Dr. Florin Ciucu

"A Modern Network Queueing Theory with Inequalities"

Since the early 1990s, a radically new approach to compute backlogs and delays in networks evolved under the name of network calculus. The key novelty of the calculus approach to queueing systems consists in the modelling of arrivals and service with bounds, and not with exact expressions as in the classical queueing theory.
In this way the derivation of end-to-end backlog and delay bounds can be carried out using elementary inequalities.
The first part of talk overviews envelopes and service curve processes--the main concepts of the calculus--and explains how to compute backlog and delay bounds in both a deterministic and probabilistic framework. This is then followed by a discussion on the key advantages of the calculus such as invariance to several scheduling algorithms, dealing with non-necessarily statistical independent arrivals/service, and the relatively straightforward multi-node extension. Finally, by modelling classical queueing scenarios such as M/M/1 and M/D/1, the talk provides arguments that the bounds derived with the calculus are tight.