Stochastic Control Problems for Processes with Long-Range Dependence & Internet Traffic

摘要

We address several stochastic control problems related to queueing networks with fractional Brownian motion(fBM) input are addressed. Abelian limit relationships among the value functions of these control problems are also established. These problems are motivated by fluid networks related to on- off queueing systems. A stochastic comparison theorem for stochastic differential equations driven by fBM is obtained. We compute optimal strategies for a class of goal problems when the state process is corrupted by a fBM noise. In the second part, we address several issues related to controlled queueing networks with impatient customers in heavy traffic. We obtain heavy traffic approximations for queue length and offered waiting time. We also address a control problem for a queueing network in heavy traffic with impatient customers. Such results are applicable for internet traffic and for the dynamics of large telephone call centers.