Abstract
We consider general large-scale service systems with multiple customer classes and multiple server (agent) pools, mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing choices) form a tree (in the graph with vertices being both customer classes and server pools). We study the behavior of the system under a natural (load balancing) routing/scheduling rule, Longest-Queue Freest-Server (LQFS-LB), in the many-server asymptotic regime, such that the exogenous arrival rates of the customer classes, as well as the number of agents in each pool, grow to infinity in proportion to some scaling parameter
Our main results are as follows. (a) We show that, quite surprisingly (given the tree assumption), for certain parameter ranges, the fluid limit of the system may be unstable in the vicinity of the equilibrium point; such instability may occur if the activity graph is not “too small.” (b) Using (a), we demonstrate that the sequence of stationary distributions of diffusion-scaled processes [measuring
Citation
Alexander L. Stolyar. Elena Yudovina. "Systems with large flexible server pools: Instability of “natural” load balancing." Ann. Appl. Probab. 23 (5) 2099 - 2138, October 2013. https://doi.org/10.1214/12-AAP895
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