Comments on "Analysis, stability, and optimization of slotted ALOHA with a finite number of buffered users"

The model of a buffered slotted ALOHA scheme presented by Saadawi and Ephremides in the above paper is improved by refining the USER and SYSTEM Markov chains. New expressions are proposed for the transition probabilities in the USER chain. The SYSTEM chain is also modified to account for the influence of an arriving packet on all possible transitions. The principle of flow balance at equilibrium (the net packet input flow rate should be equal to the rate of successful packet transmissions) is employed to justify these changes. Incorporating the proposed modifications, the packet flow equivalence condition is established analytically for the two-user, single-buffer case and numerically for systems with a larger number of users, each one having a single, finite, or an infinite buffer.