Professor Leonard Kleinrock – Tribute Volume

Stability of heterogeneous slotted ALOHA networks

“…where d is the node degree plus itself. Note that p = l / d is the optimum transmission probability to achieve network capacity [13].…”

“…The load line may intersect3 with the equilibrium contour in one, two, or no points, alternately, the network is said to be stable, unstable, or overloaded.Note that interpreting the discrete random variable B ( n ) as the average number of busy nodes, Equation 6 of the exact analysis becomes CT.'For the single buffer case, there is no difference between IFT and 3The load line tangentially intersecting the equilibrium contour is considered as having two coincident equilibrium points. the network is stable, unstable, or overloaded i f f ' = S ( M ) is the maximum network throughput[13] and S, , , = maxB{S(B)}.…”