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

A formalism for describing and simulating systems with interacting components.

This thesis addresses the problem of descriptive complexity presented by systems involving a high number of interacting components. It investigates the evaluation measure of performability and its application to such systems. A new description and simulation language, ICE and it's application to performability modelling is presented. ICE (Interacting ComponEnts) is based upon an earlier description language which was first proposed for defining reliability problems. ICE is declarative in style and has a limited number of keywords. The ethos in the development of the language has been to provide an intuitive formalism with a powerful descriptive space. The full syntax of the language is presented with discussion as to its philosophy. The implementation of a discrete event simulator using an ICE interface is described, with use being made of examples to illustrate the functionality of the code and the semantics of the language. Random numbers are used to provide the required stochastic behaviour within the simulator. The behaviour of an industry standard generator within the simulator and different methods of number allocation are shown. A new generator is proposed that is a development of a fast hardware shift register generator and is demonstrated to possess good statistical properties and operational speed. For the purpose of providing a rigorous description of the language and clarification of its semantics, a computational model is developed using the formalism of extended coloured Petri nets. This model also gives an indication of the language's descriptive power relative to that of a recognised and well developed technique. Some recognised temporal and structural problems of system event modelling are identified. and ICE solutions given. The growing research area of ATM communication networks is introduced and a sophisticated top down model of an ATM switch presented. This model is simulated and interesting results are given. A generic ICE framework for performability modelling is developed and demonstrated. This is considered as a positive contribution to the general field of performability research

Methodologies synthesis

This deliverable deals with the modelling and analysis of interdependencies between critical infrastructures, focussing attention on two interdependent infrastructures studied in the context of CRUTIAL: the electric power infrastructure and the information infrastructures supporting management, control and maintenance functionality. The main objectives are: 1) investigate the main challenges to be addressed for the analysis and modelling of interdependencies, 2) review the modelling methodologies and tools that can be used to address these challenges and support the evaluation of the impact of interdependencies on the dependability and resilience of the service delivered to the users, and 3) present the preliminary directions investigated so far by the CRUTIAL consortium for describing and modelling interdependencies

Software Performance Engineering for Cloud Applications – A Survey

Cloud computing enables application service providers to lease their computing capabilities for deploying applications depending on user QoS (Quality of Service) requirements.Cloud applications have different composition, configuration and deployment requirements.Quantifying the performance of applications in Cloud computing environments is a challenging task. Software performance engineering(SPE) techniques enable us to assess performance requirements of software applications at the early stages of development. This assessment helps the developers to fine tune their design needs so that the targeted performance goals can be met. In this paper, we try to analyseperformance related issues of cloud applications and identify any SPE techniques currently available for cloud applications

Stochastic scheduling and workload allocation : QoS support and profitable brokering in computing grids

Abstract: The Grid can be seen as a collection of services each of which performs some functionality. Users of the Grid seek to use combinations of these services to perform the overall task they need to achieve. In general this can be seen as aset of services with a workflow document describing how these services should be combined. The user may also have certain constraints on the workflow operations, such as execution time or cost ----t~ th~ user, specified in the form of a Quality of Service (QoS) document. The users . submit their workflow to a brokering service along with the QoS document. The brokering service's task is to map any given workflow to a subset of the Grid services taking the QoS and state of the Grid into account -- service availability and performance. We propose an approach for generating constraint equations describing the workflow, the QoS requirements and the state of the Grid. This set of equations may be solved using Mixed-Integer Linear Programming (MILP), which is the traditional method. We further develop a novel 2-stage stochastic MILP which is capable of dealing with the volatile nature of the Grid and adapting the selection of the services during the lifetime of the workflow. We present experimental results comparing our approaches, showing that the . 2-stage stochastic programming approach performs consistently better than other traditional approaches. Next we addresses workload allocation techniques for Grid workflows in a multi-cluster Grid We model individual clusters as MIMIk. queues and obtain a numerical solutio~ for missed deadlines (failures) of tasks of Grid workflows. We also present an efficient algorithm for obtaining workload allocations of clusters. Next we model individual cluster resources as G/G/l queues and solve an optimisation problem that minimises QoS requirement violation, provides QoS guarantee and outperforms reservation based scheduling algorithms. Both approaches are evaluated through an experimental simulation and the results confirm that the proposed workload allocation strategies combined with traditional scheduling algorithms performs considerably better in terms of satisfying QoS requirements of Grid workflows than scheduling algorithms that don't employ such workload allocation techniques. Next we develop a novel method for Grid brokers that aims at maximising profit whilst satisfying end-user needs with a sufficient guarantee in a volatile utility Grid. We develop a develop a 2-stage stochastic MILP which is capable of dealing with the volatile nature . of the Grid and obtaining cost bounds that ensure that end-user cost is minimised or satisfied and broker's profit is maximised with sufficient guarantee. These bounds help brokers know beforehand whether the budget limits of end-users can be satisfied and. if not then???????? obtain appropriate future leases from service providers. Experimental results confirm the efficacy of our approach.Imperial Users onl

Modelling and performability evaluation of Wireless Sensor Networks

This thesis presents generic analytical models of homogeneous clustered Wireless Sensor Networks (WSNs) with a centrally located Cluster Head (CH) coordinating cluster communication with the sink directly or through other intermediate nodes. The focus is to integrate performance and availability studies of WSNs in the presence of sensor nodes and channel failures and repair/replacement. The main purpose is to enhance improvement of WSN Quality of Service (QoS). Other research works also considered in this thesis include modelling of packet arrival distribution at the CH and intermediate nodes, and modelling of energy consumption at the sensor nodes. An investigation and critical analysis of wireless sensor network architectures, energy conservation techniques and QoS requirements are performed in order to improve performance and availability of the network. Existing techniques used for performance evaluation of single and multi-server systems with several operative states are investigated and analysed in details. To begin with, existing approaches for independent (pure) performance modelling are critically analysed with highlights on merits and drawbacks. Similarly, pure availability modelling approaches are also analysed. Considering that pure performance models tend to be too optimistic and pure availability models are too conservative, performability, which is the integration of performance and availability studies is used for the evaluation of the WSN models developed in this study. Two-dimensional Markov state space representations of the systems are used for performability modelling. Following critical analysis of the existing solution techniques, spectral expansion method and system of simultaneous linear equations are developed and used to solving the proposed models. To validate the results obtained with the two techniques, a discrete event simulation tool is explored. In this research, open queuing networks are used to model the behaviour of the CH when subjected to streams of traffic from cluster nodes in addition to dynamics of operating in the various states. The research begins with a model of a CH with an infinite queue capacity subject to failures and repair/replacement. The model is developed progressively to consider bounded queue capacity systems, channel failures and sleep scheduling mechanisms for performability evaluation of WSNs. Using the developed models, various performance measures of the considered system including mean queue length, throughput, response time and blocking probability are evaluated. Finally, energy models considering mean power consumption in each of the possible operative states is developed. The resulting models are in turn employed for the evaluation of energy saving for the proposed case study model. Numerical solutions and discussions are presented for all the queuing models developed. Simulation is also performed in order to validate the accuracy of the results obtained. In order to address issues of performance and availability of WSNs, current research present independent performance and availability studies. The concerns resulting from such studies have therefore remained unresolved over the years hence persistence poor system performance. The novelty of this research is a proposed integrated performance and availability modelling approach for WSNs meant to address challenges of independent studies. In addition, a novel methodology for modelling and evaluation of power consumption is also offered. Proposed model results provide remarkable improvement on system performance and availability in addition to providing tools for further optimisation studies. A significant power saving is also observed from the proposed model results. In order to improve QoS for WSN, it is possible to improve the proposed models by incorporating priority queuing in a mixed traffic environment. A model of multi-server system is also appropriate for addressing traffic routing. It is also possible to extend the proposed energy model to consider other sleep scheduling mechanisms other than On-demand proposed herein. Analysis and classification of possible arrival distribution of WSN packets for various application environments would be a great idea for enabling robust scientific research

Specification and Verification of Systems Using Model Checking and Markov Reward Models

The importance of service level management has come to the fore in recent years as computing power becomes more and more of a commodity. In order to present a consistently high quality of service systems must be rigorously analysed, even before implementation, and monitored to ensure these goals can be achieved. The tools and algorithms found in performability analysis offer a potentially ideal method to formally specify and analyse performance and reliability models. This thesis examines Markov reward models, a formalism based on continuous time Markov chains, and it's usage in the generation and analysis of service levels. The particular solution technique we employ in this thesis is model checking, using Continuous Reward Logic as a means to specify requirement and constraints on the model. We survey the current tools available allowing model checking to be performed on Markov reward models. Specifically we extended the Erlangen-Twente Markov Chain Checker to be able to solve Markov reward models by taking advantage of the Duality theorem of Continuous Stochastic Reward Logic, of which Continuous Reward Logic is a sub-logic. We are also concerned with the specification techniques available for Markov reward models, which have in the past merely been extensions to the available specification techniques for continuous time Markov chains. We implement a production rule system using Ruby, a high level language, and show the advantages gained by using it's native interpreter and language features in order to cut down on implementation time and code size. The limitations inherent in Markov reward models are discussed and we focus on the issue of zero reward states. Previous algorithms used to remove zero reward states, while preserving the numerical properties of the model, could potentially alter it's logical properties. We propose algorithms based on analysing the continuous reward logic requirement beforehand to determine whether a zero reward state can be removed safely as well as an approach based on substitution of zero reward states. We also investigate limitations on multiple reward structures and the ability to solve for both time and reward. Finally we perform a case study on a Beowulf parallel computing cluster using Markov reward models and the ETMCC tool, demonstrating their usefulness in the implementation of performability analysis and the determination of the service levels that can be offered by the cluster to it's users

Transient Reward Approximation for Continuous-Time Markov Chains

We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit

3D analytical modelling and iterative solution for high performance computing clusters

Mobile Cloud Computing enables the migration of services to the edge of the Internet. Therefore, high-performance computing clusters are widely deployed to improve computational capabilities of such environments. However, they are prone to failures and need analytical models to predict their behaviour in order to deliver desired quality-of-service and quality-of-experience to mobile users. This paper proposes a 3D analytical model and a problem-solving approach for sustainability evaluation of high-performance computing clusters. The proposed solution uses an iterative approach to obtain performance measurements to overcome the state space explosion problem. The availability modelling and evaluation of master and computing nodes are performed using a multi-repairman approach. The optimum number of repairmen is also obtained to get realistic results and reduce the overall cost. The proposed model is validated using discrete event simulation. The analytical approach is much faster and in good agreement with the simulations. The analysis focuses on mean queue length, throughput, and mean response time outputs. The maximum differences between analytical and simulation results in the considered scenarios of up to a billion states are less than1.149%,3.82%, and3.76%respectively. These differences are well within the5%of confidence interval of the simulation and the proposed model