Collaboration and Multitasking in Networks: Architectures, Bottlenecks and Capacity

Abstract

Motivated by the trend towards more collaboration in work flows, we study stochastic processing networks where some activities require the simultaneous collaboration of multiple human resources and also share some resources with other activities. We introduce the notions of collaboration architecture and unavoidable bottleneck idleness to study the maximal throughput or capacity of such networks. Collaboration and resource sharing 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.

Our positive 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 non-nested architecture, there are values of processing times for which unavoidable idleness persists.

The fundamental tradeoff between collaboration and capacity does not disappear in multi-server networks and has important ramifications to service-system staffing. Yet, even in multi-server 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.

Keywords: simultaneous collaboration, architecture, workflow design, organizational design, capacity, stability, flexibility, control, priorities, bottlenecks