Dynamical Discrete-Time Load Balancing in Distributed Systems in the Presence of Time Delays

The implementation of a load balancing policy on a continuous basis in a delay-limited distributed computing environment may not only drain the computational resources of each computational element (CE), but can also lead to an unnecessary exchange of loads between the CEs. This degrades the system performance, measured by the overall completion time of the total tasks in the system. Thus, for a given distribution of the load among the CEs, there has to be an optimal number and distribution of discrete balancing instants. This paper focuses on £xing the number of balancing instants and optimizing the completion time over the strength of load balancing, which is controlled by the so-called gain parameter, and the time when the balancing is executed. First, the case when the load balancing is implemented at a single instant per node is presented. Then, a strategy is considered where a second load balancing instant is allowed for each node. The simulations show that both strategies outperform the continuous balancing policy. Moreover, with the double load-balancing strategy the overall completion time is further reduced in comparison to the single load balancing case. It is also seen that the optimal choice of the gain parameter depends on the delay and this dependence becomes more signi£cant as the delays increase. This interplay between the strength of load balancing and the magnitude delay has a direct effect on the performance of the policy and on the sensitivity to the selection of the balancing instants.