On the Fault-Tolerant Online Bin Packing Problem
Abstract: We study the fault-tolerant variant of the online bin packing problem. Similar to the classic online bin packing problem, an online sequence of items of various sizes should be packed into a minimum number of bins of uniform capacity. For applications such as server consolidation, where bins represent servers and items represent jobs of various loads, it is necessary to maintain fault-tolerant solutions. In a fault-tolerant packing, any job is replicated into \(f+1\) servers, for some integer \(f>1\), so that the failure of up to f servers does not interrupt service. We build over a practical model, introduced by Li and Tang [SPAA 2017], in which each job of load x has a primary replica of load x and f standby replicas, each of load \(x/\eta \), where \(\eta >1\) is a parameter of the problem. Upon failure of up to f servers, any primary replica in a failed bin should be replaced by one of its standby replicas so that the extra load of the new primary replica does not cause an overflow in its bin.
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