Systems with large flexible server pools: instability of ``natural'' load balancing (Q373849)

The authors consider the behaviour of large-scale service systems with multiple customer classes and multiple server pools. The allowed activities form a tree described by the graph with the vertices being both customer classes and server pools. In the model, a natural routing/scheduling rule such as the longest-queue freest-server load balancing (LQFS-LB) is assumed. Additionally, the exogenous arrival rates of customer classes and the number of agents in each pool growing to infinity in proportion to the scaling parameter \(r\).NEWLINENEWLINEThe fluid models associated with this system are used. The obtained main results are as follows: (a) the fluid limit of the system may be unstable in the vicinity of the equilibrium point; (b) the sequence of stationary distributions of diffusion-scaled processes may be non-tight and may escape to infinity; and (c) the sequence of stationary distributions of diffusion-scaled processes is tight and the limit of stationary distributions is the stationary distribution of the limiting diffusion process. These results are very valuable and important for the further study of large-scale service systems.