Linear decoding and delivery delay for the new three-receiver module

Let $\rho=\lambda/\mu<1$ be the load factor in the three-receiver system, and consider the newly proposed coding module. Define decoding delay as the time from packet arrival at the sender until decoding by a receiver, and delivery delay as the time until in-order delivery to the application. New coding-module delay conjecture. The expected decoding delay per packet and the expected delivery delay per packet from a particular receiver's point of view both grow as $O\left(\frac{1}{1-\rho}\right)$ as $\rho\rightarrow 1$. This order matches the single-receiver lower bound and is therefore asymptotically optimal. The claim is supported by simulations in the source, while no proof of the stated asymptotic bounds is given.