Collaboration and Multitasking in Networks: Architectures, Bottlenecks, and Capacity

Motivated by the trend toward more collaboration in work flows, we study networks where some activities require the simultaneous processing by multiple types of multitasking human resources. Collaboration imposes constraints on the capacity of the process because multitasking resources have to be simultaneously at the right place. We introduce the notions of collaboration architecture and unavoidable bottleneck idleness to study the maximal throughput or capacity of such networks. Collaboration and multitasking introduce synchronization requirements that may inflict unavoidable idleness of the bottleneck resources: even when the network is continuously busy (processing at capacity), bottleneck resources can never be fully utilized. The conventional approach that equates network capacity with bottleneck capacity is then incorrect because the network capacity is below that of the bottlenecks. In fact, the gap between the two can grow linearly with the number of collaborative activities. Our main result is that networks with nested collaboration architectures have no unavoidable bottleneck idleness. Then, regardless of the processing times of the various activities, the standard bottleneck procedure correctly identifies the network capacity. We also prove necessity in the sense that, for any nonnested architecture, there are values of processing times for which unavoidable idleness persists. The fundamental trade-off between collaboration and capacity does not disappear in multiserver networks and has important ramifications to service-system staffing. Yet, even in multiserver networks, a nested collaboration architecture still guarantees that the bottleneck capacity is achievable. Finally, simultaneous collaboration, as a process constraint, may limit the benefits of flexibility. We study the interplay of flexibility and unavoidable idleness and offer remedies derived from collaboration architectures.