On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
On-line load balancing for related machines
Journal of Algorithms
On-Line Load Balancing in a Hierarchical Server Topology
SIAM Journal on Computing
On-line algorithms for the channel assignment problem in cellular networks
Discrete Applied Mathematics
Preemptive scheduling on a small number of hierarchical machines
Information and Computation
Online parallel machines scheduling with two hierarchies
Theoretical Computer Science
Online and semi-online scheduling of two machines under a grade of service provision
Operations Research Letters
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In this paper, we consider online and semi-online hierarchical scheduling for load balancing on m parallel uniform machines with two hierarchies. There are k machines with speed s and hierarchy 1 which can process all the jobs, while the remaining m-k machines with speed 1 and hierarchy 2 can only process jobs with hierarchy 2. For the model with the objective to maximize the minimum machine completion time, we show that no online algorithm can achieve bounded competitive ratio, i.e., there exists no competitive algorithm. We overcome this barrier by way of fractional assignment, where each job can be arbitrarily split between the machines. We design a best possible algorithm with competitive ratio 2ks+m-kks+m-k for any 0