System complexity as a measure of safe capacity for the emergency department

System complexity is introduced as a new measure of system state for the emergency department (ED). In its original form, the measure quantifies the uncertainty of demands on system resources. For application in the ED, the measure is being modified to quantify both workload and uncertainty to produce a single integrated measure of system state.

Complexity is quantified using an information-theoretic or entropic approach developed in manufacturing and operations research. In its original form, complexity is calculated on the basis of four system parameters: 1) the number of resources (clinicians and processing entities such as radiology and laboratory systems), 2) the number of possible work states for each resource, 3) the probability that a resource is in a particular work state, and 4) the probability of queue changes (i.e., where a queue is defined by the number of patients or patient orders being managed by a resource) during a specified time period.

An example is presented to demonstrate how complexity is calculated and interpreted for a simple system composed of three resources (i.e., emergency physicians) managing varying patient loads. The example shows that variation in physician work states and patient queues produces different scores of complexity for each physician. It also illustrates how complexity and workload differ.

System complexity is a viable and technically feasible measurement for monitoring and managing surge capacity in the ED.