Collaboration and Multitasking in Networks: Prioritization and Achievable Capacity

Abstract

Motivated by the trend toward more collaboration in workflows, 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 [Gurvich I, Van Mieghem JA (GVM1) Collaboration and multitasking in networks: Architectures, bottlenecks, and capacity. Manufacturing Service Oper. Management 17(1):16–33], 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. This paper studies how task prioritization impacts the achievable capacity of such hierarchical networks using a conceptual queueing framework that formalizes coordination and switching idleness. To maximize the capacity of a collaborative network, highest priority must 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 fundamental tension between flexibility in task prioritization (ability to adjust quality of service) and capacity (productivity) 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. The online companion is available at https://doi.org/10.1287/mnsc.2017.2722 . This paper was accepted by Noah Gans, stochastic models and simulation.