Capacity planning of a perinatal network with generalised loss network model with overflow

• We develop a generalised loss network for capacity planning of a perinatal network.
• The model captures overflow and rejection from each hospital of the network.
• A two-moment approximation is performed for the steady state solution of the system.
• Number of required cots can be determined based on the rejection probability.
• UCLH and Barnet require additional cots to keep the rejection level low.

Recent literature shows that the arrival and discharge processes in hospital intensive care units do not satisfy the Markovian property, that is, interarrival times and length of stay tend to have a long tail. In this paper we develop a generalised loss network framework for capacity planning of a perinatal network in the UK. Decomposing the network by hospitals, each unit is analysed with a GI/G/c/0 overflow loss network model. A two-moment approximation is performed to obtain the steady state solution of the GI/G/c/0 loss systems, and expressions for rejection probability and overflow probability have been derived. Using the model framework, the number of required cots can be estimated based on the rejection probability at each level of care of the neonatal units in a network. The generalisation ensures that the model can be applied to any perinatal network for renewal arrival and discharge processes.