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Dagstuhl Seminar 24141

Network Calculus

( Apr 01 – Apr 04, 2024 )

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Network calculus has become a mature and versatile methodology for the analysis of queueing systems with a broad variety of applications ranging from Internet Quality of Service (QoS), wireless networks, to Ethernet with delay guarantees, real-time systems, and feedback control. This is achieved through complementary, problem-specific representations in min-plus or max-plus algebra and the use of worst-case or statistical bounds. The goal of this Dagstuhl Seminar is to gather the deterministic and stochastic Network Calculus community, to discuss recent research activities, to identify future directions, and to strengthen cooperation. The challenges to be discussed arise in these areas:

Algebras, performance metrics and bounds: Network Calculus has a fundamental representation as a systems theory under the min-plus algebra. Related are theories, e.g., for discrete-event systems, that use a max-plus algebra, and there is also a branch of the Network Calculus that uses max-plus. An important application is recent age-of-information research. A further, methodological connection with the min-plus/max-plus systems theory of the Network Calculus may be developed in the field of feedback control of max-plus linear systems. We expect that input from the control and discrete event community to the seminar will give fresh momentum and may motivate novel joint research.

Network topology and parallel systems: A remarkable quality of the Network Calculus is its modeling power: a wide variety of systems, such as links, traffic shapers, and scheduling policies can be modeled and composed into arbitrary topologies. Some advanced results from the deterministic Network Calculus, namely the pay bursts/multiplexing only once phenomena, have only recently been incorporated into the stochastic Network Calculus. Continuing this effort requires a strong cooperation between both communities, given their complementary expertise. Another important aspect to be advanced together are parallel systems, as found in multi-path transport and in fork-join models.

TSN, DetNet, URLLC: Since recently, there has been a surge of interest in technologies for reliable and low-latency communications. Prominent examples are IEEE Time Sensitive Networking (TSN), IETF Deterministic Networking (DetNet), and 5G Ultra-Reliable Low Latency Communications (URLLC). These technologies are closely intertwined with the Network Calculus with essential applications in, e.g., factory automation, aerospace onboard, and automotive in-vehicle networks.

Algorithms and tools: Recent developments in Network Calculus algorithms can be classified as a) combining modular and optimization approaches; and b) highly parallelizable methods that iteratively improve the performance bounds. The former trend requires finding an appropriate decomposition, which can, for example, be resolved with machine learning techniques. Integrating these streams and their tool development opens up the opportunity for rapid dissemination of novel results, extensive community-based research artifact evaluation and reproducibility verification.

Design automation and configuration synthesis: Rather than aiming for a performance analysis of a fully configured system, constructive methods seek to design and configure a system that meets given performance requirements. Adapting Network Calculus for design automation and configuration is a fundamental challenge. How Network Calculus modeling and analysis can allow for such an adapted procedure with open parameters is not yet investigated in sufficient detail. Among the tools that could be used for solving such problems are, again, optimization and machine learning.

Copyright Steffen Bondorf, Anne Bouillard, Markus Fidler, and Jörg Liebeherr


  • Networking and Internet Architecture
  • Performance

  • Network calculus
  • effective bandwidths
  • queueing network
  • performance evaluation
  • age of information