2016/09/14 by Robert, Philippe, Véber, Amandine
#FOS: Computer and information sciences #FOS: Mathematics #Networking and Internet Architecture (cs.NI) #Probability (math.PR)
paper · doi:10.48550/arxiv.1609.04180
The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has x requests to transmit, then it receives a fraction of the capacity proportional to log(1+L), the logarithm of its current load L. A stochastic model of such an algorithm is investigated in the case of the star network, in which J nodes can transmit simultaneously, but interfere with a central node 0 in such a way that node 0 cannot transmit while one of the other nodes does. One studies the impact of the log policy on these J+1 interacting communication nodes. A fluid scaling analysis of the network is derived with the scaling parameter N being the norm of the initial state. It is shown that the asymptotic fluid behaviour of the system is a consequence of the evolution of the state of the network on a specific time scale (Nt, t∈(0,1)). The main result is that, on this time scale and under appropriate conditions, the state of a node with index j≥ 1 is of the order of Naj(t), with 0≤aj(t)