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We consider $$GI/Ph/n+M$$ G I / P h / n + M parallel-server systems with a renewal arrival process, a phase-type service time distribution, $$n$$ n homogenous servers, and an exponential patience time distribution with positive rate. We show that in the Halfin–Whitt regime, the sequence of stationary distributions corresponding to the normalized state processes is tight. As a consequence,...
For a multi-dimensional diffusion process, an important problem is whether the associated basic adjoint relationship (BAR) uniquely characterizes the stationary distribution of the diffusion process. A key step in this characterization is an open problem that any solution to BAR does not change sign. This note describes the open problem precisely in the context of two classes of diffusion processes...
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