Power Control for Mobile Communications With Delayed State Information in Heavy Traffic

Heavy traffic methods are well studied in wireline queueing networks but only recently have been applied to wireless queueing systems with their random environments (due to channel variations, multi-access interference, etc.). Under the heavy traffic method, one can obtain a limit model approximating the queueing dynamics and it typically has the form of a stochastic differential equation with reflection (SDER). With the emergence of large high-speed wireless networks, modeling even small delays is important as they can strongly affect the network dynamics. In this paper, we consider a delayed version of the SDER (DSDER) where we introduce a deterministic delay in the state representing the queueing dynamics. Due to the special structure of DSDER, we observe that delayed state information enters the dynamics only through the controller so the control problem can viewed as control under partial observation. For solving the control problem we apply the separation principle as an approximation in a numerical Markov chain method approach. Simulation results are presented showing the promise of this approach