Performance of the IEEE 802.16e sleep mode mechanism in the presence of bidirectional traffic

We refine existing performance studies of the WiMAX sleep mode operation to take into account uplink as well as downlink traffic. This as opposed to previous studies which neglected the influence of uplink traffic. We obtain numerically efficient procedures to compute both delay and energy efficiency characteristics. A test scenario with an Individual Subscriber Internet traffic model in both directions shows that even a small amount of uplink traffic has a profound effect on the system performance

The NxD-BMAP/G/1 queueing model : queue contents and delay analysis

We consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of these quantities, we will derive an expression for their steady-state probability generating function, and from these results, we derive closed-form expressions for key performance measures such as their mean value, variance, and tail distribution. A lot of emphasis is put on finding closed-form expressions for these quantities that reduce all numerical calculations to an absolute minimum

Analysis of a Queueing Model with MAP Arrivals and Heterogeneous Phase-Type Group Services

Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into two sectors: manufacturing and service. These two sectors cover everything we deal with on a day-to-day basis. Queues in which the services are offered in blocks (or groups or batches) are well established in the literature and have a wide variety of applications in practice. In this paper, we look at one such queueing model in which the arrivals occur according to a Markovian arrival process and the services are offered in batches of varying sizes from 1 to a finite pre-determined constant, say, b. The service times are assumed to be of phase type with representation depending on the size of the group. Thus, the distributions considered are heterogeneous from both the representation and rate points of view. The model can be studied as a G I/M/1-type queue or as a QBD-model. The model is analyzed in steady state by establishing results including on the rate matrix and the waiting time distribution and providing a number of illustrative examples

Performance and reliability modelling of computing systems using spectral expansion

PhD ThesisThis thesis is concerned with the analytical modelling of computing and other discrete event systems, for steady state performance and dependability. That is carried out using a novel solution technique, known as the spectral expansion method. The type of problems considered, and the systems analysed, are represented by certain two-dimensional Markov-processes on finite or semi-infinite lattice strips. A sub set of these Markov processes are the Quasi-Birth-and-Death processes. These models are important because they have wide ranging applications in the design and analysis of modern communications, advanced computing systems, flexible manufacturing systems and in dependability modelling. Though the matrixgeometric method is the presently most popular method, in this area, it suffers from certain drawbacks, as illustrated in one of the chapters. Spectral expansion clearly rises above those limitations. This also, is shown with the aid of examples. The contributions of this thesis can be divided into two categories. They are, • The theoretical foundation of the spectral expansion method is laid. Stability analysis of these Markov processes is carried out. Efficient numerical solution algorithms are developed. A comparative study is performed to show that the spectral expansion algorithm has an edge over the matrix-geometric method, in computational efficiency, accuracy and ease of use. • The method is applied to several non-trivial and complicated modelling problems, occuring in computer and communication systems. Performance measures are evaluated and optimisation issues are addressed

Use of GPU for time series analysis

The Global Navigation Satellite System (GNSS) provides the position of stations with millimetre accuracy. These positions are not constant over time due to motion of the tectonic plates on which they are installed. The motion of tectonic plates is not the same all over the world, leading stress to build up in some areas, thus increasing the occurrence of earthquakes. The knowledge of such movements is of extreme importance, as is the determination of their uncertainty. The tectonic motion is a very slow process that is constant over thousands of years. As a result, the motion can be represented by a linear trend. Programs such as Hector can estimate linear trends in time series with temporal correlated noise. Correlated noise means that GNSS observations made today are similar to those of the days before, and it implies that one actually has less information than when all observations were independent. This is the reason why the real uncertainty of the estimated tectonic motion is between 5 to 11 times larger than when this temporal correlation was not considered. Unfortunately, taking this temporal correlation into account in the analysis slows down the computations considerably. With the ever growing number of GNSS stations and the increasing length of the existing time series, it is necessary to speed up these computations. This behaviour can also be found in other geodetic time series such as sea level observed at tide gauges, and surface temperature time series. For climate change studies it is important that besides estimating sea level rise or an increase in temperature, also the associated uncertainties are realistic. The Hector software package was developed with also the aim to reduce the computation time as much as possible. In this thesis we will investigate if the use of a powerful Graphics Processing Unit (GPU) can further reduce this computation time. So far, no Hector-like software uses GPUs to perform data processing. This dissertation is therefore the first attempt to go in that direction.Os Sistemas de Navegação por Satélite, (do inglês Global Navigation Satellite System - GNSS) fornecem a posição de estações com uma precisão milimétrica. Estas posições não são constantes ao longo do tempo devido ao movimento das placas tectónicas nas quais as estações se encontram instaladas. O movimento das placas tectónicas não é igual em todas as partes do globo, o que leva à acumulação de stress em algumas áreas, aumentado assim a ocorrência de movimentos sísmicos. O conhecimento de tais movimentos é de extrema importância, bem como a determinação da sua incerteza. O movimento tectónico é um processo muito lento e constante ao longo de milhares de anos. Como resultado, o movimento pode ser representado por uma tendência linear. Programas como o Hector podem estimar tendências lineares em séries temporais com ruído temporal correlacionado. Ruído correlacionado significa que as observações dos Sistemas de Navegação por Satélite feitas hoje são similares às dos dias anteriores, o que implica que haja menos informação do que se as observações fossem independentes. Esta é a razão pela qual a incerteza real do movimento tectónico estimado é entre 5 a 11 vezes maior do que quando esta correlação temporal não é considerada. Infelizmente, ter em consideração essa correlação temporal na análise aumenta consideravelmente o tempo de computação. Com o crescente número de estações GNSS e o aumento da duração das séries temporais existentes, é necessário acelerar essa computação. Este comportamento também pode ser encontrado em outras séries temporais geodésicas, como as do nível do mar observado em medidores de maré ou séries temporais da temperatura da superfície. Para estudos das alterações climáticas, é importante que, para além de estimar a elevação do nível do mar ou um aumento da temperatura, também as incertezas associadas sejam realísticas. O conjunto de software Hector foi desenvolvido com o objetivo de reduzir o tempo de computação tanto quanto possível. Nesta tese, investigaremos se o uso de uma potente Unidade de Processamento Gráfico (do inglês Graphics Processing Unit), vulgarmente conhecida como placa gráfica, pode reduzir ainda mais este tempo de computação. Até ao momento, nenhum software semelhante ao Hector usa placas gráficas para realizar o processamento de dados. Esta dissertação é, portanto, a primeira tentativa a ir nesse sentido

Performability modelling of homogenous and heterogeneous multiserver systems with breakdowns and repairs

This thesis presents analytical modelling of homogeneous multi-server systems with reconfiguration and rebooting delays, heterogeneous multi-server systems with one main and several identical servers, and farm paradigm multi-server systems. This thesis also includes a number of other research works such as, fast performability evaluation models of open networks of nodes with repairs and finite queuing capacities, multi-server systems with deferred repairs, and two stage tandem networks with failures, repairs and multiple servers at the second stage. Applications of these for the popular Beowulf cluster systems and memory servers are also accomplished. Existing techniques used in performance evaluation of multi-server systems are investigated and analysed in detail. Pure performance modelling techniques, pure availability models, and performability models are also considered. First, the existing approaches for pure performance modelling are critically analysed with the discussions on merits and demerits. Then relevant terminology is defined and explained. Since the pure performance models tend to be too optimistic and pure availability models are too conservative, performability models are used for the evaluation of multi-server systems. Fault-tolerant multi-server systems can continue service in case of certain failures. If failure does not occur at a critical point (such as breakdown of the head processor of a farm paradigm system) the system continues serving in a degraded mode of operation. In such systems, reconfiguration and/or rebooting delays are expected while a processor is being mapped out from the system. These delay stages are also taken into account in addition to failures and repairs, in the exact performability models that are developed. Two dimensional Markov state space representations of the systems are used for performability modelling. Following the critical analysis of the existing solution techniques, the Spectral Expansion method is chosen for the solution of the models developed. In this work, open queuing networks are also considered. To evaluate their performability, existing modelling approaches are expanded and validated by simulations, for performability analysis of multistage open networks with finite queuing capacities. The performances of two extended modelling approaches are compared in terms of accuracy for open networks with various queuing capacities. Deferred repair strategies are becoming popular because of the cost reductions they can provide. Effects of using deferred repairs are analysed and performability models are provided for homogeneous multi-server systems and highly available farm paradigm multi-server systems. Since one of the random variables is used to represent the number of jobs in one of the queues, analytical models for performance evaluation of two stage tandem networks suffer because of numerical cumbersomeness. Existing approaches for modelling these systems are actually pure performance models since breakdowns and repairs cannot be considered. One way of modelling these systems can be to divide one of the random variables to present both the operative and non-operative states of the server in one dimension. However, this will give rise to state explosion problem severely limiting the maximum queue capacity that can be handled. In order to overcome this problem a new approach is presented for modelling two stage tandem networks in three dimensions. An approximate solution is presented to solve such a system. This approach manifests itself as a novel contribution for alleviating the state space explosion problem for large and/or complex systems. When two state tandem networks with feedback are modelled using this approach, the operative states can be handled independently and this makes it possible to consider multiple operative states at the second stage. The analytical models presented can be used with various parameters and they are extendible to consider systems with similar architectures. The developed three dimensional approach is capable to handle two stage tandem networks with various characteristics for performability measures. All the approaches presented give accurate results. Numerical solutions are presented for all models developed. In case the solution presented is not exact, simulations are performed to validate the accuracy of the results obtained

Perturbation Analysis of a Variable M/M/1 Queue: A Probabilistic Approach

Motivated by the problem of the coexistence on transmission links of telecommunication networks of elastic and unresponsive traffic, we study in this paper the impact on the busy period of an M/M/1 queue of a small perturbation in the server rate. The perturbation depends upon an independent stationary process (X(t)) and is quantified by means of a parameter \eps \ll 1. We specifically compute the two first terms of the power series expansion in \eps of the mean value of the busy period duration. This allows us to study the validity of the Reduced Service Rate (RSR) approximation, which consists in comparing the perturbed M/M/1 queue with the M/M/1 queue where the service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process (X(t)) play a key role