Collaboration and Multitasking in Networks: Aligning Task Priorities and Collaboration Levels

Motivated by the trend towards more collaboration in team work, we study networks where some tasks require the simultaneous processing by multiple types of multitasking human or indivisible resources. The capacity of such networks is generally smaller than the bottleneck capacity. In Gurvich and Van Mieghem (2015) we proved that both capacities are equal in networks with a hierarchical collaboration architecture, which define a collaboration level for each task depending on how many types of resources it requires relative to other network tasks. This paper studies how task prioritization impacts the capacity of such hierarchical networks using a conceptual queuing framework that formalizes coordination and switching idleness. To maximize the capacity of a team, highest priority should be given to the tasks that require the most collaboration. Otherwise, a mismatch between priority levels and collaboration levels inevitably inflicts a capacity loss. We demonstrate this essential trade-off between task prioritization and capacity in a basic collaborative network and in parallel networks. To manage this trade-off, we present a hierarchical threshold priority policy that balances switching and coordination idleness.