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 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 an simulator in $R$. Our results indicate that our analytical formula is an acceptable approximation under any situation of practical interest.
翻译：提供不间断反应服务对紧急医疗服务至关重要,无论业务情况如何,因此,可靠估计到危急状态的时间(在危急状态下没有可用的服务器来应对下一个呼叫),成为衡量系统性能的非常有用的尺度。我们为此制定了一个关键业绩指标,为短缺状况的平均时间提供一个明确的公式。我们对这一平均时间的分析表达方式取决于平行服务器的数量以及抵达之间和服务时间。我们假设分析表达方式中的时间的指数分布,但在更现实的假设下,我们通过对逻辑正常服务时间分布进行详尽的模拟,对临界状态的平均值第一通行时间进行评估,我们验证我们的结果。我们为此任务采用了一个模拟器,以美元为模拟器。我们的结果表明,在任何实际感兴趣的情况下,我们的分析公式是一种可以接受的近似值。
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