On the λ'-optimality of s-geodetic digraphs

For a strongly connected digraph D the restricted arc-connectivity λ'(D) is defined as the minimum cardinality of an arc-cut over all arc-cuts S satisfying that D − S has a non trivial strong component D1 such that D − V (D1) contains an arc. Let S be a subset of vertices of D. We denote by ω+(S) the set of arcs uv with u ∈ S and v ∈ S, and by ω−(S) the set of arcs uv with u ∈ S and v ∈ S. A digraph D = (V,A) is said to be λ'-optimal if λ'(D) = ξ'(D), where ξ'(D) is the minimum arc-degree of D defined as ξ(D) = min{ξ'(xy) : xy ∈ A}, and ξ'(xy) = min{|ω+({x, y})|, |ω−({x, y})|, |ω+(x)∪ω−(y)|, |ω−(x)∪ω+(y)|}. In this paper a sufficient condition for a s-geodetic strongly connected digraph D to be λ'-optimal is given in terms of its diameter.Further we see that the h-iterated line digraph Lh(D) of a s-geodetic digraph is λ'-optimal for certain iteration h.Peer Reviewe

Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010

Peer Reviewe

Journal of Telecommunications and Information Technology, 2010, nr 3

kwartalni

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Communication-constrained feedback stability and Multi-agent System consensusability in Networked Control Systems

With the advances in wireless communication, the topic of Networked Control Systems (NCSs) has become an interesting research subject. Moreover, the advantages they offer convinced companies to implement and use data networks for remote industrial control and process automation. Data networks prove to be very efficient for controlling distributed systems, which would otherwise require complex wiring connections on large or inaccessible areas. In addition, they are easier to maintain and more cost efficient. Unfortunately, stability and performance control is always going to be affected by network and communication issues, such as band-limited channels, quantization errors, sampling, delays, packet dropouts or system architecture. The first part of this research aims to study the effects of both input and output quantization on an NCS. Both input and output quantization errors are going to be modeled as sector bounded multiplicative uncertainties, the main goal being the minimization of the quantization density, while maintaining feedback stability. Modeling quantization errors as uncertainties allows for robust optimal control strategies to be applied in order to study the accepted uncertainty levels, which are directly related to the quantization levels. A new feedback law is proposed that will improve closed-loop system stability by increasing the upper bound of allowed uncertainty, and thus allowing the use of a coarser quantizer. Another aspect of NCS deals with coordination of the independent agents within a Multi-agent System (MAS). This research addresses the consensus problem for a set of discrete-time agents communicating through a network with directed information flow. It examines the combined effect of agent dynamics and network topology on agents\u27 consensusability. Given a particular consensus protocol, a sufficient condition is given for agents to be consensusable. This condition requires the eigenvalues of the digraph modeling the network topology to be outer bounded by a fan-shaped area determined by the Mahler measure of the agents\u27 dynamics matrix

Routing on the Channel Dependency Graph:: A New Approach to Deadlock-Free, Destination-Based, High-Performance Routing for Lossless Interconnection Networks

In the pursuit for ever-increasing compute power, and with Moore's law slowly coming to an end, high-performance computing started to scale-out to larger systems. Alongside the increasing system size, the interconnection network is growing to accommodate and connect tens of thousands of compute nodes. These networks have a large influence on total cost, application performance, energy consumption, and overall system efficiency of the supercomputer. Unfortunately, state-of-the-art routing algorithms, which define the packet paths through the network, do not utilize this important resource efficiently. Topology-aware routing algorithms become increasingly inapplicable, due to irregular topologies, which either are irregular by design, or most often a result of hardware failures. Exchanging faulty network components potentially requires whole system downtime further increasing the cost of the failure. This management approach becomes more and more impractical due to the scale of today's networks and the accompanying steady decrease of the mean time between failures. Alternative methods of operating and maintaining these high-performance interconnects, both in terms of hardware- and software-management, are necessary to mitigate negative effects experienced by scientific applications executed on the supercomputer. However, existing topology-agnostic routing algorithms either suffer from poor load balancing or are not bounded in the number of virtual channels needed to resolve deadlocks in the routing tables. Using the fail-in-place strategy, a well-established method for storage systems to repair only critical component failures, is a feasible solution for current and future HPC interconnects as well as other large-scale installations such as data center networks. Although, an appropriate combination of topology and routing algorithm is required to minimize the throughput degradation for the entire system. This thesis contributes a network simulation toolchain to facilitate the process of finding a suitable combination, either during system design or while it is in operation. On top of this foundation, a key contribution is a novel scheduling-aware routing, which reduces fault-induced throughput degradation while improving overall network utilization. The scheduling-aware routing performs frequent property preserving routing updates to optimize the path balancing for simultaneously running batch jobs. The increased deployment of lossless interconnection networks, in conjunction with fail-in-place modes of operation and topology-agnostic, scheduling-aware routing algorithms, necessitates new solutions to solve the routing-deadlock problem. Therefore, this thesis further advances the state-of-the-art by introducing a novel concept of routing on the channel dependency graph, which allows the design of an universally applicable destination-based routing capable of optimizing the path balancing without exceeding a given number of virtual channels, which are a common hardware limitation. This disruptive innovation enables implicit deadlock-avoidance during path calculation, instead of solving both problems separately as all previous solutions

Semantic Networks for Hybrid Processes.

Simulation models are often used in parallel with a physical system to facilitate control, diagnosis and monitoring. Model based methods for control, diagnosis and monitoring form the basis for the popular sobriquets `intelligent', `smart' or `cyber-physical'. We refer to a configuration where a model and a physical system are run in parallel as a emph{hybrid process}. Discrepancies between the model and the process may be caused by a fault in the process or an error in the model. In this work we focus on correcting modeling errors and provide methods to correct or update the model when a discrepancy is observed between a model and process operating in parallel. We then show that some of the methods developed for model adaptation and diagnosis can be used for control systems design. There are five main contributions. The first contribution is an analysis of the practical considerations and limitations of a networked implementation of a hybrid process. The analysis considers both the delay and jitter in a packet switching network as well as limits on the accuracy of clocks used to synchronize the model and process. The second contribution is a semantic representation of hybrid processes which enables improvements to the accuracy and scope of algorithms used to update the model. We demonstrate how model uncertainty can be balanced against signal uncertainty and how the structure of interconnections between model components can be automatically reconfigured if needed. The third contribution is a diagnostic approach to isolate model components responsible for a discrepancy between model and process, for a structure preserving realization of a system of ODEs. The fourth contribution is an extension of the diagnostic strategy to include larger graphs with cycles, model uncertainty and measurement noise. The method uses graph theoretic tools to simplify the graph and make the problem more tractable and robust to noise. The fifth contribution is a simulation of a distributed control system to illustrate our contributions. Using a coordinated network of electric vehicle charging stations as an example, a consensus based decentralized charging policy is implemented using semantic modeling and declarative descriptions of the interconnection network.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99903/1/danand_1.pd