 by some fundamentals of queueing theory [@refL0; @refL0; @refL0; @refD0], the condition in can be rewritten as $$\label{ZEqnNum000000}  {\mathbb{E}}\left(\left. \Delta _{{\rm {\mathcal L}}} \right|Z_{R_{j} }^{*} \left(\pi _{S} \right)\right)\le -\varepsilon \left|Z_{R_{j} }^{*} \left(\pi _{S} \right)\right|