Distributed nonlinear optimization algorithms for general network problems

There are a number of large networks which occur in many problems dealing with the flow of power, communication signals, water, gas, transportable goods, etc. Both design and planning of these networks involve optimization problems. The first part of this paper introduces the common characteristics of a nonlinear network (the network may be linear, the objective function may be non linear, or both may be nonlinear). The second part develops a mathematical model trying to put together some important constraints based on the abstraction for a general network. The third part deals with solution procedures; it converts the network to a matrix based system of equations, gives the characteristics of the matrix and suggests two solution procedures, one of them being a new one. The fourth part handles spatially distributed networks and evolves a number of decomposition techniques so that we can solve the problem with the help of a distributed computer system. Algorithms for parallel processors and spatially distributed systems have been described.There are a number of common features that pertain to networks. A network consists of a set of nodes and arcs. In addition at every node, there is a possibility of an input (like power, water, message, goods etc) or an output or none. Normally, the network equations describe the flows amoungst nodes through the arcs. These network equations couple variables associated with nodes. Invariably, variables pertaining to arcs are constants; the result required will be flows through the arcs. To solve the normal base problem, we are given input flows at nodes, output flows at nodes and certain physical constraints on other variables at nodes and we should find out the flows through the network (variables at nodes will be referred to as across variables).The optimization problem involves in selecting inputs at nodes so as to optimise an objective function; the objective may be a cost function based on the inputs to be minimised or a loss function or an efficiency function. The above mathematical model can be solved using Lagrange Multiplier technique since the equalities are strong compared to inequalities. The Lagrange multiplier technique divides the solution procedure into two stages per iteration. Stage one calculates the problem variables % and stage two the multipliers lambda. It is shown that the Jacobian matrix used in stage one (for solving a nonlinear system of necessary conditions) occurs in the stage two also.A second solution procedure has also been imbedded into the first one. This is called total residue approach. It changes the equality constraints so that we can get faster convergence of the iterations.Both solution procedures are found to coverge in 3 to 7 iterations for a sample network.The availability of distributed computer systems — both LAN and WAN — suggest the need for algorithms to solve the optimization problems. Two types of algorithms have been proposed — one based on the physics of the network and the other on the property of the Jacobian matrix. Three algorithms have been deviced, one of them for the local area case. These algorithms are called as regional distributed algorithm, hierarchical regional distributed algorithm (both using the physics properties of the network), and locally distributed algorithm (a multiprocessor based approach with a local area network configuration). The approach used was to define an algorithm that is faster and uses minimum communications. These algorithms are found to converge at the same rate as the non distributed (unitary) case.

Exact bounds for distributed graph colouring

A distributed system is a collection of networked autonomous processing units which must work in a cooperative manner. Currently, large-scale distributed systems, such as various telecommunication and computer networks, are abundant and used in a multitude of tasks. The field of distributed computing studies what can be computed efficiently in such systems. Distributed systems are usually modelled as graphs where nodes represent the processors and edges denote communication links between processors. This thesis concentrates on the computational complexity of the distributed graph colouring problem. The objective of the graph colouring problem is to assign a colour to each node in such a way that no two nodes connected by an edge share the same colour. In particular, it is often desirable to use only a small number of colours. This task is a fundamental symmetry-breaking primitive in various distributed algorithms. A graph that has been coloured in this manner using at most k different colours is said to be k-coloured. This work examines the synchronous message-passing model of distributed computation: every node runs the same algorithm, and the system operates in discrete synchronous communication rounds. During each round, a node can communicate with its neighbours and perform local computation. In this model, the time complexity of a problem is the number of synchronous communication rounds required to solve the problem. It is known that 3-colouring any k-coloured directed cycle requires at least ½(log* k - 3) communication rounds and is possible in ½(log* k + 7) communication rounds for all k ≥ 3. This work shows that for any k ≥ 3, colouring a k-coloured directed cycle with at most three colours is possible in ½(log* k + 3) rounds. In contrast, it is also shown that for some values of k, colouring a directed cycle with at most three colours requires at least ½(log* k + 1) communication rounds. Furthermore, in the case of directed rooted trees, reducing a k-colouring into a 3-colouring requires at least log* k + 1 rounds for some k and possible in log* k + 3 rounds for all k ≥ 3. The new positive and negative results are derived using computational methods, as the existence of distributed colouring algorithms corresponds to the colourability of so-called neighbourhood graphs. The colourability of these graphs is analysed using Boolean satisfiability (SAT) solvers. Finally, this thesis shows that similar methods are applicable in capturing the existence of distributed algorithms for other graph problems, such as the maximal matching problem.

Generating synchronizable test sequences based on finite-statemachine with distributed ports

In the area of testing communication systems, the interfaces between systems to be tested and their testers have great impact on test generation and fault detectability. Several types of such interfaces have been standardized by the International Standardization Organization (ISO). A general distributed test architecture, containing distributed interfaces, has been presented in the literature for testing distributed systems based on the Open Distributing Processing (ODP) Basic Reference Model (BRM), which is a generalized version of ISO distributed test architecture. We study in this paper the issue of test selection with respect to such an test architecture. In particular, we consider communication systems that can be modeled by finite state machines with several distributed interfaces, called ports. A test generation method is developed for generating test sequences for such finite state machines, which is based on the idea of synchronizable test sequences. Starting from the initial effort by Sarikaya, a certain amount of work has been done for generating test sequences for finite state machines with respect to the ISO distributed test architecture, all based on the idea of modifying existing test generation methods to generate synchronizable test sequences. However, none studies the fault coverage provided by their methods. We investigate the issue of fault coverage and point out a fact that the methods given in the literature for the distributed test architecture cannot ensure the same fault coverage as the corresponding original testing methods. We also study the limitation of fault detectability in the distributed test architecture.

Access Control in Communication Systems

Access control is an important component in the security of communication systems. While cryptography has rightfully been a significant component in the design of large scale communication systems, its relation to access control, especially its complementarity, has not often been brought out in full. With the wide availability of SELinux, a comprehensive model of access control has all the more become important. In many large scale systems, access control and trust management have become important components in the design. In survivable systems, models of group communication systems may have to be integrated with access control models. In this paper, we discuss the problem of integrating various formalisms often encountered in large scale communication systems, especially in connection with dynamic access control policies as well as trust management

Failure detectors and communication efficiency in the crash and general omisión failure models

122 p.

Zmienne graficzne sygnatur punktowych w mobilnym systemie rozszerzonej rzeczywistości

Wydział Nauk Geograficznych i Geologicznych

Priority-Based Synchronization of Distributed Data

We consider the general problem of synchronizing the data on two devices using a minimum amount of communication, a core infrastructural requirement for a large variety of distributed systems. Our approach considers the interactive synchronization of prioritized data, where, for example, certain information is more time-sensitive than other information. We propose and analyze a new scheme for efficient priority-based synchronization, which promises benefits over conventional synchronization.

Load Profiling in Distributed Real-Time Systems

Load balancing is often used to ensure that nodes in a distributed systems are equally loaded. In this paper, we show that for real-time systems, load balancing is not desirable. In particular, we propose a new load-profiling strategy that allows the nodes of a distributed system to be unequally loaded. Using load profiling, the system attempts to distribute the load amongst its nodes so as to maximize the chances of finding a node that would satisfy the computational needs of incoming real-time tasks. To that end, we describe and evaluate a distributed load-profiling protocol for dynamically scheduling time-constrained tasks in a loosely-coupled distributed environment. When a task is submitted to a node, the scheduling software tries to schedule the task locally so as to meet its deadline. If that is not feasible, it tries to locate another node where this could be done with a high probability of success, while attempting to maintain an overall load profile for the system. Nodes in the system inform each other about their state using a combination of multicasting and gossiping. The performance of the proposed protocol is evaluated via simulation, and is contrasted to other dynamic scheduling protocols for real-time distributed systems. Based on our findings, we argue that keeping a diverse availability profile and using passive bidding (through gossiping) are both advantageous to distributed scheduling for real-time systems.

Service Provisioning in Mobile Networks Through Distributed Coordinated Resource Management

The pervasiveness of personal computing platforms offers an unprecedented opportunity to deploy large-scale services that are distributed over wide physical spaces. Two major challenges face the deployment of such services: the often resource-limited nature of these platforms, and the necessity of preserving the autonomy of the owner of these devices. These challenges preclude using centralized control and preclude considering services that are subject to performance guarantees. To that end, this thesis advances a number of new distributed resource management techniques that are shown to be effective in such settings, focusing on two application domains: distributed Field Monitoring Applications (FMAs), and Message Delivery Applications (MDAs). In the context of FMA, this thesis presents two techniques that are well-suited to the fairly limited storage and power resources of autonomously mobile sensor nodes. The first technique relies on amorphous placement of sensory data through the use of novel storage management and sample diffusion techniques. The second approach relies on an information-theoretic framework to optimize local resource management decisions. Both approaches are proactive in that they aim to provide nodes with a view of the monitored field that reflects the characteristics of queries over that field, enabling them to handle more queries locally, and thus reduce communication overheads. Then, this thesis recognizes node mobility as a resource to be leveraged, and in that respect proposes novel mobility coordination techniques for FMAs and MDAs. Assuming that node mobility is governed by a spatio-temporal schedule featuring some slack, this thesis presents novel algorithms of various computational complexities to orchestrate the use of this slack to improve the performance of supported applications. The findings in this thesis, which are supported by analysis and extensive simulations, highlight the importance of two general design principles for distributed systems. First, a-priori knowledge (e.g., about the target phenomena of FMAs and/or the workload of either FMAs or DMAs) could be used effectively for local resource management. Second, judicious leverage and coordination of node mobility could lead to significant performance gains for distributed applications deployed over resource-impoverished infrastructures.

Collocation Games and Their Application to Distributed Resource Management

We introduce Collocation Games as the basis of a general framework for modeling, analyzing, and facilitating the interactions between the various stakeholders in distributed systems in general, and in cloud computing environments in particular. Cloud computing enables fixed-capacity (processing, communication, and storage) resources to be offered by infrastructure providers as commodities for sale at a fixed cost in an open marketplace to independent, rational parties (players) interested in setting up their own applications over the Internet. Virtualization technologies enable the partitioning of such fixed-capacity resources so as to allow each player to dynamically acquire appropriate fractions of the resources for unencumbered use. In such a paradigm, the resource management problem reduces to that of partitioning the entire set of applications (players) into subsets, each of which is assigned to fixed-capacity cloud resources. If the infrastructure and the various applications are under a single administrative domain, this partitioning reduces to an optimization problem whose objective is to minimize the overall deployment cost. In a marketplace, in which the infrastructure provider is interested in maximizing its own profit, and in which each player is interested in minimizing its own cost, it should be evident that a global optimization is precisely the wrong framework. Rather, in this paper we use a game-theoretic framework in which the assignment of players to fixed-capacity resources is the outcome of a strategic "Collocation Game". Although we show that determining the existence of an equilibrium for collocation games in general is NP-hard, we present a number of simplified, practically-motivated variants of the collocation game for which we establish convergence to a Nash Equilibrium, and for which we derive convergence and price of anarchy bounds. In addition to these analytical results, we present an experimental evaluation of implementations of some of these variants for cloud infrastructures consisting of a collection of multidimensional resources of homogeneous or heterogeneous capacities. Experimental results using trace-driven simulations and synthetically generated datasets corroborate our analytical results and also illustrate how collocation games offer a feasible distributed resource management alternative for autonomic/self-organizing systems, in which the adoption of a global optimization approach (centralized or distributed) would be neither practical nor justifiable.

Emergence: a paradigm for robust and scalable distributed applications

Natural distributed systems are adaptive, scalable and fault-tolerant. Emergence science describes how higher-level self-regulatory behaviour arises in natural systems from many participants following simple rulesets. Emergence advocates simple communication models, autonomy and independence, enhancing robustness and self-stabilization. High-quality distributed applications such as autonomic systems must satisfy the appropriate nonfunctional requirements which include scalability, efficiency, robustness, low-latency and stability. However the traditional design of distributed applications, especially in terms of the communication strategies employed, can introduce compromises between these characteristics. This paper discusses ways in which emergence science can be applied to distributed computing, avoiding some of the compromises associated with traditionally-designed applications. To demonstrate the effectiveness of this paradigm, an emergent election algorithm is described and its performance evaluated. The design incorporates nondeterministic behaviour. The resulting algorithm has very low communication complexity, and is simultaneously very stable, scalable and robust.

Architecture for real-time coordination of multiple autonomous mobile units

Interest on using teams of mobile robots has been growing, due to their potential to cooperate for diverse purposes, such as rescue, de-mining, surveillance or even games such as robotic soccer. These applications require a real-time middleware and wireless communication protocol that can support an efficient and timely fusion of the perception data from different robots as well as the development of coordinated behaviours. Coordinating several autonomous robots towards achieving a common goal is currently a topic of high interest, which can be found in many application domains. Despite these different application domains, the technical problem of building an infrastructure to support the integration of the distributed perception and subsequent coordinated action is similar. This problem becomes tougher with stronger system dynamics, e.g., when the robots move faster or interact with fast objects, leading to tighter real-time constraints. This thesis work addressed computing architectures and wireless communication protocols to support efficient information sharing and coordination strategies taking into account the real-time nature of robot activities. The thesis makes two main claims. Firstly, we claim that despite the use of a wireless communication protocol that includes arbitration mechanisms, the self-organization of the team communications in a dynamic round that also accounts for variable team membership, effectively reduces collisions within the team, independently of its current composition, significantly improving the quality of the communications. We will validate this claim in terms of packet losses and communication latency. We show how such self-organization of the communications can be achieved in an efficient way with the Reconfigurable and Adaptive TDMA protocol. Secondly, we claim that the development of distributed perception, cooperation and coordinated action for teams of mobile robots can be simplified by using a shared memory middleware that replicates in each cooperating robot all necessary remote data, the Real-Time Database (RTDB) middleware. These remote data copies, which are updated in the background by the selforganizing communications protocol, are extended with age information automatically computed by the middleware and are locally accessible through fast primitives. We validate our claim showing a parsimonious use of the communication medium, improved timing information with respect to the shared data and the simplicity of use and effectiveness of the proposed middleware shown in several use cases, reinforced with a reasonable impact in the Middle Size League of RoboCup.

Evolving Distributed Algorithms with Genetic Programming

Distributed systems are one of the most vital components of the economy. The most prominent example is probably the internet, a constituent element of our knowledge society. During the recent years, the number of novel network types has steadily increased. Amongst others, sensor networks, distributed systems composed of tiny computational devices with scarce resources, have emerged. The further development and heterogeneous connection of such systems imposes new requirements on the software development process. Mobile and wireless networks, for instance, have to organize themselves autonomously and must be able to react to changes in the environment and to failing nodes alike. Researching new approaches for the design of distributed algorithms may lead to methods with which these requirements can be met efficiently. In this thesis, one such method is developed, tested, and discussed in respect of its practical utility. Our new design approach for distributed algorithms is based on Genetic Programming, a member of the family of evolutionary algorithms. Evolutionary algorithms are metaheuristic optimization methods which copy principles from natural evolution. They use a population of solution candidates which they try to refine step by step in order to attain optimal values for predefined objective functions. The synthesis of an algorithm with our approach starts with an analysis step in which the wanted global behavior of the distributed system is specified. From this specification, objective functions are derived which steer a Genetic Programming process where the solution candidates are distributed programs. The objective functions rate how close these programs approximate the goal behavior in multiple randomized network simulations. The evolutionary process step by step selects the most promising solution candidates and modifies and combines them with mutation and crossover operators. This way, a description of the global behavior of a distributed system is translated automatically to programs which, if executed locally on the nodes of the system, exhibit this behavior. In our work, we test six different ways for representing distributed programs, comprising adaptations and extensions of well-known Genetic Programming methods (SGP, eSGP, and LGP), one bio-inspired approach (Fraglets), and two new program representations called Rule-based Genetic Programming (RBGP, eRBGP) designed by us. We breed programs in these representations for three well-known example problems in distributed systems: election algorithms, the distributed mutual exclusion at a critical section, and the distributed computation of the greatest common divisor of a set of numbers. Synthesizing distributed programs the evolutionary way does not necessarily lead to the envisaged results. In a detailed analysis, we discuss the problematic features which make this form of Genetic Programming particularly hard. The two Rule-based Genetic Programming approaches have been developed especially in order to mitigate these difficulties. In our experiments, at least one of them (eRBGP) turned out to be a very efficient approach and in most cases, was superior to the other representations.