A Game-theoretic Formulation of the Homogeneous Self-Reconfiguration Problem

In this paper we formulate the homogeneous two- and three-dimensional self-reconfiguration problem over discrete grids as a constrained potential game. We develop a game-theoretic learning algorithm based on the Metropolis-Hastings algorithm that solves the self-reconfiguration problem in a globally optimal fashion. Both a centralized and a fully distributed algorithm are presented and we show that the only stochastically stable state is the potential function maximizer, i.e. the desired target configuration. These algorithms compute transition probabilities in such a way that even though each agent acts in a self-interested way, the overall collective goal of self-reconfiguration is achieved. Simulation results confirm the feasibility of our approach and show convergence to desired target configurations.Comment: 8 pages, 5 figures, 2 algorithm

Coalition Formation and Combinatorial Auctions; Applications to Self-organization and Self-management in Utility Computing

In this paper we propose a two-stage protocol for resource management in a hierarchically organized cloud. The first stage exploits spatial locality for the formation of coalitions of supply agents; the second stage, a combinatorial auction, is based on a modified proxy-based clock algorithm and has two phases, a clock phase and a proxy phase. The clock phase supports price discovery; in the second phase a proxy conducts multiple rounds of a combinatorial auction for the package of services requested by each client. The protocol strikes a balance between low-cost services for cloud clients and a decent profit for the service providers. We also report the results of an empirical investigation of the combinatorial auction stage of the protocol.Comment: 14 page

A Game-Theoretic Approach for Elastic Distributed Data Stream Processing

Distributed data stream processing applications are structured as graphs of interconnected modules able to ingest high-speed data and to transform them in order to generate results of interest. Elasticity is one of the most appealing features of stream processing applications. It makes it possible to scale up/down the allocated computing resources on demand in response to fluctuations of the workload. On clouds, this represents a necessary feature to keep the operating cost at affordable levels while accommodating user-defined QoS requirements. In this article, we study this problem from a game-theoretic perspective. The control logic driving elasticity is distributed among local control agents capable of choosing the right amount of resources to use by each module. In a first step, we model the problem as a noncooperative game in which agents pursue their self-interest. We identify the Nash equilibria and we design a distributed procedure to reach the best equilibrium in the Pareto sense. As a second step, we extend the noncooperative formulation with a decentralized incentive-based mechanism in order to promote cooperation by moving the agreement point closer to the system optimum. Simulations confirm the results of our theoretical analysis and the quality of our strategies

Control of Vehicle Platoons with Collision Avoidance Using Noncooperative Differential Games

This paper considers a differential game approach to the predecessor-following vehicle platoon control problem without and with collision avoidance. In this approach, each vehicle tries to minimize the performance index (PI) of its control objective, which is reaching consensual velocity with the predecessor vehicle while maintaining a small inter-vehicle distance from it. Two differential games were formulated. The differential game problem for platoon control without collision avoidance is solved for the open-loop Nash equilibrium and its associated state trajectories. The second differential game problem for platoon control with collision avoidance has a non-quadratic PI, which poses a greater challenge to obtaining its open-loop Nash equilibrium. Since the exact solution is unavailable, we propose an estimated Nash strategy approach that is greatly simplified for implementation. An illustrative example of a vehicle platoon control problem was solved under both the without and with collision avoidance scenarios. The results showed the effectiveness of the models and their solutions for both scenarios.Comment: This paper was presented at IEEE ITSC 202

Algorithms for Modular Self-reconfigurable Robots: Decision Making, Planning, and Learning

Modular self-reconfigurable robots (MSRs) are composed of multiple robotic modules which can change their connections with each other to take different shapes, commonly known as configurations. Forming different configurations helps the MSR to accomplish different types of tasks in different environments. In this dissertation, we study three different problems in MSRs: partitioning of modules, configuration formation planning and locomotion learning, and we propose algorithmic solutions to solve these problems. Partitioning of modules is a decision-making problem for MSRs where each module decides which partition or team of modules it should be in. To find the best set of partitions is a NP-complete problem. We propose game theory based both centralized and distributed solutions to solve this problem. Once the modules know which set of modules they should team-up with, they self-aggregate to form a specific shaped configuration, known as the configuration formation planning problem. Modules can be either singletons or connected in smaller configurations from which they need to form the target configuration. The configuration formation problem is difficult as multiple modules may select the same location in the target configuration to move to which might result in occlusion and consequently failure of the configuration formation process. On the other hand, if the modules are already in connected configurations in the beginning, then it would be beneficial to preserve those initial configurations for placing them into the target configuration as disconnections and re-connections are costly operations. We propose solutions based on an auction-like algorithm and (sub) graph-isomorphism technique to solve the configuration formation problem. Once the configuration is built, the MSR needs to move towards its goal location as a whole configuration for completing its task. If the configuration’s shape and size is not known a priori, then planning its locomotion is a difficult task as it needs to learn the locomotion pattern in dynamic time – the problem is known as adaptive locomotion learning. We have proposed reinforcement learning based fault-tolerant solutions for locomotion learning by MSRs

A Control-Theoretic Methodology for Adaptive Structured Parallel Computations

Adaptivity for distributed parallel applications is an essential feature whose impor- tance has been assessed in many research fields (e.g. scientific computations, large- scale real-time simulation systems and emergency management applications). Especially for high-performance computing, this feature is of special interest in order to properly and promptly respond to time-varying QoS requirements, to react to uncontrollable environ- mental effects influencing the underlying execution platform and to efficiently deal with highly irregular parallel problems. In this scenario the Structured Parallel Programming paradigm is a cornerstone for expressing adaptive parallel programs: the high-degree of composability of parallelization schemes, their QoS predictability formally expressed by performance models, are basic tools in order to introduce dynamic reconfiguration processes of adaptive applications. These reconfigurations are not only limited to imple- mentation aspects (e.g. parallelism degree modifications), but also parallel versions with different structures can be expressed for the same computation, featuring different levels of performance, memory utilization, energy consumption, and exploitation of the memory hierarchies. Over the last decade several programming models and research frameworks have been developed aimed at the definition of tools and strategies for expressing adaptive parallel applications. Notwithstanding this notable research effort, properties like the optimal- ity of the application execution and the stability of control decisions are not sufficiently studied in the existing work. For this reason this thesis exploits a pioneer research in the context of providing formal theoretical tools founded on Control Theory and Game Theory techniques. Based on these approaches, we introduce a formal model for control- ling distributed parallel applications represented by computational graphs of structured parallelism schemes (also called skeleton-based parallelism). Starting out from the performance predictability of structured parallelism schemes, in this thesis we provide a formalization of the concept of adaptive parallel module per- forming structured parallel computations. The module behavior is described in terms of a Hybrid System abstraction and reconfigurations are driven by a Predictive Control ap- proach. Experimental results show the effectiveness of this work, in terms of execution cost reduction as well as the stability degree of a system reconfiguration: i.e. how long a reconfiguration choice is useful for targeting the required QoS levels. This thesis also faces with the issue of controlling large-scale distributed applications composed of several interacting adaptive components. After a panoramic view of the existing control-theoretic approaches (e.g. based on decentralized, distributed or hierar- chical structures of controllers), we introduce a methodology for the distributed predictive control. For controlling computational graphs, the overall control problem consists in a set of coupled control sub-problems for each application module. The decomposition is- sue has a twofold nature: first of all we need to model the coupling relationships between control sub-problems, furthermore we need to introduce proper notions of negotiation and convergence in the control decisions collectively taken by the parallel modules of the application graph. This thesis provides a formalization through basic concepts of Non-cooperative Games and Cooperative Optimization. In the notable context of the dis- tributed control of performance and resource utilization, we exploit a formal description of the control problem providing results for equilibrium point existence and the compari- son of the control optimality with different adaptation strategies and interaction protocols. Discussions and a first validation of the proposed techniques are exploited through exper- iments performed in a simulation environment