Decentralized Rate Regulation in Random Access Channels

We consider a time-slotted multipacket reception channel, shared by a finite number of mobile users who transmit to a common base station. Each user is allocated a fixed data rate, which may be imposed by the base station or self-determined. For sustaining the required rate over time, each user may adjust a single parameter which determines the individual transmission probability in a given slot. An equilibrium point is attained when the assigned data rates are met with equality. This paper analyzes the equilibrium points which result in this system, with a focus on power efficiency of the solution. While multiple equilibrium points exist in general, we establish that one of these equilibria is best for all users, in the sense that the transmission probability (hence the power investment) of each user is minimal. Further to the existence of worse equilibrium points, we point to the possibility of a partial- equilibrium with starvation, where stronger users (in terms of received power) satisfy their data rates, while preventing weaker ones from obtaining their respective rates. To avoid these sub- optimal working points, we suggest a distributed mechanism that converges to the best equilibrium point. Further analysis is provided for a specific channel model which involves perfect capture.