Fluctuating Efforts and Interdependencies in Collaborative Work

We present a dynamical model of cooperative efforts comprised of concurrently performed, interrelated tasks. The model contains a stochastic component to account for temporal fluctuations both in task performance and in the effect of a given unit of work on the project as a whole. We show that as the number of concurrent tasks increases, so does the average completion time. Also, for fixed system size, the dynamics of individual project realizations can exhibit large deviations from the average when fluctuations increase past a certain threshold, causing long delays in completion times. These effects are in agreement with empirical observation. We also show that the negative effects of both large groups and long delays caused by fluctuations may be mitigated by arranging projects in a hierarchical or modular structure. Our model is applicable to any arrangement of interdependent tasks, providing an analytical prediction for the average completion time as well as a numerical threshold for the fluctuation strength beyond which long delays are likely. In conjunction with previous modeling techniques, it thus provides managers with a predictive tool to be used in the design of a project’s architecture.