Maximum Queue Length of a Fluid Model with a Gaussian Input

A fractional Brownian queueing model, that is, a fluid model with an input of a fractional Brownian motion, was proposed in the 1990s to capture the self-similarity and long-range dependence observed in Internet traffic. Since then, a Gaussian queueing model, which is a queueing model with an input of a continuous Gaussian process, has received much attention. In this dissertation, a Gaussian queueing model is discussed and the maximum queue length over a time interval [0, t] is analyzed. Under some mild assumptions, it is shown that a limit of the maximum queue length suitably normalized is determined by a suitable function of the asymptotic variance of the Gaussian input. Some Gaussian queueing models, such as a queue with an input of several independent fractional Brownian motions and a queue with an input of an integrated Ornstein-Uhlenbeck process, are discussed as examples. For a fractional Brownian queueing model, the main results extend some related known results in the literature. The results on the maximum queue length provide insights for the occurrence of large excursions, which are also called congestion events, in a queueing process. In the context of a fractional Brownian queueing model the temporal properties of congestion events, such as the duration and the inter-congestion event time, are analyzed. A new method based on a Poisson clumping approximation is proposed to evaluate these properties. By comparing with simulation results, it is illustrated that the proposed methodology produces satisfying results for estimating the temporal properties of congestion events in a fractional Brownian queueing model

A study of self-similar traffic generation for ATM networks

This thesis discusses the efficient and accurate generation of self-similar traffic for ATM networks. ATM networks have been developed to carry multiple service categories. Since the traffic on a number of existing networks is bursty, much research focuses on how to capture the characteristics of traffic to reduce the impact of burstiness. Conventional traffic models do not represent the characteristics of burstiness well, but self-similar traffic models provide a closer approximation. Self-similar traffic models have two fundamental properties, long-range dependence and infinite variance, which have been found in a large number of measurements of real traffic. Therefore, generation of self-similar traffic is vital for the accurate simulation of ATM networks. The main starting point for self-similar traffic generation is the production of fractional Brownian motion (FBM) or fractional Gaussian noise (FGN). In this thesis six algorithms are brought together so that their efficiency and accuracy can be assessed. It is shown that the discrete FGN (dPGN) algorithm and the Weierstrass-Mandelbrot (WM) function are the best in terms of accuracy while the random midpoint displacement (RMD) algorithm, successive random addition (SRA) algorithm, and the WM function are superior in terms of efficiency. Three hybrid approaches are suggested to overcome the inefficiency or inaccuracy of the six algorithms. The combination of the dFGN and RMD algorithm was found to be the best in that it can generate accurate samples efficiently and on-the-fly. After generating FBM sample traces, a further transformation needs to be conducted with either the marginal distribution model or the storage model to produce self-similar traffic. The storage model is a better transformation because it provides a more rigorous mathematical derivation and interpretation of physical meaning. The suitability of using selected Hurst estimators, the rescaled adjusted range (R/S) statistic, the variance-time (VT) plot, and Whittle's approximate maximum likelihood estimator (MLE), is also covered. Whittle's MLE is the better estimator, the R/S statistic can only be used as a reference, and the VT plot might misrepresent the actual Hurst value. An improved method for the generation of self-similar traces and their conversion to traffic has been proposed. This, combined with the identification of reliable methods for the estimators of the Hurst parameter, significantly advances the use of self-similar traffic models in ATM network simulation

Reactive traffic control mechanisms for communication networks with self-similar bandwidth demands

Communication network architectures are in the process of being redesigned so that many different services are integrated within the same network. Due to this integration, traffic management algorithms need to balance the requirements of the traffic which the algorithms are directly controlling with Quality of Service (QoS) requirements of other classes of traffic which will be encountered in the network. Of particular interest is one class of traffic, termed elastic traffic, that responds to dynamic feedback from the network regarding the amount of available resources within the network. Examples of this type of traffic include the Available Bit Rate (ABR) service in Asynchronous Transfer Mode (ATM) networks and connections using Transmission Control Protocol (TCP) in the Internet. Both examples aim to utilise available bandwidth within a network. Reactive traffic management, like that which occurs in the ABR service and TCP, depends explicitly on the dynamic bandwidth requirements of other traffic which is currently using the network. In particular, there is significant evidence that a wide range of network traffic, including Ethernet, World Wide Web, Varible Bit Rate video and signalling traffic, is self-similar. The term self-similar refers to the particular characteristic of network traffic to remain bursty over a wide range of time scales. A closely associated characteristic of self-similar traffic is its long-range dependence (LRD), which refers to the significant correlations that occur with the traffic. By utilising these correlations, greater predictability of network traffic can be achieved, and hence the performance of reactive traffic management algorithms can be enhanced. A predictive rate control algorithm, called PERC (Predictive Explicit Rate Control), is proposed in this thesis which is targeted to the ABR service in ATM networks. By incorporating the LRD stochastic structure of background traffic, measurements of the bandwidth requirements of background traffic, and the delay associated with a particular ABR connection, a predictive algorithm is defined which provides explicit rate information that is conveyed to ABR sources. An enhancement to PERC is also described. This algorithm, called PERC+, uses previous control information to correct prediction errors that occur for connections with larger round-trip delay. These algorithms have been extensively analysed with regards to their network performance, and simulation results show that queue lengths and cell loss rates are significantly reduced when these algorithms are deployed. An adaptive version of PERC has also been developed using real-time parameter estimates of self-similar traffic. This has excellent performance compared with standard ABR rate control algorithms such as ERICA. Since PERC and its enhancement PERC+ have explicitly utilised the index of self-similarity, known as the Hurst parameter, the sensitivity of these algorithms to this parameter can be determined analytically. Research work described in this thesis shows that the algorithms have an asymmetric sensitivity to the Hurst parameter, with significant sensitivity in the region where the parameter is underestimated as being close to 0.5. Simulation results reveal the same bias in the performance of the algorithm with regards to the Hurst parameter. In contrast, PERC is insensitive to estimates of the mean, using the sample mean estimator, and estimates of the traffic variance, which is due to the algorithm primarily utilising the correlation structure of the traffic to predict future bandwidth requirements. Sensitivity analysis falls into the area of investigative research, but it naturally leads to the area of robust control, where algorithms are designed so that uncertainty in traffic parameter estimation or modelling can be accommodated. An alternative robust design approach, to the standard maximum entropy approach, is proposed in this thesis that uses the maximum likelihood function to develop the predictive rate controller. The likelihood function defines the proximity of a specific traffic model to the traffic data, and hence gives a measure of the performance of a chosen model. Maximising the likelihood function leads to optimising robust performance, and it is shown, through simulations, that the system performance is close to the optimal performance as compared with maximising the spectral entropy. There is still debate regarding the influence of LRD on network performance. This thesis also considers the question of the influence of LRD on traffic predictability, and demonstrates that predictive rate control algorithms that only use short-term correlations have close performance to algorithms that utilise long-term correlations. It is noted that predictors based on LRD still out-perform ones which use short-term correlations, but that there is Potential simplification in the design of predictors, since traffic predictability can be achieved using short-term correlations. This thesis forms a substantial contribution to the understanding of control in the case where self-similar processes form part of the overall system. Rather than doggedly pursuing self-similar control, a broader view has been taken where the performance of algorithms have been considered from a number of perspectives. A number of different research avenues lead on from this work, and these are outlined

Analytical Modelling of Scheduling Schemes under Self-similar Network Traffic. Traffic Modelling and Performance Analysis of Centralized and Distributed Scheduling Schemes.

High-speed transmission over contemporary communication networks has drawn many research efforts. Traffic scheduling schemes which play a critical role in managing network transmission have been pervasively studied and widely implemented in various practical communication networks. In a sophisticated communication system, a variety of applications co-exist and require differentiated Quality-of-Service (QoS). Innovative scheduling schemes and hybrid scheduling disciplines which integrate multiple traditional scheduling mechanisms have emerged for QoS differentiation. This study aims to develop novel analytical models for commonly interested scheduling schemes in communication systems under more realistic network traffic and use the models to investigate the issues of design and development of traffic scheduling schemes. In the open literature, it is commonly recognized that network traffic exhibits self-similar nature, which has serious impact on the performance of communication networks and protocols. To have a deep study of self-similar traffic, the real-world traffic datasets are measured and evaluated in this study. The results reveal that selfsimilar traffic is a ubiquitous phenomenon in high-speed communication networks and highlight the importance of the developed analytical models under self-similar traffic. The original analytical models are then developed for the centralized scheduling schemes including the Deficit Round Robin, the hybrid PQGPS which integrates the traditional Priority Queueing (PQ) and Generalized Processor Sharing (GPS) schemes, and the Automatic Repeat reQuest (ARQ) forward error control discipline in the presence of self-similar traffic. Most recently, research on the innovative Cognitive Radio (CR) techniques in wireless networks is popular. However, most of the existing analytical models still employ the traditional Poisson traffic to examine the performance of CR involved systems. In addition, few studies have been reported for estimating the residual service left by primary users. Instead, extensive existing studies use an ON/OFF source to model the residual service regardless of the primary traffic. In this thesis, a PQ theory is adopted to investigate and model the possible service left by selfsimilar primary traffic and derive the queue length distribution of individual secondary users under the distributed spectrum random access protocol

Application of learning algorithms to traffic management in integrated services networks.

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN027131 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

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

Performance modelling and analysis of congestion control mechanisms for communication networks with quality of service constraints. An investigation into new methods of controlling congestion and mean delay in communication networks with both short range dependent and long range dependent traffic.

Active Queue Management (AQM) schemes are used for ensuring the Quality of Service (QoS) in telecommunication networks. However, they are sensitive to parameter settings and have weaknesses in detecting and controlling congestion under dynamically changing network situations. Another drawback for the AQM algorithms is that they have been applied only on the Markovian models which are considered as Short Range Dependent (SRD) traffic models. However, traffic measurements from communication networks have shown that network traffic can exhibit self-similar as well as Long Range Dependent (LRD) properties. Therefore, it is important to design new algorithms not only to control congestion but also to have the ability to predict the onset of congestion within a network. An aim of this research is to devise some new congestion control methods for communication networks that make use of various traffic characteristics, such as LRD, which has not previously been employed in congestion control methods currently used in the Internet. A queueing model with a number of ON/OFF sources has been used and this incorporates a novel congestion prediction algorithm for AQM. The simulation results have shown that applying the algorithm can provide better performance than an equivalent system without the prediction. Modifying the algorithm by the inclusion of a sliding window mechanism has been shown to further improve the performance in terms of controlling the total number of packets within the system and improving the throughput. Also considered is the important problem of maintaining QoS constraints, such as mean delay, which is crucially important in providing satisfactory transmission of real-time services over multi-service networks like the Internet and which were not originally designed for this purpose. An algorithm has been developed to provide a control strategy that operates on a buffer which incorporates a moveable threshold. The algorithm has been developed to control the mean delay by dynamically adjusting the threshold, which, in turn, controls the effective arrival rate by randomly dropping packets. This work has been carried out using a mixture of computer simulation and analytical modelling. The performance of the new methods that haveMinistry of Higher Education in Egypt and the Egyptian Cultural Centre and Educational Bureau in Londo

Traffic Characteristics and Queueing Theory: Implications and Applications to Web Server Systems

Businesses rely increasingly on Internet services as the basis of their income. Downtime and poor performance of such services can therefore be directly translated into loss of revenue. In order to plan and design services sufficiently capable of meeting minimumQuality of Service (QoS) requirements and Service Level Agreements(SLA), an understanding of how network traffic and job service demand affect the system is necessary. Traditionally, arrival and service processes have been modelled as Poisson processes. However, research done over the years suggests that the assumption of Poisson traffic is fallible in many cases. This work considers performance of a web server under different traffic and service demand conditions. Moreover, we consider theoretical models of queues, response time formulas derived from this models and their validity for a web server system. We try to make a simple approach to a complex problem by modelling a web server as one simple queueing system. In addition, we investigate the phenomenon known as self-similarity which has been observed in web traffic inter-arrival processes. We have found indications that traffic with identical expectation values for inter-arrival and service time differing in distribution type affects the response time differently. Moreover, classical queueingmodels are found unsuited for doing capacity planning. Instead we suggest ”a worst case scenario” approach in order for service providers to meet service level targets. Much of the previous work within these areas is of a highly mathematical and theoretical nature. We investigate from a more pragmatic viewpoint