Modelling large timescale and small timescale service variability

The performance of service units might depend on various randomly changing environmental effects. It is quite often the case that these effects varies on different time scales. In this paper we consider short and long scale service variability, where the short scale variability affects the instantaneous service speed of the service unit and the large scale effect is defined by a modulating background Markov chain. The main modelling challenge is that the considered short and long range variation results randomness along different axes, the short scale variability along the time axis and the long scale variability along the work axis. The work presents mostly simulation results; the mathematical setup for analytical results is provided, but the actual analysis is subject to future research.