  Networks are integral parts of modern safety-critical systems and
certification demands the provision of guarantees for data transmissions.
Deterministic Network Calculus (DNC) can compute a worst-case bound on a data
flow's end-to-end delay. Accuracy of DNC results has been improved steadily,
resulting in two DNC branches: the classical algebraic analysis and the more
recent optimization-based analysis. The optimization-based branch provides a
theoretical solution for tight bounds. Its computational cost grows, however,
(possibly super-)exponentially with the network size. Consequently, a heuristic
optimization formulation trading accuracy against computational costs was
proposed. In this paper, we challenge optimization-based DNC with a new
algebraic DNC algorithm.
  We show that: (i) no current optimization formulation scales well with the
network size and (ii) algebraic DNC can be considerably improved in both
aspects, accuracy and computational cost. To that end, we contribute a novel
DNC algorithm that transfers the optimization's search for best attainable
delay bounds to algebraic DNC. It achieves a high degree of accuracy and our
novel efficiency improvements reduce the cost of the analysis dramatically. In
extensive numerical experiments, we observe that our delay bounds deviate from
the optimization-based ones by only 1.142% on average while computation times
simultaneously decrease by several orders of magnitude.
