Optimal sampling of independent increment processes

Trends and Issues

Our studies have revealed that VoIP jitter can be modeled by self-similar processes, and through a decomposition based on Haar wavelet it is shown a possible reason of the presence of long range dependence (LRD) in VoIP jitter. On the other hand, we used a description of VoIP packet loss based on microscopic and macroscopic packet loss behaviors, where these behaviors can be modeled by 2-state and 4-state Markov chains, respectively. Besides, the distributions of the number of consecutive received and lost packets (namely gap and burst, respectively) are modeled from the transition probabilities of 2-state and 4-state Markov chains. Based on the above mentioned description, we presented a methodology for simulating packet loss and proposed a new model that allows to relate the Hurst parameter (H) with the packet loss rate (PLR). These models can be used by other researchers as input to problems related to the design of VoIP applications, performance evaluation of IP networks, and th...

2011

In this paper, we analyze the jitter and packet loss behavior of Voice over Internet Protocol (VoIP) traffic by means of networks measurements and simulations results. As result of these analyses, we provide a detailed characterization and accurate modeling of these Quality of Service (QoS) parameters. Our studies have revealed that VoIP jitter can be modeled by self-similar processes with short range dependence (SRD) or long range dependence (LRD). The discovery of LRD (a kind of asymptotic fractal scaling) in VoIP jitter was followed by a further work that shows the evidence of multifractal behavior. The implication of these behaviors for VoIP and other interactive multimedia services is that receiver de-jitter buffer may not be large enough to mask the jitter with LRD and multifractal characteristics. On the other hand, we use a description of VoIP packet loss based on microscopic and macroscopic packet loss behaviors, where these behaviors can be modeled by 2-state and 4-state Markov chains, respectively. Based on the above mentioned points, we present a methodology for simulating packet loss. Besides, we found relationships between Hurst parameter (H) with the packet loss rate (PLR); these relationships are based on voice traffic measurements and can be modeled by means of a power-law function, characterized by three fitted parameters. The proposed models can be used to: (i) design a de-jitter buffer, (ii) to implement a synthetic generator of VoIP jitter data traces, where the synthetic jitter data traces can be used as test vectors to carry out the performance evaluation of a de-jitter buffer of VoIP system, and (iii) design effective schemes for packet loss recovery.

Advances in Electrical and Electronic Engineering, 2012

This article deals with modelling the Probability density function of IPTV traffic packet delay variation. The use of this modelling is in an efficient dejitter buffer estimation. When an IP packet travels across a network, it experiences delay and its variation. This variation is caused by routing, queueing systems and other influences like the processing delay of the network nodes. When we try to separate these at least three types of delay variation, we need a way to measure these types separately. This work is aimed to the delay variation caused by queueing systems which has the main implications to the form of the Probability density function.

The Internet is rapidly growing in number of users, traffic levels and topological complexities. A vital component to understand the requirements, its capabilities and extension of the network is its traffic analysis. In literature, conventional traffic model does not capture today’s burstiness in Internet traffic with the assumption that inter-arrival time is independent and identically distributed. The Internet forwarding scheme has given provision for correlated inter-arrival times which are rampant when streams of packets arrive to a destination at the same time. Modern researchers are contemplating of modulating Poisson process with another distribution in form of Compound Poisson Process, Markov Modulated Poisson Process or use of Pareto model to tract actual traffic characteristics. Pareto is assumed in literature to have facility to cater for burstiness. This paper uses goodness of fit test to detect the exponential nature of the inter arrival times of Pareto generated netwo...

2013

Abstract: The finding that Pareto distributions are adequate to model Internet packet interarrival times has motivated the proposal of methods to evaluate steady-state performance measures of Pareto/D/1/k queues. Some limited analytical derivation for queue models has been proposed in the literature, but their solutions are often of a great mathematical challenge. To overcome such limitations, simulation tools that can deal with general queueing system must be developed. Despite certain limitations, simulation algorithms provide a mechanism to obtain insight and good numerical approximation to parameters of queues. In this work, we give an overview of some of these methods and compare them with our simulation approach, which are suited to solve queues with Generalized-Pareto interarrival time distributions. The paper discusses the properties and use of the Pareto distribution. We propose a real time trace simulation model for estimating the steady-state probability showing the tail-...

2010

In many real-time applications the Quality of Service (QoS) is dominated by jitter. Currently jitter generators are based on Laplace distribution. Nevertheless, the observed jitter measurements depart from that distribution. As a matter of fact data resembles those of a t-Student distribution, and it is also known that Internet traffic presents heavy tailed behavior that can be modeled with alpha-stable distributions. The intention of this work is to find which of these distributions has the best fitting. For this purpose, we collect extensive (round trip time) RTT measurements, and show that the alpha-stable distribution models the jitter adequately. Fitness test included Kullback-Leibler divergence and P-P plot criteria.

Electronic Journal of Statistics, 2010

In this paper we show empirical data from Internet traffic measurements. Collected measurements are analyzed for different protocols, such as TCP and UDP. We perform statistical analysis through the correlation coefficients, covariance, and self-similarity degree i.e. Hurst parameter. Our experimental studies captured traffic with Hurst parameter around 0.7-0.75, which is near half way between values of 0.5 (it is not a self-similar) and 1 (strong self-similar properties). We use Maximum Likelihood approach to fit the obtained time series to existing distributions, such as Pareto and exponential distribution, where the first one is a self-similar process and the second is not. The analysis pointed out that Internet traffic with such values for the Hurst parameter could be modeled with similar accuracy using either distribution, Pareto and exponential.

2008

In many real-time applications the quality of service (QoS) is dominated by jitter. In this paper RTT (round trip time) measurements were collected in order to find a probabilistic jitter model. From collected measurements the tail index was close to unit, this relates us to Cauchy's distribution. In this paper we show that the jitter has direct influence in the network performance. The purpose of this paper is to show how jitter dispersion affects the QoS in some applications.

2011 3rd International Congress on Ultra Modern Telecommunications and Control Systems and Workshops, 2011

VoIP (Voice over IP) is a modern service with enormous potential for yet further growth. It uses the already available and universally implemented IP transport platform. One significant problem, however, is ensuring the Quality of Service, abbreviated QoS. This paper addresses exactly that issue. In an extensive investigation the influence of jitter buffers on QoS is being examined in depth. Two implementations, namely a passive FIFO buffer and an active PJSIP buffer are considered. The results obtained are presented in several diagrams and interpreted. They provide valuable insights and indications as to how procedures to ensure QoS in IP networks can be planned and implemented. The paper concludes with a summary and outlook on further work.

In this paper we consider a discrete time queueing model to calculate end-to-end delays and jitter in packet networks. The arrival process is formed by a discrete time renewal (foreground stream) and a batch process (background stream). By this model we are able to trace the foreground stream as it passes through a multiplexer where it will be disturbed by crossing packet streams (background traffic). In particular we have analyzed the distribution of the time between two successive departures. By approximating the output foreground stream with a renewal stream and applying this as the input to the next node, by applying the queueing model recursively, we get an end-to-end description. Especially the evolution of the jitter, but also the end-to-end delay will be analyzed more accurately than given by the conventional convolutions approach. Some numerical examples are given and discussed for both evolution of jitter and end-to-end delay. For the end-to-end delay we also compare the r...