A Robust Decentralized Control for Channel Sharing Communication

We consider the problem of controlling the transmission rate in a communication network where each node adjusts its own transmission rate exclusively based on the physical medium occupation (the band occupancy of the aggregate complementary nodes). We show how to design a decentralized control for maximizing band occupancy and fairness. If the network is fully connected, the problem admits a simple solution. Difficulties arise in the case of partially connected networks, and in the presence of time-varying network topologies and delays. General conditions are given which, by properly tuning control parameters, ensure stability. These conditions are conservative and affect system performance. However, we show that in the case of symmetric connections, stability can be studied based on the system eigenvalues even in the presence of topology switchings. Less conservative bounds can be inferred by exploiting known properties of the eigenvalues of the adjacency matrix of a graph. We finally consider the multichannel case, in which nodes may jump among channels: the previous scheme can be extended to this case and asymptotically ensures uniform channel exploitation.