Use and misuse of Queueing Theory for hospital capacity decisions

This chapter is based on experiences with applying Queueing Theory at an NHS acute hospital trust in Greater Manchester in the UK, for resizing its paediatric inpatient department. With an average bed occupancy of 54%, the hospital management thought it would be possible to reduce the number of beds, as according to a rule of thumb a target bed occupancy of 85% should be possible. Originating from a Monte Carlo computer simulation study, the 85-bed occupancy target had found its way into acute hospitals within the NHS, despite of the fact that the setting of the simulation study could be very different from the setting looked at. Certainly, in this case as in paediatrics, most admissions are emergency, and children cannot be transferred to another ward.

By applying the basics of Queueing Theory to the setting of the paediatric department, is was possible to show that using a bed occupancy target of 85% would result in a risk of 33% that all beds would be full – which was clearly unacceptable – and that using a very low risk of all beds full of 0.1% (as data for English hospitals suggest for paediatrics) would result in an average bed occupancy of 55%. So, no bed reduction was recommended.

In this chapter, examples are also provided of the use of Queueing Theory for pooling wards, and for reducing the variation in arrivals and in service times.