Comparing the number of Emergency Medical Dispatchers (EMDs) scheduled based on the judgment of the managers with predictions of the Erlang C formula: a brief report

Introduction: Currently, at Tehran Emergency Medical Service (EMS) centre, Emergency Medical Dispatchers (EMDs) are scheduled based on the managers’ experimental estimates. In this study, we planned to evaluate the conformity of managers’ predictions with the Erlang C formula estimates in scheduling EMDs. 
Methods: First, the Emergency Medical Communication Centre (EMCC) performance was evaluated over one week. Afterwards, the number of required EMDs was calculated using the Erlang C formula. Finally, the predictions of the Erlang C formula were compared with those of managers’ judgments.
Results: During the study period, 79,583 calls were received by the Tehran EMCC. The average number of EMDs per hour ranged between 9.5 and 22.7. The actual number of EMDs was more than Erlang C formula predictions during the 24 hours in all but three time points, i.e. 14:00–14:59, 15:00–15:59 and 18:00–18:59. In all hours, 90% of calls were answered in less than 10 seconds, and the average waiting time for a total of one week was 7.3 seconds. Also, only 2.1% of all calls were answered after 10 seconds. 
Conclusion: In the current study, we found that the number of EMDs scheduled based on the managers’ experimental estimates was higher than that of the Erlang C formula calculations. Also, it was found that the waiting time for emergency calls was lower than the defined standards. Although the primary results of the current study indicated that, at least on paper, the Erlang C formula has the potential to be used as a predicting model in the Tehran EMCC, further research is required to evaluate its effect on the actual performance of the EMCCs. 