On the performance figures of queuing systems with context-dependent service times

This paper deals with the performance evaluation of systems whose service rates are dependent on external variables, such as the level of resource availability in computing systems, the intensity of background traffic or the failures affecting telecommunications networks. A well-established class of performance models for systems belonging to this class is represented by Markov-modulated queuing networks. Motivated by a review of the results available in the literature, we propose in this work a very simple and generalizable analytical approach to compute the expected service time when the number of servers is very large and can be modeled as being infinite. Our analytical approach is a new one. With it, we are able to re-obtain in this paper results that are already known in the performance modeling and evaluation community. Moreover, we show through examples how the straightforward mathematical treatment we define can be applied to classes of models for which no analytical results are yet available.