Robust Stability and Performance of a p-Persistent Communication Protocol

A p-persistent transmission protocol, recently proposed in the literature, for a network of transmitting nodes sharing a common channel is studied. Such a protocol is based on a fully decentralized control that adjusts the message transmission rate of each node to the estimated density of surrounding transmitting nodes. The system does not require enumeration of nodes nor control messages, the only input to the control coming from the physical medium occupation. Stability conditions are considered under time-varying network topologies and delays. General stability conditions for tuning the control parameters are given which assure stability under arbitrary topology variations. It is shown that such conditions are conservative, penalize the network parameters and compromise the systems performance. Thus the problem is investigated in details in order to provide conditions in terms of performance. It is shown that under network symmetry assumption stability can be studied in terms of system eigenvalues even under topology switching. Moreover, under symmetry assumption, the problem has interesting connections with the known problem of the characterization of the eigenvalues of the adjacency matrix of a graph. © 2011 IFAC.