Power Control for a Wireless Queueing System with Delayed State Information: Heavy Traffic Modeling and Numerical Analysis

A resource allocation problem (power control) in a wireless queueing system using heavy traffic methods is extended to incorporate delay. Modeling delay is important in highspeed wireless networks for stability and good performance. Under the heavy traffic method without delay the queue dynamics are approximated by a limit model which is a controlled reflected diffusion. The delay case is obtained by "adding" in delay in queue state information into the limit model for the case without delay; this yields a (controlled) stochastic delay differential equation with reflection. An associated stochastic control problem for the delay case is solved numerically by a combination of the Markov chain approximation method and an application of the separation principle. We study the affect of delay on the performance of the system. In particular, we give simulation results detailing the cost and control, parameterized by the delay. We also give initial simulation results for a fixed delay case, but with varying arrival rates