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46 Forecasting the demand profile for a physician-led pre-hospital care service using a mathematical model
  1. CEJ Moultrie1,2,
  2. AR Corfield1,2,3,
  3. J Pell2,
  4. D Mackay2
  1. 1Scottish Ambulance Service ScotSTAR
  2. 2University of Glasgow
  3. 3NHS Greater Glasgow and Clyde


Aim We aimed to investigate if a queueing-theory derived, stochastic, computerised mathematical model could accurately predict the number and seasonal pattern of primary pre-hospital missions undertaken by a physician-led pre-hospital and retrieval service in 2016.

Methods We used queueing theory to derive parameters for a computer model built using the MATLAB software suite Simulink program. The model was primed with retrospective data, validated with contemporaneous data and then used to forecast 1 year ahead. A total of 100 iterations of the model were studied. The model output was compared to the real-world data with regard to total number of missions and seasonal pattern using standard statistical tests.

Results Our model forecast 547 missions (95% CI 516–586) during the prospective study period, compared to 565 real-world missions. (t-test p=0.21). The seasonal patterns were adequately matched to generate a non-significant result under the Kolmogorov-Smirnov test (p=0.14).

Conclusion Our model was able to correctly predict the number of pre-hospital primary retrieval missions undertaken by the ScotSTAR Emergency Medical Retrieval Service (EMRS) by demonstrating no statistically significant differences to the real-world mission numbers or distribution. This suggests that a queueing theory derived model is able to accurately replicate, and forecast, the real-world performance of ScotSTAR EMRS operations. This finding presents useful implications for resource utilisation, asset allocation and investigating system capability.


  1. Kendall DG. Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain. The Annals of Mathematical Statistics 24(3):1953.

Conflict of interest None declared.

Funding Scottish Ambulance Service ScotSTAR

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