Load rebalancing games in dynamic systems with migration costs

8 years 10 days ago

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We consider the following dynamic load balancing game: Given an initial assignment of jobs to identical parallel machines, the system is modiﬁed; speciﬁcally, some machines are added or removed. Each job’s cost is the load on the machine it is assigned to; thus, when machines are added, jobs have an incentive to migrate to the new unloaded machines. When machines are removed, the jobs assigned to them must be reassigned. Consequently, other jobs might also beneﬁt from migrations. In our job-extension penalty model, for a given extension parameter δ ≥ 0, if the machine on which a job is assigned to in the modiﬁed schedule is diﬀerent from its initial machine, then the job’s processing time is extended by δ. We provide answers to the basic questions arising in this model. Namely, the existence and calculation of a Nash Equilibrium and a Strong Nash Equilibrium, and their ineﬃciency compared to an optimal schedule. Our results show that the existence of job-migration ...

Sofia Belikovetsky, Tami Tamir

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