On stochastic models of service system with dependent process characteristics

We consider a generalization of a service system model introduced by I. Kaj and M. Taqqu. Unlike their setting, we drop the unnatural assumption of independence between the duration and required resources quantity of a service process. We present a number of limit theorems for the process of integral workload. Wiener process, Fractional Brownian motion, or Stable Lévy process may show up as the limits.