Stochastic ordering of needy patients in Erlang-R and closed ward models

Let $Q^b_1(\infty)$, $Q_1^h(\infty)$ and $Q_1^J(\infty)$ denote the stationary number of needy patients in the Erlang-R model with blocking, holding and the closed ward, respectively. Here $\preceq_{\rm st}$ denotes stochastic ordering. Ordering conjecture.

$$Q_1^b(\infty) \preceq_{\rm st} Q_1^h(\infty) \preceq_{\rm st} Q_1^J(\infty).$$

This conjecture is motivated by simulations across multiple parameter settings, which suggest that the holding model is stochastically bounded between the blocking model and the closed ward model. Its general validity is not established in the source.