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Time-delay systems: an overview of some recent advances and open problems

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

This paper gives a broad overview of the stability and control of time-delay systems. Emphasis is on the more recent progress and engineering applications. Examples of practical problems, mathematical descriptions, stability and performance analysis, and feedback control are discussed.

Survey on Recent Results in the Stability and Control of Time-Delay Systems*

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation, or transport phenomena in shared environments, in heredity, and in competition in population dynamics. This monograph addresses the problem of stability analysis and the stabilisation of dynamical systems subjected to time-delays. It presents a wide and self-contained panorama of analytical methods and computational algorithms using a unified eigenvalue-based approach illustrated by examples and applications in electrical and mechanical engineering, biology, and complex network analysis.

Stability and Stabilization of Systems with Time Delay

A deterministic dynamic nonlinear time-delay system is developed to model load balancing in a cluster of computer nodes used for parallel computations. The model is shown to be self consistent in that the queue lengths cannot go negative and the total number of tasks in all the queues and the network are conserved (i.e., load balancing can neither create nor lose tasks). Further, it is shown that using the proposed load balancing algorithms, the system is stable in the sense of Lyapunov. Experimental results are presented and compared with the predicted results from the analytical model. In particular, simulations of the models are compared with an experimental implementation of the load balancing algorithm on a distributed computing network.

/pdf/the-effect-of-time-delays-on-the-stability-of-load-balancing-52l22ajlu9.pdf

The effect of time delays on the stability of load balancing algorithms for parallel computations

Parallel computer architectures utilize a set of computational elements (CE) to achieve performance that is not attainable on a single processor, or CE, computer. A common architecture is the cluster of otherwise independent computers communicating through a shared network. To make use of parallel computing resources, problems must be broken down in to smaller units that can be solved individually by each CE while exchanging information with CEs solving other problems.

/pdf/dynamic-time-delay-models-for-load-balancing-part-i-sl3f7u1lfa.pdf

Dynamic Time Delay Models for Load Balancing. Part I: Deterministic Models

A linear time-delay system is proposed to model load balancing in a cluster of computer nodes used for parallel computations. The linear model is analysed for stability in terms of the delays in the transfer of information between nodes and the gains in the load balancing algorithm. This model is compared with an experimental implementation of the algorithm on a parallel computer network.

/pdf/linear-time-delay-model-for-studying-load-balancing-2cemviwgo5.pdf

Linear time delay model for studying load balancing instabilities in parallel computations

Deterministic dynamic nonlinear time-delay systems are developed to model load balancing in a cluster of computer nodes used for parallel computations. The model is shown to be self consistent in that the queue lengths cannot go negative and the total number of tasks in all the queues are conserved (i.e., load balancing can neither create nor lose tasks). Further, it is shown that using the proposed load balancing algorithms, the system is stable. Experimental results are presented and compared with the predicted results from the analytical model. In particular, simulations of the models are compared with an experimental implementation of the load balancing algorithm on a parallel computer network.

/pdf/the-effect-of-time-delays-in-the-stability-of-load-balancing-379jks01bj.pdf

The effect of time delays in the stability of load balancing algorithms for parallel computations

A deterministic dynamic nonlinear time-delay system is developed to model load balancing in a cluster of computer nodes used for parallel computations. This model refines a model previously proposed by the authors to account for the fact that the load balancing operation involves processor time which cannot be used to process tasks. Consequently, there is a trade-off between using processor time/network bandwidth and the advantage of distributing the load evenly between the nodes to reduce overall processing time. The new model is shown to be self consistent in that the queue lengths cannot become negative and the total number of tasks in all the queues Is conserved (i.e., load balancing can neither create nor lose tasks). It is shown that the proposed model is (Lyapunov) stable for any input, but not necessarily asymptotically stable. Experimental results are presented and compared with the predicted results from the analytical model. In particular, simulations of the models are compared with an experimental implementation of the load balancing algorithm on a parallel computer network.

/pdf/a-time-delay-model-for-load-balancing-with-processor-d1fuk0q1r8.pdf

Zhong Tang

Papers

The effect of time delays on the stability of load balancing algorithms for parallel computations

Dynamic Time Delay Models for Load Balancing. Part I: Deterministic Models

Linear time delay model for studying load balancing instabilities in parallel computations

The effect of time delays in the stability of load balancing algorithms for parallel computations

A time delay model for load balancing with processor resource constraints