Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Stochastic analysis and control of real-time systems with random time delays
Automatica (Journal of IFAC)
Heavy traffic analysis of controlled multiplexing systems
Queueing Systems: Theory and Applications
Exponential stabilisability of finite-dimensional linear systems with limited data rates
Automatica (Journal of IFAC)
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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.