Modelling patient flow and processes in emergency care
The core of my PhD. An emergency department is a queueing network coupled to finite resources, clinical decisions and a saturated hospital downstream. I build models there whose purpose is to let a reorganisation be tried before it is applied to real patients: where to place a nurse, how to order a queue, whether to open a bed.
The work falls into four stages. An exploratory analysis first characterises the department in its own right — who arrives and when, which pathways, which durations, how occupancy moves minute by minute — and determines what a model needs to represent. A deterministic compartmental model gives an aggregate reading of it, built by successive additions of mechanisms, each evaluated before the next is introduced. Then comes a discrete-event simulation, following patients one by one: routing is learned by gradient-boosted models specific to each area, durations are estimated from visits observed under low congestion, and delays emerge from queues, capacities and blocking rather than being supplied as parameters. Once validated, it serves as a laboratory for comparing organisational levers, each scenario replaying the same patients at the same arrival times. Out of this work came EDSim, a patient-flow modelling tool for emergency departments, which separates the simulation engine from the configuration of a given department.