pp 1–22 | Cite as

Structural properties of feasible bookings in the European entry–exit gas market system

  • Lars Schewe
  • Martin SchmidtEmail author
  • Johannes Thürauf
Research Paper


In this work, we analyze the structural properties of the set of feasible bookings in the European entry–exit gas market system. We present formal definitions of feasible bookings and then analyze properties that are important if one wants to optimize over them. Thus, we study whether the sets of feasible nominations and bookings are bounded, convex, connected, conic, and star-shaped. The results depend on the specific model of gas flow in a network. Here, we discuss a simple linear flow model with arc capacities as well as nonlinear and mixed-integer nonlinear models of passive and active networks, respectively. It turns out that the set of feasible bookings has some unintuitive properties. For instance, we show that the set is nonconvex even though only a simple linear flow model is used.


Gas networks Bookings Entry–exit system Convexity Flow models 

Mathematics Subject Classification

90-XX 90B10 90C90 90C35 



This research has been performed as part of the Energie Campus Nürnberg and is supported by funding of the Bavarian State Government. The first and second author also thank the DFG for their support within Projects A05, B07, and B08 in CRC TRR 154. Finally, we want to thank Fränk Plein for carefully reading a former version of this manuscript and for his comments that helped to improve the quality of the paper.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Friedrich-Alexander-Universität Erlangen-Nürnberg, Discrete OptimizationErlangenGermany
  2. 2.Energie Campus NürnbergNürnbergGermany
  3. 3.Department of MathematicsTrier UniversityTrierGermany
  4. 4.School of MathematicsUniversity of EdinburghEdinburghUK

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