A Markov Chain Model for Transient Analysis of Handoff Process in Emergency Departments

Transfer of care between multiple units or facilities is of significant importance for patient safety, care quality, and operation efficiency. Such transfers are often referred to as handoffs in hospitals, which need to be carried out timely, safely, and smoothly with accurate information. This article introduces a Markov chain model to study the transients of handoff process in hospital emergency departments. The handoff process is modeled by a stochastic process with unavailability of service, which characterizes the constraints in bed capacity, staff shortage, and coordination issues, etc. For systems only allowing one transfer request waiting, the transient performance is obtained through Laplace transform and its inverse transform. Such a result is then used as a building block to study the systems allowing multiple requests waiting through an iteration process, which can reduce the computation complexity substantially. Numerical studies show that such a method can provide estimates of transient performance in the handoff process with acceptable accuracy.