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Book Description
This dissertation is concerned with heavy traffic and Markov modulated diffusion models that are applied to resource allocation problems in wireless communication system and the numerical analysis for their associated continuous time stochastic control problems. To be specific, the heavy traffic model is a two-dimensional stochastic differential equation with reflection (SDER), and the other model is a second-order Markov modulated diffusion process. With the proliferation of wireless applications having large capacity requirements, such as multimedia, internet, gaming, etc., and the limitations of realizing spectral efficiency gains, wireless queueing systems will be operating a near-capacity levels, so called "Heavy traffic". Under this assumption, SDER has been developed as an approximation model for a multi-buffer and various channel state wireless communication system. Building on the seminal work of Buche and Kushner [13], we study how the reflection process can affect the solution of the SDER and the resource (reserve power) allocation theoretically and numerically. We have shown that Multi-Completely S is a necessary condition for the existence and uniqueness for the SDER instead of the well known Completely S in the wireline system [69]. The whole resource (reserve transmission power) allocation is modeled as a stochastic control problem subject to the SDER. Using Markov Chain Approximation (MCA) method [51], various effects of factors, especially the reflection processes (nominal power reallocation) are studied via numerical experiments. After optimal control policies are obtained via MCA method under an appropriate grid size setting, Monte Carlo and real time simulation experiments are done using heavy traffic policies v.s. heuristic wedge control policies. The performance of heavy traffic policies is better than that of wedge policies under various traffic patterns including aggregated OND FF process (Long Range Dependence & Heavy Tailed) which.