On Stochastic Models of Service System with Dependent Process Characteristics

Abstract

A generalization of a service system model introduced by I. Kaj and M. Taqqu is considered. Unlike the original model, the unnatural assumption on independence between the duration and required resources quantity of a service process is dropped. A number of limit theorems for the process of integral workload is presented. Among the considered limit processes are the Winer process, fractional Brownian motion, and stable Lévy process.