On closed form solutions for equilibrium probabilities in the closed Lu-kumar network under various buffer priority policies

Abstract

We seek closed form solutions for the equilibrium probability distribution of the two station closed reentrant Lu-Kumar network under all possible static buffer priority policies. We show special properties and investigate theoretical insights in the network. For the LBFS policy, an explicit closed form is obtained for the equilibrium probabilities. For the FBFS policy, sufficient structure exists for us to obtain expressions for the equilibrium probabilities in many states, but a reduced dimension Toeplitz matrix must still be inverted for a complete solution. The remaining buffer priority policies do not possess sufficient structure to be amenable to solution. We use the results to compute the throughput and asymptotic losses of the system. We finally compare the policies in terms of throughput.