@article {IOPORT.05717823,
    author       = {Ghosh, Arka P. and Roitershtein, Alexander and Weerasinghe, Ananda},
    title        = {Optimal control of a stochastic processing system driven by a fractional Brownian motion input.},
    year         = {2010},
    journal      = {Advances in Applied Probability},
    volume       = {42},
    number       = {1},
    issn         = {0001-8678},
    pages        = {183-209},
    publisher    = {Applied Probability Trust, Sheffield},
    doi          = {10.1239/aap/1269611149},
    abstract     = {A real-valued stochastic process ${W_H} = {({W_H}(t))_{t \geqslant 0}}$ is called a fractional Brownian motion with Hurst parameter $H \in (0,1)$ if ${W_H}(0) = 0$ and ${W_H}$ is a continuous zero-mean Gaussian process with stationary increments and covariance function $\text {cov} ({W_H}(s),{W_H}(t)) = \frac{1}{2}[{t^{2H}} + {s^{2H}} - {\left| {t - s} \right|^{2H}}]$, $s \geqslant 0,t \geqslant 0$. The paper considers a single-server stochastic processing network having deterministic service process with rate $\mu > 0$. The cumulative work input to the system over the time interval $[0,t]$ is given by $\lambda t + {W_H}(t)$, where $\lambda $ is a fixed constant. It is assumed that $\lambda < \mu $ and that the parameter $\mu $ can be controlled. The paper investigates three basic stochastic control problems of the workload process, namely the long-run average cost problem, the infinite horizon discounted cost problem, and the finite-horizon cost problem.},
    reviewer     = {Oleg K. Zakusilo (Ky{\"\i}v)},
    identifier   = {05717823},
}