Periodic Little’s Law

Motivated by our recent study of patient flow data from an Israeli emergency department (ED), we establish a sample path periodic Little’s law (PLL), which extends the sample path Little’s law (LL). The ED data analysis led us to propose a periodic stochastic process to represent the aggregate ED occupancy level, with the length of a periodic cycle being 1 week. Because we conducted the ED data analysis over successive hours, we construct our PLL in discrete time. The PLL helps explain the remarkable similarities between the simulation estimates of the average hourly ED occupancy level over a week using our proposed stochastic model fit to the data and direct estimates of the ED occupancy level from the data. We also establish a steady-state stochastic PLL, similar to the time-varying LL.

The e-companion is available at https://doi.org/10.1287/opre.2018.1766.