Algorithm 1. Proposed heuristic control policy.

if${\sum }_{k=1}^n{x}_k<{\mathcal{A}}_i$then       admit type-i packet to queue 1   end if if${\sum }_{k=1}^n{x}_k\ge {\mathcal{A}}_i$ and $\mathcal{I}\left(x\right)\ge i$ and ${\sum }_{k=1}^n{x}_k\ge {\mathcal{R}}_{\mathcal{I}\left(x\right)}$ then       admit type-i packet to queue 1 and route type-$\mathcal{I}\left(x\right)$ packet to queue 2   else      do no admit type-i packet   end if