Heavy traffic control policies for wireless systems with time-varying channels

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). In one of the first works applied to wireless (Buche and Kushner, 2002), an important assumption was made on the reflection process in order lo get existence and uniqueness of a SDER limit model. Here we obtain the optimal control policies in a wireless system with the SDER limit model using numerical methods for continuous-time stochastic control problems. The simulation results indicate the influence of the reflection process on the optimal control polices which motivates further investigation into the strength of the reflection assumption. The optimal policies have the form of a "Max Weight" discipline and are similar to results obtained analytically under simplifying assumptions.