Closed form solutions for the equilibrium probability distribution in the closed Lu-Kumar network under two buffer priority policies

We seek closed form solutions for the equilibrium probability distribution of the two station closed reentrant Lu-Kumar network under two static buffer priority policies. For the last buffer first served (LBFS) policy, an explicit closed form is obtained. For the first buffer first served (FBFS) policy, sufficient structure exists for us to obtain expressions for many states, but a reduced dimension Toeplitz matrix must still be inverted for a complete solution. We use the results to compute the throughput and asymptotic losses of the system.