Erlang-R: A Time-Varying Queue with Reentrant Customers, in Support of Healthcare Staffing

Galit B. Yom-Tov () and Avishai Mandelbaum ()
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Galit B. Yom-Tov: Technion–Israel Institute of Technology, Technion City, Haifa 32000, Israel
Avishai Mandelbaum: Technion–Israel Institute of Technology, Technion City, Haifa 32000, Israel

Manufacturing & Service Operations Management, 2014, vol. 16, issue 2, 283-299

Abstract: We analyze a queueing model that we call Erlang-R, where the “R” stands for reentrant customers. Erlang-R accommodates customers who return to service several times during their sojourn within the system, and its modeling power is most pronounced in time-varying environments. Indeed, it was motivated by healthcare systems, in which offered-loads vary over time and patients often go through a repetitive service process. Erlang-R helps answer questions such as how many servers (physicians/nurses) are required to achieve predetermined service levels. Formally, it is merely a two-station open queueing network, which, in a steady state, evolves like an Erlang-C ( M / M / s ) model. In time-varying environments, on the other hand, the situation differs: here one must account for the reentrant nature of service to avoid excessive staffing costs or undesirable service levels. We validate Erlang-R against an emergency ward (EW) operating under normal conditions as well as during a mass casualty event (MCE). In both scenarios, we apply time-varying fluid and diffusion approximations: the EW is critically loaded and the MCE is overloaded. In particular, for the EW we propose a time-varying square-root staffing policy, based on the modified offered-load, which is proved to perform well over small-to-large systems.

Keywords: healthcare; queueing networks; modified offered-load; time-varying queues; Halfin–Whitt regime; QED regime; ED regime; emergency department staffing; mass casualty events; patient flow (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (46)

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