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

Electr. & Comput. Eng. Dept., Univ. of Tennessee, Knoxville, TN, USA
IEEE Transactions on Control Systems Technology (Impact Factor: 2.47). 12/2005; 13(6):932 - 942. DOI: 10.1109/TCST.2005.854339
Source: IEEE Xplore


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.

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    • "For example, in order to model vehicular traffic flow [48]-[49], the reaction delays of drivers should be considered, and for different drivers, the reaction delays are different depending on physical conditions, drivers' cognitive and physiological states, etc. Moreover, in the load balancing problem [50], for a computing network consisting of n computers (also called nodes), except for the different communication delays, the task-transfer delays τ jk also should be considered, which depends on the number of tasks to be transferred from node k to node j. More related examples can be found in [51] and references therein. "
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