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Time Delay Implies Cost on Task Switching: A Model to Investigate the Efficiency of Task Partitioning

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Abstract

Task allocation, and task switching have an important effect on the efficiency of distributed, locally controlled systems such as social insect colonies. Both efficiency and workload distribution are global features of the system which are not directly accessible to workers and can only be sampled locally by an individual in a distributed system. To investigate how the cost of task switching affects global performance we use social wasp societies as a metaphor to construct a simple model system with four interconnected tasks. Our goal is not the accurate description of the behavior of a given species, but to seek general conclusions on the effect of noise and time delay on a behavior that is partitioned into subtasks. In our model a nest structure needs to be constructed by the cooperation of individuals that carry out different tasks: builders, pulp and water foragers, and individuals storing water. We report a simulation study based on a model using delay-differential equations to analyze the trade-off between task switching costs and keeping a high degree of adaptivity in a dynamic, noisy environment. Combining the methods of time-delayed equations and stochastic processes we are able to represent the influence of swarm size and task switching sensitivity. We find that the system is stable for reasonable choices of parameters but shows oscillations for extreme choices of parameters and we find that the system is resilient to perturbations. We identify a trade-off between reaching equilibria of high performance and having short transients.

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Acknowledgements

We thank the anonymous reviewers for precise comments that helped to improve the manuscript significantly. Authors T. Schmickl and H. Hamann were supported by the following grants: EU-IST-FET project ‘SYMBRION’, no. 216342; EU-ICT project ‘REPLICATOR’, no. 216240. T. Schmickl was also supported by the following grants: EU-ICT ‘CoCoRo’, no. 270382; EU-ICT ‘ASSISIbf’, no. 601074; Austrian Science Fund (FWF) research grant P23943-N13 (REBODIMENT). The authors thank Wayne G. Basler for establishing the Chair of Excellence for the Integration of the Arts, Rhetoric and Science and East Tennessee State University for supporting T. Schmickl as Basler Chair and I. Karsai as Basler Host 2012. I. Karsai was supported by 12-005M RDC and E82141 grants from ETSU.

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Authors and Affiliations

  1. Department of Computer Science, University of Paderborn, Zukunftsmeile 1, 33102, Paderborn, Germany

    Heiko Hamann

  2. Department of Biological Sciences, East Tennessee State University, P.O. Box 70703, Johnson City, TN, 37614-0703, USA

    Istvan Karsai

  3. Artificial Life Laboratory of the Department of Zoology, Karl-Franzens University Graz, Universitätsplatz 2, 8010, Graz, Austria

    Thomas Schmickl

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  1. Heiko Hamann
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Correspondence to Heiko Hamann.

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Hamann, H., Karsai, I. & Schmickl, T. Time Delay Implies Cost on Task Switching: A Model to Investigate the Efficiency of Task Partitioning. Bull Math Biol 75, 1181–1206 (2013). https://doi.org/10.1007/s11538-013-9851-4

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  • DOI: https://doi.org/10.1007/s11538-013-9851-4

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