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Title: Load Balancing Under Strict Compatibility Constraints
Consider a system with N identical single-server queues and a number of task types, where each server is able to process only a small subset of possible task types. Arriving tasks select [Formula: see text] random compatible servers and join the shortest queue among them. The compatibility constraints are captured by a fixed bipartite graph between the servers and the task types. When the graph is complete bipartite, the mean-field approximation is accurate. However, such dense compatibility graphs are infeasible for large-scale implementation. We characterize a class of sparse compatibility graphs for which the mean-field approximation remains valid. For this, we introduce a novel notion, called proportional sparsity, and establish that systems with proportionally sparse compatibility graphs asymptotically match the performance of a fully flexible system. Furthermore, we show that proportionally sparse random compatibility graphs can be constructed, which reduce the server degree almost by a factor [Formula: see text] compared with the complete bipartite compatibility graph.  more » « less
Award ID(s):
2113027
NSF-PAR ID:
10323989
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Mathematics of Operations Research
ISSN:
0364-765X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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