well enough, the degree of data relationships will eventually become unimportant by scaling. The N-Flow traffic model was used to determine the burstiness of internet traffic in finite sessions. The Empirical and Theoretical CDF graph was used to determine the discrepancies between them. In the end, it was discovered that the data best fit normal distribution. From experimental and theoretical analysis, it is clear that the internet traffic behaviour in Ghana Technology University College is normally distributed.

 

Author(s)details:-

 

Emmanuel Kwame Mensah
Department of Computer and Telecommunication Engineering, Faculty of Engineering, Ghana Communication Technology, PMB 100 Accra-North, Ghana.

 

Please See the book here :-  https://doi.org/10.9734/bpi/rumcs/v7/2039G

Stability-Preserving Stochastic Perturbations | Book Publisher International

The stability of equilibria is a topic of importance in mathematical models in many branches of science. Since systems generally do not start in equilibrium states, the equilibria of chief scientific interest are those which are attracting, in the sense that the system converges to these equilibria over time. Perhaps the simplest mathematical model which captures this is a deterministic differential equation, and we can study the long-time behaviour of the solution of the equation.

Such simple models, however, may underplay the role that randomness may play in the evolution of the system. The character of the stochastic disturbance may be of many types: one type, which this considers, is when the intensity of the random term is independent of the state of the system, but varies over time. This models persistent stochastic shocks. The question now is: which (possibly fading) time-varying intensities of the shock preserve the stability of the system, and which render the equilibrium unstable. The book seeks to answer this question for one-dimensional linear (and possibly) nonlinear differential equations in a very comprehensive manner. The book involves stochastic calculus (mainly stochastic differential equations), and also some ideas from the theory of differential equations which we will study. According to the writers’ interest, one can ask whether numerical simulations of the stochastic equation preserve the asymptotic behaviour of the original continuous-time problem. The research outcome is most relevant to Probability and Finance (as well as Simulation for Finance, if numerical studies are involved) as well as Ito calculus.

This book is concerned with the study of linear differential and difference equations which are subjected to an outside force. Any equation without any External force is considered to be “stable “in a sense we make precise below.

The question we address is: what are precisely the conditions on this external force for which this stability is preserved, and if these conditions are not satisfied, what then is the long–time behaviour of the solution?

The stochastic differential equations (SDEs) driven by Brownian motions have been attracting lots of attentions. When some unexpected events happen, some jumps may be needed to model the effects of those events. For example, the out break of a new disease can cause the National Economy have some instability in the country. To take both the continuous and discontinuous random effects into consideration, SDEs driven by both Brownian motions and Poisson jumps are often employed as a generalisation of the SDEs only driven by Brownian motions. Despite the wide applications, the explicit solutions to SDEs are hardly found. Therefore, to construct some efficient numerical methods is of great importance.

In general, we are able to characterise whether the solution has retained its stability, or whether the solution remain under control, but is not convergent, or whether the solution become unbounded.

Author(s) Details:

Dr. Miya Nakazwe Hoyer,
Department of Financial Mathematics, Dublin City University, Republic of Ireland.

Prof. John Appleby,
School of Mathematical Sciences, Dublin City University, Republic of Ireland.

Please see the link here: https://stm.bookpi.org/SPSP/article/view/13328

Estimation of the Parameter of Certain Distributions with Known Coe_cient of Variation by U-Statistics | Chapter 13 | Theory and Practice of Mathematics and Computer Science Vol. 1

 

In this work we consider the problem of estimation of the location parameter of certain distributions

with known coe_cient of variation by U-statistics. We discussed the general technique of estimating

the location parameter of a distribution with known coe_cient of variation using the theory of Ustatistics.

The method has been illustrated in obtaining the estimator of the location parameter

(mean) of normal, logistic and double exponential distributions. The e_ciency properties of our

estimator in each case when compared with certain other commonly available estimators are also

discussed.

 

Author (s) Details

N. K. Sajeevkumar

Department of Statistics, Government College Kariavattom, Thiruvananthapuram-695581, India.

View Book :-https://bp.bookpi.org/index.php/bpi/catalog/book/237

Estimation of the Location Parameter of Certain Distributions with Known Coefficient of Variation by Order Statistics | Chapter 10 | Recent Studies in Mathematics and Computer Science Vol. 3

 We discuss the general technique of estimating the location parameter of certain distributions with

known coefficient of variation by order statistics.Also we estimate the location parameter of normal
distribution,logistic distribution , exponential distribution and right triangular distribution using
order statistics .Also we include a real life data to estimate the location parameter of a normal
distribution with known coefficient of variation using order statistics.

Author(s) Details

Dr. N. K. Sajeevkumar
Department of Statistics, Govt. College Kariavattom, Thiruvananthapuram-695 581, India.

View Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/233

Record Values in the Estimation of a Parameter of Some Distributions with Known Coefficient of Variation | Chapter 7 | Recent Studies in Mathematics and Computer Science Vol. 2

We discuss the general technique of estimating the location parameter of certain distributions with known coefficient of variation by record values.Also we estimate the location parameters of normal distribution,logistic distribution and exponential distribution using upper record values .Al so we include a real life data to estimate the location parameter of a logistic distribution using upper record values.

Author(s) Details

Dr. N. K. Sajeevkumar
Department of Statistics, Government College, Kariavattom, Trivandrum-695581, India.

View Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/182