The application of non-linear dynamics to teletraffic modelling.

PhDAbstract not availableEngineering and Physical Science Research Council (EPSRC) and NORTE

A Survey of Performance Evaluation and Control for Self-Similar Network Traffic

This paper surveys techniques for the recognition and treatment of self-similar network or internetwork traffic. Various researchers have reported traffic measurements that demonstrate considerable burstiness on a range of time scales with properties of self-similarity. Rapid technological development has widened the scope of network and Internet applications and, in turn, increased traffic volume. The exponential growth of the number of servers, as well as the number of users, causes Internet performance to be problematic as a result of the significant impact that long-range dependent traffic has on buffer requirements. Consequently, accurate and reliable measurement, analysis and control of Internet traffic are vital. The most significant techniques for performance evaluation include theoretical analysis, simulation, and empirical study based on measurement. In this research, we discuss existing and recent developments in performance evaluation and control tools used in network traffic engineering

Techniques for the Fast Simulation of Models of Highly dependable Systems

With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system

Global Modeling and Prediction of Computer Network Traffic

We develop a probabilistic framework for global modeling of the traffic over a computer network. This model integrates existing single-link (-flow) traffic models with the routing over the network to capture the global traffic behavior. It arises from a limit approximation of the traffic fluctuations as the time--scale and the number of users sharing the network grow. The resulting probability model is comprised of a Gaussian and/or a stable, infinite variance components. They can be succinctly described and handled by certain 'space-time' random fields. The model is validated against simulated and real data. It is then applied to predict traffic fluctuations over unobserved links from a limited set of observed links. Further, applications to anomaly detection and network management are briefly discussed

From Data Processing to Distributional Modelling of Traffic Measurements

This thesis is motivated by the need to analyse measured traffic data from networks. It develops and applies statistical methods to characterize and to model such data. The application areas are related to teletraffic and telecommunication networks, vehicular traffic and road/street networks, and Internet of Things applications. The research is based on four scientific publications, augmented with the statistical framework and theoretical development included in this summary. From the applications' point of view, the addressed research problems diverge on the types of the engineering problems, while from the statistical point of view, they share common theoretical methods. The application problems are: i) to study whether a Gaussian process is a feasible model for aggregated Internet traffic, ii) to obtain aggregated flow level models for flow sizes, flow durations and their bivariate joint distribution, iii) to deduce vehicular traffic routes from correlated counts of vehicles that are observed at different locations of a street network, and iv) to develop a data reduction algorithm that works with limited computational capacity and can be deployed by Internet of Things applications. This summary provides the statistical framework that combines the developed and applied methodologies and emphasizes their common features. Rigorous mathematical proofs are given for certain less-known, possibly novel, results about mutual information of pairs of order statistics, and a convergence result related to simultaneous estimation of several quantiles. These were used in the publications or, alternatively, bring new statistical insight to the methods that were used in the publications.Tutkimuksen motiivina on ollut löytää tilastollisia menetelmiä liikennedatan analysointiin. Liikennedata käsittää tässä sekä tieto- että ajoneuvoliikenteestä mitattua, liikenteen määrää kuvaavaa dataa. Menetelmiä kehitetään liikenteen ominaisuuksien karakterisointiin ja jakaumien mallintamiseen. Tutkimus sisältää neljä julkaisua sekä yhteenveto-osuuden. Julkaisuissa käsitellyt sovellukset ovat kaikki hyvin erilaisia, mutta niiden tilastollisessa lähestymistavassa on paljon yhteisiä piirteitä. Julkaisuissa käsitellyt tilastolliset ongelmat ovat seuraavat. Ensimmäisessä julkaisussa tutkitaan, soveltuuko Gaussinen prosessi aggregoidun eli monesta yksittäisestä liikennevirrasta muodostetun yhdistetyn liikennevirran malliksi. Jo usean vuosikymmenen ajan on tiedetty, että tietoliikenteen yhdistäminen ei käyttäydy tilastollisessa mielessä yhtä hyvin kuin esimerkiksi puheliikenteen yhdistäminen. Yhdistetyn tietoliikenteen purskeisuus ei lievene yksittäisten liikennevirtojen määrän kasvaessa vaan purskeisuus näkyy useissa eri aikaskaaloissa ja aikasarjana siinä esiintyy pitkän aikavälin riippuvuuksia. Julkaisun menetelmät sisältävät keinoja aikasarjan stationaarisuuden ja normaalijakaumaoletuksen tutkimiseen tällaisissa tilanteissa. Toisessa julkaisussa tutkitaan mobiilidatayhteyksien ominaisuuksia, joita voidaan mitata aggregoidusta liikennevirrasta rekonstruoimalla yksittäisiä yhteyksiä. Niitä ovat verkosta ladattujen tiedostojen kokojakauma, latauksiin kuluneen ajan jakauma ja näiden kahden suureen yhteisjakauma. Lisäksi mallinnetaan näiden kahden suureen osamäärän jakaumaa, joka kuvastaa yksittäisen mobiilidatakäyttäjän kokemaa keskimääräistä tiedonsiirtonopeutta. Erona tavanomaisempiin menetelmiin mitata käyttäjän saamaa tiedonsiirtonopeutta on se, että julkaisun menetelmillä sitä voidaan mitata aggregoidusta liikennevirrasta eli verkon sisältä. Julkaisussa myös tutkitaan kokojakauman paksuhäntäisyyttä. Kolmas julkaisu käsittelee autoliikenteen mallintamista. Esimerkiksi liikennevalojen yhteydessä on usein sensoreita, jotka havaitsevat ohi ajavat kulkuneuvot. Sensoreiden tuottamaa dataa voidaan jalostaa mittaamaan kulkuneuvojen lukumääriä esimerkiksi 15 minuutin mittaisilla aikaväleillä. Julkaisun menetelmillä tällaista dataa voidaan hyödyntää reaaliajassa esimerkiksi laskemalla ennuste luottamusväleineen meneillään olevan tai tulevan 15 minuutin aikavälin liikennemäärälle. Neljäs julkaisu liittyy esineiden ja asioiden Internetiin. Siinä esitellään algoritmi, jolla voidaan tiivistää esimerkiksi sensorin tuottamaa numeerista mittausdataa jakaumamuotoon. Algoritmin tarvitsemat laskennalliset resurssit, prosessoriaika ja muistin tarve ovat hyvin pienet. Tiivistäminen on mielekästä esimerkiksi tilanteissa, joissa mittauksien tekeminen on käytettävissä olevien resurssien kannalta halpaa, mutta tiedonsiirto kallista. Algoritmia voidaan soveltaa myös liikennemäärien mittaamiseen. Yhteenveto-osuudessa käsitellään edellä mainituissa julkaisuissa kehitettyjen tilastollisten menetelmien yhteistä teoriapohjaa. Teoriapohjaan kuuluvat järjestystunnusluvut ja kvantiilit, moniulotteiset jakaumat sekä aikasarjan stationaarisuuteen ja autokorrelaatioihin liittyvä teoria. Yhteenveto-osuus sisältää myös vähemmän tunnettuja, mahdollisesti uusia matemaattisia tuloksia jotka liittyvät järjestystunnuslukujen sisältämän keskinäisen informaation määrään sekä usean kvantiilin yhtäaikaisen estimoinnin ongelmiin, kun estimointi tapahtuu samasta numeerisesta datavirrasta

A Conversation with Chris Heyde

Born in Sydney, Australia, on April 20, 1939, Chris Heyde shifted his interest from sport to mathematics thanks to inspiration from a schoolteacher. After earning an M.Sc. degree from the University of Sydney and a Ph.D. from the Australian National University (ANU), he began his academic career in the United States at Michigan State University, and then in the United Kingdom at the University of Sheffield and the University of Manchester. In 1968, Chris moved back to Australia to teach at ANU until 1975, when he joined CSIRO, where he was Acting Chief of the Division of Mathematics and Statistics. From 1983 to 1986, he was a Professor and Chairman of the Department of Statistics at the University of Melbourne. Chris then returned to ANU to become the Head of the Statistics Department, and later the Foundation Dean of the School of Mathematical Sciences (now the Mathematical Sciences Institute). Since 1993, he has also spent one semester each year teaching at the Department of Statistics, Columbia University, and has been the director of the Center for Applied Probability at Columbia University since its creation in 1993. Chris has been honored worldwide for his contributions in probability, statistics and the history of statistics. He is a Fellow of the International Statistical Institute and the Institute of Mathematical Statistics, and he is one of three people to be a member of both the Australian Academy of Science and the Australian Academy of Social Sciences. In 2003, he received the Order of Australia from the Australian government. He has been awarded the Pitman Medal and the Hannan Medal. Chris was conferred a D.Sc. honoris causa by University of Sydney in 1998. Chris has been very active in serving the statistical community, including as the Vice President of the International Statistical Institute, President of the Bernoulli Society and Vice President of the Australian Mathematical Society. He has served on numerous editorial boards, most notably as Editor of Stochastic Processes and Their Applications from 1983 to 1989, and as Editor-in-Chief of Journal of Applied Probability and Advances in Applied Probability since 1990.Comment: Published at http://dx.doi.org/10.1214/088342306000000088 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Change detection in teletraffic models

In this paper, we propose a likelihood-based ratio test to detect distributional changes in common teletraffic models. These include traditional models like the Markov modulated Poisson process and processes exhibiting long range dependency, in particular, Gaussian fractional ARIMA processes. A practical approach is also developed for the case where the parameter after the change is unknown. It is noticed that the algorithm is robust enough to detect slight perturbations of the parameter value after the change. A comprehensive set of numerical results including results for the mean detection delay is provided

Modelling of self-similar teletraffic for simulation

Recent studies of real teletraffic data in modern computer networks have shown that teletraffic exhibits self-similar (or fractal) properties over a wide range of time scales. The properties of self-similar teletraffic are very different from the traditional models of teletraffic based on Poisson, Markov-modulated Poisson, and related processes. The use of traditional models in networks characterised by self-similar processes can lead to incorrect conclusions about the performance of analysed networks. These include serious over-estimations of the performance of computer networks, insufficient allocation of communication and data processing resources, and difficulties ensuring the quality of service expected by network users. Thus, full understanding of the self-similar nature in teletraffic is an important issue. Due to the growing complexity of modern telecommunication networks, simulation has become the only feasible paradigm for their performance evaluation. In this thesis, we make some contributions to discrete-event simulation of networks with strongly-dependent, self-similar teletraffic. First, we have evaluated the most commonly used methods for estimating the self-similarity parameter H using appropriately long sequences of data. After assessing properties of available H estimators, we identified the most efficient estimators for practical studies of self-similarity. Next, the generation of arbitrarily long sequences of pseudo-random numbers possessing specific stochastic properties was considered. Various generators of pseudo-random self-similar sequences have been proposed. They differ in computational complexity and accuracy of the self-similar sequences they generate. In this thesis, we propose two new generators of self-similar teletraffic: (i) a generator based on Fractional Gaussian Noise and Daubechies Wavelets (FGN-DW), that is one of the fastest and the most accurate generators so far proposed; and (ii) a generator based on the Successive Random Addition (SRA) algorithm. Our comparative study of sequential and fixed-length self-similar pseudo-random teletraffic generators showed that the FFT, FGN-DW and SRP-FGN generators are the most efficient, both in the sense of accuracy and speed. To conduct simulation studies of telecommunication networks, self-similar processes often need to be transformed into suitable self-similar processes with arbitrary marginal distributions. Thus, the next problem addressed was how well the self-similarity and autocorrelation function of an original self-similar process are preserved when the self-similar sequences are converted into suitable self-similar processes with arbitrary marginal distributions. We also show how pseudo-random self-similar sequences can be applied to produce a model of teletraffic associated with the transmission of VBR JPEG /MPEG video. A combined gamma/Pareto model based on the application of the FGN-DW generator was used to synthesise VBR JPEG /MPEG video traffic. Finally, effects of self-similarity on the behaviour of queueing systems have been investigated. Using M/M/1/∞ as a reference queueing system with no long-range dependence, we have investigated how self-similarity and long-range dependence in arrival processes affect the length of sequential simulations being executed for obtaining steady-state results with the required level of statistical error. Our results show that the finite buffer overflow probability of a queueing system with self-similar input is much greater than the equivalent queueing system with Poisson or a short-range dependent input process, and that the overflow probability increases as the self-similarity parameter approaches one

Investigation of delay jitter of heterogeneous traffic in broadband networks

Scope and Methodology of Study: A critical challenge for both wired and wireless networking vendors and carrier companies is to be able to accurately estimate the quality of service (QoS) that will be provided based on the network architecture, router/switch topology, and protocol applied. As a result, this thesis focuses on the theoretical analysis of QoS parameters in term of inter-arrival jitter in differentiated services networks by deploying analytic/mathematical modeling technique and queueing theory, where the analytic model is expressed in terms of a set of equations that can be solved to yield the desired delay jitter parameter. In wireless networks with homogeneous traffic, the effects on the delay jitter in reference to the priority control scheme of the ARQ traffic for the two cases of: 1) the ARQ traffic has a priority over the original transmission traffic; and 2) the ARQ traffic has no priority over the original transmission traffic are evaluated. In wired broadband networks with heterogeneous traffic, the jitter analysis is conducted and the algorithm to control its effect is also developed.Findings and Conclusions: First, the results show that high priority packets always maintain the minimum inter-arrival jitter, which will not be affected even in heavy load situation. Second, the Gaussian traffic modeling is applied using the MVA approach to conduct the queue length analysis, and then the jitter analysis in heterogeneous broadband networks is investigated. While for wireless networks with homogeneous traffic, binomial distribution is used to conduct the queue length analysis, which is sufficient and relatively easy compared to heterogeneous traffic. Third, develop a service discipline called the tagged stream adaptive distortion-reducing peak output-rate enforcing to control and avoid the delay jitter increases without bound in heterogeneous broadband networks. Finally, through the analysis provided, the differential services, was proved not only viable, but also effective to control delay jitter. The analytic models that serve as guidelines to assist network system designers in controlling the QoS requested by customer in term of delay jitter