Markov modulated periodic arrival process offered to an ATM multiplexer

When a superposition of on/off sources is offered to a deterministic server, a particular queueing system arises whose analysis has a significant role in ATM based networks. Periodic cell generation during active times is a major feature of these sources. In this paper a new analytical method is provided to solve for this queueing system via an approximation to the transient behavior of the nD/D/1 queue. The solution to the queue length distribution is given in terms of a solution to a linear differential equation with variable coefficients. The technique proposed here has close similarities with the fluid flow approximations and is amenable to extension for more complicated queueing systems with such correlated arrival processes. A numerical example for a packetized voice multiplexer is finally given to demonstrate our results

Estimation of buffer overflow probabilities and economies of scale in ATM multiplexers by analysis of a model of packetized voice traffic

We obtain upper bounds on the probability of buffer overflow for an ATM multiplexer of L identical packetized voice sources. The multiplexer is modelled by a FCFS single server queue. The arrivals at the multiplexer are a homogenous superposition of the arrivals from L independent identical sources, with each source modelled by a copy of a discrete time Markov Chain which we call the Cell Level Model. Throughout, appropriate parameters are scaled with L, to maintain a constant load over all superposition sizes. The probability that, the queue-length (q^) of the queue in a finite buffer exceeds the buffer size b, is bounded above by the probability that the queue-length (qL) of the queue m an infinite buffer exceeds length b In order to bound the former above, we find upper bounds or approximations for the latter by using the theory of, • Large Deviations, to determine its asymptotics for large b, • Martingales, to obtain upper bounds, valid for all positive b, • Large Deviations, to determine its asymptotics for large L for time rescaled (proportional to L) arrival processes. These demonstrate the multiplexing gam and economies of scale obtainable from large and small buffers and large multiplexers, respectively

On the large deviations of a class of modulated additive processes

We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically. The sojourn times determine how long the phase process spends in a state once it has been selected. The main tool is a representation formula for the sample paths of the empirical laws of the phase process. Then, based on assumed joint large deviation behavior of the state selection and sojourn processes, we prove that the empirical laws of the phase process satisfy a sample path large deviation principle. From this large deviation principle, the large deviations behavior of a class of modulated additive processes is deduced. As an illustration of the utility of the general results, we provide an alternate proof of results for modulated L´evy processes. As a practical application of the results, we calculate the large deviation rate function for a processes that arises as the International Telecommunications Union’s standardized stochastic model of two-way conversational speech

Quality aspects of Internet telephony

Internet telephony has had a tremendous impact on how people communicate. Many now maintain contact using some form of Internet telephony. Therefore the motivation for this work has been to address the quality aspects of real-world Internet telephony for both fixed and wireless telecommunication. The focus has been on the quality aspects of voice communication, since poor quality leads often to user dissatisfaction. The scope of the work has been broad in order to address the main factors within IP-based voice communication. The first four chapters of this dissertation constitute the background material. The first chapter outlines where Internet telephony is deployed today. It also motivates the topics and techniques used in this research. The second chapter provides the background on Internet telephony including signalling, speech coding and voice Internetworking. The third chapter focuses solely on quality measures for packetised voice systems and finally the fourth chapter is devoted to the history of voice research. The appendix of this dissertation constitutes the research contributions. It includes an examination of the access network, focusing on how calls are multiplexed in wired and wireless systems. Subsequently in the wireless case, we consider how to handover calls from 802.11 networks to the cellular infrastructure. We then consider the Internet backbone where most of our work is devoted to measurements specifically for Internet telephony. The applications of these measurements have been estimating telephony arrival processes, measuring call quality, and quantifying the trend in Internet telephony quality over several years. We also consider the end systems, since they are responsible for reconstructing a voice stream given loss and delay constraints. Finally we estimate voice quality using the ITU proposal PESQ and the packet loss process. The main contribution of this work is a systematic examination of Internet telephony. We describe several methods to enable adaptable solutions for maintaining consistent voice quality. We have also found that relatively small technical changes can lead to substantial user quality improvements. A second contribution of this work is a suite of software tools designed to ascertain voice quality in IP networks. Some of these tools are in use within commercial systems today