An approximation of the inpatient distribution in hospitals with patient relocation using Markov chains

Many hospitals struggle with insufficient capacity for their inpatients. As a result, hospitals may benefit from an approach that evaluates the occupancy of inpatient wards. In this study, we approximate the occupancy distributions of inpatient wards, accounting for the cases where patients relocate due to a shortage of beds. The approximation employs a homogeneous continuous-time Markov chain to evaluate each ward as a queue containing multiple classes of patients. We avoid computational intractability by evaluating each ward separately and accommodating patients arriving from the remaining wards by interrupting the arrival processes, where the interruption times follow hyper-exponential distributions. Numerical experimentation shows that our approach is robust concerning the type of length-of-stay distribution and generally results in a minor loss of accuracy. Further validation indicates that our model reflects the occupancy distributions of inpatient wards in a Danish hospital.