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Publication# Effect of replica placement on the reliability of large scale data storage systems

Résumé

Replication is a widely used method to protect large- scale data storage systems from data loss when storage nodes fail. It is well known that the placement of replicas of the different data blocks across the nodes affects the time to rebuild. Several systems described in the literature are designed based on the premise that minimizing the rebuild times maximizes the system reliability. Our results however indicate that the reliability is essentially unaffected by the replica placement scheme. We show that, for a replication factor of two, all possible placement schemes have mean times to data loss (MTTDLs) within a factor of two for practical values of the failure rate, storage capacity, and rebuild bandwidth of a storage node. The theoretical results are confirmed by means of event-driven simulation. For higher replication factors, an analytical derivation of MTTDL becomes intractable for a general placement scheme. We therefore use one of the alternate measures of reliability that have been proposed in the literature, namely, the probability of data loss during rebuild in the critical mode of the system. Whereas for a replication factor of two this measure can be directly translated into MTTDL, it is only speculative of the MTTDL behavior for higher replication factors. This measure of reliability is shown to lie within a factor of two for all possible placement schemes and any replication factor. We also show that for any replication factor, the clustered placement scheme has the lowest probability of data loss during rebuild in critical mode among all possible placement schemes, whereas the declustered placement scheme has the highest probability. Simulation results reveal however that these properties do not hold for the corresponding MTTDLs for a replication factor greater than two. This indicates that some alternate measures of reliability may not be appropriate for comparing the MTTDL of different placement schemes.

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The development of robot motion planning algorithms is inherently a challenging task. This is more than ever true when the latest trends in motion planning are considered. Some motion planners can deal with kinematic and dynamic constraints induced by the mechanical structure of the robot. Another class of motion planners fulfill various types of optimality conditions, yet others include means of dealing with uncertainty about the robot and its environment. Sensor-based motion planners gather information typically afflicted with errors about a partially known environment in order to plan a trajectory therein. In another research area it is investigated how multiple robots best cooperate to solve a common task. In order to deal with the complexity of developing motion planning algorithms, it is proposed in this document to resort to a simulation environment. The advantages of doing so are outlined and a system named Ibex presented which is well suited to support motion planner development. The developed framework makes use of rigid body dynamics algorithms as simulation kernel. Further, various components are included which integrate the simulation into existing engineering environments. Simulation content can be conveniently developed through extensions of well-established 3D modelling tools. The co-simulation with components from other domains of physics is provided by the integration into a leading dynamic modelling environment. Robotic actuator models can be combined with a rigid body dynamics simulation using this mechanism. The same configuration also allows to conveniently develop control algorithms for a rigid body dynamics setup and offers powerful tools for handling and analysing simulation data. The developed simulation framework also offers physics-based models for simulating various sensors, most prominently a model for sensor types based on wave propagation, such as laser range finding devices. Application examples of the simulation framework are presented from the mobile robotics rough-terrain motion planning domain. Three novel rough-terrain planning algorithms are presented which are extensions of known approaches. To quantify the navigational difficulty on rough terrain, a new generic measure named "obstacleness" is proposed which forms the basis of the proposed algorithms. The first algorithm is based on Randomised Potential Field Planners (RPP) and consequently is a local algorithm. The second proposed planner extends RRTconnect , a bi-directional Rapidly Exploring Random Tree (RRT) algorithm and biases exploration of the search space towards easily traversable regions. The third planner is an extension of the second approach and uses the same heuristic to grow a series of additional local RRTs. This allows it to plan trajectories through complex distributions of navigational difficulty benefitting from easy regions throughout the motion plan. A complete example is shown in which the proposed algorithms form the basis for sensor-based dynamic re-planning simulated in the presented framework. In the scenario, a simulated planetary rover navigates a long distance over rough terrain while gathering sensor data about the terrain topography. Where obstacles are sensed which interfere with the original motion plan, dynamic re-planning routines are applied to circumnavigate the hindrances. In the course of this document a complete simulation environment is presented by means of a theoretical background and application examples which can significantly support the development of robot motion planning algorithms. The framework is capable of simulating setups which fulfil the requirements posed by stateof-the-art motion planning algorithm development.

Modern data storage systems are extremely large and consist of several tens or hundreds of nodes. In such systems, node failures are daily events, and safeguarding data from them poses a serious design challenge. The focus of this thesis is on the data reliability analysis of storage systems and, in particular, on the effect of different design choices and parameters on the system reliability. Data redundancy, in the form of replication or advanced erasure codes, is used to protect data from node failures. By storing redundant data across several nodes, the surviving redundant data on surviving nodes can be used to rebuild the data lost by the failed nodes if node failures occur. As these rebuild processes take a finite amount of time to complete, there exists a nonzero probability of additional node failures during rebuild, which eventually may lead to a situation in which some of the data have lost so much redundancy that they become irrecoverably lost from the system. The average time taken by the system to suffer an irrecoverable data loss, also known as the mean time to data loss (MTTDL), is a measure of data reliability that is commonly used to compare different redundancy schemes and to study the effect of various design parameters. The theoretical analysis of MTTDL, however, is a challenging problem for non-exponential real-world failure and rebuild time distributions and for general data placement schemes. To address this issue, a methodology for reliability analysis is developed in this thesis that is based on the probability of direct path to data loss during rebuild. The reliability analysis is detailed in the sense that it accounts for the rebuild times involved, the amounts of partially rebuilt data when additional nodes fail during rebuild, and the fact that modern systems use an intelligent rebuild process that will first rebuild the data having the least amount of redundancy left. Through rigorous arguments and simulations it is established that the methodology developed is well-suited for the reliability analysis of real-world data storage systems. Applying this methodology to data storage systems with different types of redundancy, various data placement schemes, and rebuild constraints, the effect of the design parameters on the system reliability is studied. When sufficient network bandwidth is available for rebuild processes, it is shown that spreading the redundant data corresponding to the data on each node across a higher number of other nodes and using a distributed and intelligent rebuild process will improve the system MTTDL. In particular, declustered placement, which corresponds to spreading the redundant data corresponding to each node equally across all other nodes of the system, is found to potentially have significantly higher MTTDL values than other placement schemes, especially for large storage systems. This implies that more reliable data storage systems can be designed merely by changing the data placement without compromising on the storage efficiency or performance. The effect of a limited network rebuild bandwidth on the system reliability is also analyzed, and it is shown that, for certain redundancy schemes, spreading redundant data across more number of nodes can actually have a detrimental effect on reliability. It is also shown that the MTTDL values are invariant in a large class of node failure time distributions with the same mean. This class includes the exponential distribution as well as the real-world distributions, such as Weibull or gamma. This result implies that the system MTTDL will not be affected if the failure distribution is changed to a corresponding exponential one with the same mean. This observation is also of great importance because it suggests that the MTTDL results obtained in the literature by assuming exponential node failure distributions may still be valid for real-world storage systems despite the fact that real-world failure distributions are non-exponential. In contrast, it is shown that the MTTDL is sensitive to the node rebuild time distribution. A storage system reliability simulator is built to verify the theoretical results mentioned above. The simulator is sufficiently complex to perform all required failure events and rebuild tasks in a storage system, to use real-world failure and rebuild time distributions for scheduling failures and rebuilds, to take into account partial rebuilds when additional node failures occur, and to simulate different data placement schemes and compare their reliability. The simulation results are found to match the theoretical predictions with high confidence for a wide range of system parameters, thereby validating the methodology of reliability analysis developed.

Software engineering always cares to provide solutions for building applications as close as possible to what they should be, according to the requirements and the final users needs. Systems behavior simulation is a very common application to virtually reproduce and often predict the real-world behavior. Simulation is one of the most operational research tool in a large variety of engineering and scientific domains: Transport, telecommunication, medicine, chemical processes, physics, etc. The complexity of such application is relative to the increasing complexity of the systems. In this context, it is relevant to bring together different tools and formalisms such as markovian chain, Petri nets, etc., to improve the existent approaches and so to answer the simulations performances needs. The principle objective of this thesis is to bring together techniques from software engineering and safety engineering in order to improve the state of the art of modeling and simulation of dynamic systems in the industrial context. In addressing this objective, this work initially involves defining the essential limitations of the used formalisms, methods and tools regarding from one hand the software engineering modeling and simulation techniques and from the other hand the existent risk analysis methodologies. This work is conducted with respect to the problem of danger identification, considering the context of the complex systems behavior and their interaction with the human operator. In software engineering, it is well known that Petri/high-level nets have attractive characteristics to be used in systems simulation and behavior prediction such as the natural graphical representation, and their well-defined semantic. They are well-suited for the description of complex situations with concurrency (interleaving and true concurrency depending on the underlying semantics), conflict and confusion. However, the absence of structuring capabilities has been one of the main criticisms raised against Petri nets/high-level nets. Thus, there have been many attempts to introduce structuring principles in nets of this kind [BCM88] [Kie89] [JR91]. The attractive characteristics of Petri/high-level nets have prompted researchers to enrich these formalisms with object-oriented features. CO-OPN (Concurrent Object-Oriented Petri Net) approach, brings together the power of both Petri/high-level nets and object-orientation techniques, it has been devised so as to offer an adequate framework for the specification and design of large scale concurrent system [BG91]. CO-OPN, as a powerful modeling tool, has been used in a limited way to simulate systems. This work aims to provide a CO-OPN extension to allow a more realistic systems' simulation. Actually, its simulator semantic uses to be a suitable approach for modeling near closed systems and software components, because they need to loose coupling with external world. But, when we model more realistic problems like industrial processes, where human interaction is a relevant event, this approach is not sufficient to catch all system activity attributes. Moreover, the CO-OPN interpretation process does not allow interaction with the object internal states. This work provides a new solution to overcome CO-OPN simulation limitations and a set of prototypes to assist dynamic systems simulations. Furthermore, this work has been conducted in a Risk Analysis (RA) context, a domain where computer-based simulations research are of utmost interest. Actually, classical approaches used to address complex workplace hazard in a limited way, using checklists or sequence models. Moreover, the use of single oriented methods, such as AEA (man-oriented), FMEA (machine oriented) or HAZOP (process oriented), is not satisfactory to overcome the increasing sophistication of industrial processes. The automation of a part of the analysis process as well as the multiple-oriented approach allowed by dynamic modeling may indeed enhance significantly the analysis completeness and reduce the time analyzing time. This work, based on Object Oriented Petri net formalism (CO-OPN), propose an alternative multi-oriented approach where existent methods limitations have been criticized to develop a dynamic model, MORM (Man-machine Occupational Risk Modeling). A real industrial system (metal wire making process) has been specified to implement the different approach steps (system identification, model application, system simulation, system analysis).