Using Queue Theory and Load-Leveling Principles to Identify a Simple Metric for Resource Planning in a Pediatric Emergency Department

Abstract

Increased waiting time in pediatric emergency departments is a well-recognized and complex problem in a resource-limited US health care system. Efforts to reduce emergency department wait times include modeling arrival rates, acuity, process flow, and human resource requirements. The aim of this study was to investigate queue theory and load-leveling principles to model arrival rates and to identify a simple metric for assisting with determination of optimal physical space and human resource requirements. We discovered that pediatric emergency department arrival rates vary based on time of day, day of the week, and month of the year in a predictable pattern and that the hourly change in pediatric emergency department waiting room census may be useful as a simple metric to identify target times for shifting resources to better match supply and demand at no additional cost.

Design of a mathematical model for staff planning in an emergency department

“…Table 3 shows a greater negative deviation (D jklm -) in the proposal. However, in shift 1, which has the highest weekly patient demand (37.48 %), the capacity deficit is lower in the optimization proposal with 4.09 % versus 8.60 % in the current situation, indicating adequate planning of medical staff according to the demand in each shift of the day, as mentioned in [2,7,9,10]. This capacity deficit results in an average waiting time for patients on shift 1 of 18.37 minutes in the current situation versus 16.62 minutes in the proposal.…”

“…Finally, a second mathematical model was designed based on the model of section 2.2, where the objective function (1) was modified by minimizing the number of physicians, as shown in (8). Furthermore, the constraint that ensures the deviations are positive (5) was changed by the capacity constraints presented in (9).…”

“…Medical staffing planning in the ED is to meet patient demand during aggregate blocks of time [5,7]. Planning human resources adjusted to patient demand is one strategy to reduce overcrowding and waiting times in EDs [9,10].…”