End-to-End Worst-Case Analysis of Non-FIFO Systems

In this report, delay bounds in data flow systems with nonFIFO service disciplines are explored. It is shown that conventional network calculus definitions of a service curve are not satisfying under the assumption of non-FIFO service. Either the definition is too strict to allow for a concatenation and consequent beneficial end-to-end analysis, or it is too loose and thus results in infinite delay bounds. Hence, a new definition is proposed and demonstrated to achieve both finite delay bounds and a concatenation of systems resulting in a favourable end-toend analysis. In particular, we show that the celebrated pay bursts only once phenomenon is retained under non-FIFO service. This is contrary to a finding by Rizzo and Le Boudec [20]. The reasons for this contradiction are also discussed. The new service curve definition preserves the min-plus algebraic approach known from network calculus at the cost of a loss of tightness of delay bounds under certain circumstances. This is shown by devising an alternative method that achieves tight bounds; this method departs from the algebraic approach. Yet, despite the loss of tightness the algebraic approach bears a number of advantages. Most important, it allows to deal elegantly with the frequent situation of a mixture of FIFO and non-FIFO servers, eventually resulting in better delay bounds.