Itai Gurvich

Gurvich, Itai and Jan A. Van Mieghem. 2015. Collaboration and multitasking in networks: Architectures, Bottlenecks and Throughput. Manufacturing & Service Operations Management (M&SOM). 17(1): 16-33.

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. Collaboration introduces resource synchronization requirements that are not captured in the standard procedure (formalized through a static planning problem) to identify bottlenecks and theoretical capacity. We introduce the notions of collaboration architecture and unavoidable idleness. In general, collaboration architectures may feature unavoidable idleness so that the theoretical capacity exceeds the maximal achievable throughput or actual capacity. This fundamental tradeoff between collaboration and throughput does not disappear in multi-server networks and has important ramifications to service-system staffing. We identify a special class of collaboration architectures that have no unavoidable idleness and present a condition on this architecture that guarantees, regardless of the processing times of the various activities, that the standard bottleneck procedure in fact identifies the actual capacity of the network. In multi-server cases this class of networks guarantees that the theoretical capacity is achievable provided one has the right number of floaters. Finally, we study the subtleties that collaboration introduces to questions of flexibility investment. Unavoidable idleness may limit the ability to materialize the benefits of flexibility. We study the interplay of flexibility and unavoidable idleness and offer remedies derived from collaboration architecture.

Gurvich, Itai. 2014. Validity of heavy-traffic steady-state approximations in multiclass queueing networks: The case of queue-ratio disciplines. Mathematics of Operations Research. 39(1): 121-162.

A class of stochastic processes known as semi-martingale reflecting Brownian motions (SRBMs) is often used to approximate the dynamics of heavily loaded queueing networks. In two influential papers, Bramson (1998) and Williams (1998) laid out a general and structured approach for proving the validity of such heavy-traffic approximations, in which an SRBM is obtained as a diffusion limit from a sequence of suitably normalized workload processes. However, for multiclass networks it is still not known in general whether the steady-state distribution of the SRBM provides a valid approximation for the steady-state distribution of the original network. In this paper we study the case of queue-ratio disciplines and provide a set of sufficient conditions under which the above question can be answered in the affirmative. In addition to standard assumptions made in the literature towards the stability of the pre- and post-limit processes and the existence of diffusion limits, we add a requirement that solutions to the fluid model are attracted to the invariant manifold at linear rate. For the special case of static-priority networks such linear attraction is known to hold under certain conditions on the network primitives. The analysis elucidates some interesting connections between stability of the pre- and post-limit processes, their respective fluid models and state-space collapse, and identifies the respective roles played by all of the above in establishing validity of heavy-traffic steady-state approximations.