Time delay implies cost on task switching: a model to investigate the efficiency of task partitioning

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.