Time to Critical Condition in Emergency Services

Pedro A Pury

doi:10.3390/mca26040070

Abstract

Providing uninterrupted response service is of paramount importance for emergency medical services, regardless of the operating scenario. Thus, reliable estimates of the time to the critical condition, under which there will be no available servers to respond to the next incoming call, become very useful measures of the system’s performance. In this contribution, we develop a key performance indicator by providing an explicit formula for the average time to the shortage condition. Our analytical expression for this average time is a function of the number of parallel servers and the inter-arrival and service times. We assume exponential distributions of times in our analytical expression, but for evaluating the mean first-passage time to the critical condition under more realistic scenarios, we validate our result through exhaustive simulations with lognormal service time distributions. For this task, we have implemented a simulator in R. Our results indicate that our analytical formula is an acceptable approximation under any situation of practical interest.

Highlights

The problem of assigning resources to respond to a stochastic demand is a ubiquitous topic in operational research
We provide an explicit analytical expression for the mean first-passage time (MFPT) to the critical condition, and, on the other hand, under more realistic conditions, we analyze the validity of our assumptions through exhaustive simulations
We have presented a closed-form expression to calculate the MFPT for a system of servers in parallel, and we provide a simulation framework for the MFPT

Summary

Introduction

The problem of assigning resources to respond to a stochastic demand is a ubiquitous topic in operational research. The development of Key Performance Indicators (KPIs) to objectively quantify the performance across the operational, clinical and financial departments is a current demand of an industry increasingly data driven. Among the most intuitive and used operational KPIs in EMS are the successive times involved in the service cycle: call reception, patient triage, dispatch, ambulance turnout, travel from the base to the emergency site, paramedic care, eventual transfer of the patient to a hospital, and return of the ambulance to its base. Response time (the interval between the reception of an emergency call and the arrival of a paramedic at the scene of the event) is a common operational metric of EMS and it is considered a good indication of the quality offered by the service [1].

Objectives

Results

Conclusion