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International Conference on Complex Networks and Their Applications

COMPLEX NETWORKS 2019: Complex Networks and Their Applications VIII pp 349–361Cite as

Rejection-Based Simulation of Non-Markovian Agents on Complex Networks

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 881))

Abstract

Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often the preferred—sometimes the only feasible—way to investigate such systems. Previous research focused primarily on Markovian models where the random time until an interaction happens follows an exponential distribution.

In this work, we study a general framework to model systems where each agent is in one of several states. Agents can change their state at random, influenced by their complete neighborhood, while the time to the next event can follow an arbitrary probability distribution. Classically, these simulations are hindered by high computational costs of updating the rates of interconnected agents and sampling the random residence times from arbitrary distributions.

We propose a rejection-based, event-driven simulation algorithm to overcome these limitations. Our method over-approximates the instantaneous rates corresponding to inter-event times while rejection events counter-balance these over-approximations. We demonstrate the effectiveness of our approach on models of epidemic and information spreading.

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Notes

  1. 1.

    github.com/gerritgr/non-markovian-simulation.

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Acknowledgements

We thank Guillaume St-Onge for helpful comments on non-Markovian dynamics. This research was been partially funded by the German Research Council (DFG) as part of the Collaborative Research Center “Methods and Tools for Understanding and Controlling Privacy”.

Author information

Authors and Affiliations

  1. Saarland University, 66123, Saarbrücken, Germany

    Gerrit Großmann, Luca Bortolussi & Verena Wolf

  2. University of Trieste, Trieste, Italy

    Luca Bortolussi

Authors
  1. Gerrit Großmann
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  2. Luca Bortolussi
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  3. Verena Wolf
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Corresponding author

Correspondence to Gerrit Großmann .

Editor information

Editors and Affiliations

  1. University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  2. Università degli Studi di Milano, Milan, Italy

    Sabrina Gaito

  3. University of Aveiro, Aveiro, Portugal

    José Fernendo Mendes

  4. Universidad Carlos III de Madrid, Leganés, Madrid, Spain

    Esteban Moro

  5. Indiana University, Bloomington, IN, USA

    Luis Mateus Rocha

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Großmann, G., Bortolussi, L., Wolf, V. (2020). Rejection-Based Simulation of Non-Markovian Agents on Complex Networks. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 881. Springer, Cham. https://doi.org/10.1007/978-3-030-36687-2_29

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