WIAS Preprint No. 2158, (2015)

Feasibility of nominations in stationary gas networks with random load


  • Gotzes, Claudia
  • Heitsch, Holger
    ORCID: 0000-0002-2692-4602
  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Schultz, Rüdiger

2010 Mathematics Subject Classification

  • 90B15 90C15


  • stationary gas networks, random nominations, spheric-radial decomposition, Gaussian probability of feasible loads




The paper considers the computation of the probability of feasible load constellations in a stationary gas network with uncertain demand. More precisely, a network with a single entry and several exits with uncertain loads is studied. Feasibility of a load constellation is understood in the sense of an existing flow meeting these loads along with given pressure bounds in the pipes. In a first step, feasibility of deterministic exit loads is characterized algebraically and these general conditions are specified to networks involving at most one cycle. This prerequisite is essential for determining probabilities in a stochastic setting when exit loads are assumed to follow some (joint) Gaussian distribution when modeling uncertain customer demand. The key of our approach is the application of the spheric-radial decomposition of Gaussian random vectors coupled with Quasi Monte-Carlo sampling. This approach requires an efficient algorithmic treatment of the mentioned algebraic relations moreover depending on a scalar parameter. Numerical results are illustrated for different network examples and demonstrate a clear superiority in terms of precision over simple generic Monte-Carlo sampling. They lead to fairly accurate probability values even for moderate sample size.

Appeared in

  • Math. Methods Oper. Res., 84 (2016) pp. 427--457, changed title: On the quantification of nomination feasibility in stationary gas networks with random load.

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