title: Queueing theory applied to pre-hospital and retrieval medicine
Creators: name: Moultrie, Christopher E.J.
Publisher: name: University of Glasgow
Year: 2021

description: Background: Pre-hospital and Retrieval Medicine is a healthcare specialty focussed on the provision of advanced, specialist care to patients in any clinical setting - from the roadside to a major hospital. The ScotSTAR division of the Scottish Ambulance Service has a national remit for providing such services within Scotland. High clinical acuity and long travel time challenge the service by generating a significant workload from relatively few patients. ScotSTAR teams comprise only one or two servers, so waiting times are potentially long, and there is a relatively high per-patient cost. Aims: Firstly, this thesis aims to investigate if standard queueing theory could be used to describe two ScotSTAR teams: the Scottish Paediatric Retrieval Service (SPRS) and the Emergency Medical Retrieval Service (EMRS). The thesis then aims to develop a Discrete Event Simulation (DES) model and validate it against the real-world. From this model, the thesis then aims to describe the performance of the ScotSTAR teams using metrics which are unmeasurable in the real-world. Finally, the thesis aims to establish the performance frontiers of the ScotSTAR teams. Methods: Analysis of the ScotSTAR teams to map their operation with standard queueing theory was undertaken. This was used to develop a DES model, which performed 1000 simulation iterations of a 4-year period. The output was compared to the real-world data for accuracy with regard to: number of missions, activation time of day, inter-arrival time, mission duration, and server utilization. The validated model was then used to derive values for length of queue, waiting time, and proportion of simultaneous retrievals. Finally, the model was run in an extended Monte-Carlo format to establish the relationship of the current system to proposed performance frontiers based on waiting time, simultaneous retrievals, and missed missions. Results: This thesis demonstrated that standard queueing theory could describe the operations of the ScotSTAR systems, describing M/G/1 and M/G/2 queue types for SPRS and EMRS respectively. The DES model based on this was able to accurately replicate the real-world system in retrospective simulation (mean model accuracy: SPRS = 91.0%, EMRS = 91.9%), and partially replicate the contemporaneous state of the system (mean model accuracy: SPRS = 82.2%, EMRS = 89.0%). The model then derived plausible values for length of queue, waiting times, and simultaneous retrieval proportions. Lastly, the model demonstrated a 95th percentile of waiting time (Wq95) of 1 hour for secondary retrievals as being the most significant performance frontier. SPRS was demonstrated to be operating approximately 196 missions per year over this frontier, EMRS had capacity for an extra 26 primary or 23 secondary missions per year before reaching the frontier. Conclusions: Standard queueing theory is able to accurately describe the constituent parameters of the ScotSTAR systems. A discrete event simulation model can, with some limitations, accurately replicate the real-world to allow the derivation of performance descriptors which are unmeasurable in the real-world. Furthermore, such a model can also demonstrate the relationship between the current state of the system and potential performance frontiers.