论文标题
紧急呼叫中心的计算瞬时界限：分层定时培养皿网
Computing Transience Bounds of Emergency Call Centers: a Hierarchical Timed Petri Net Approach
论文作者
论文摘要
分析紧急呼叫中心的一个基本问题是估计在发生不寻常的事件之后，返回无拥堵政权所需的时间，并大量呼叫到达。呼叫中心通常可以用具有分层结构的定时培养皿网表示，其中几层描述了呼叫治疗的连续步骤。我们研究培养皿网动力学的连续近似（具有无限令牌）。然后，我们表明，计数器功能，测量了对固定机制的偏差，与半马尔可夫决策问题的价值函数一致。然后，我们建立了有限的时间收敛结果，利用了培养皿网的分层结构。我们获得了瞬态时间的显式绑定，这是初始标记和周时间的函数。这是基于随机最短路径理论和非线性perron--frobenius理论的方法。我们说明了医疗紧急呼叫中心的案例研究的界限。
A fundamental issue in the analysis of emergency call centers is to estimate the time needed to return to a congestion-free regime after an unusual event with a massive arrival of calls. Call centers can generally be represented by timed Petri nets with a hierarchical structure, in which several layers describe the successive steps of treatments of calls. We study a continuous approximation of the Petri net dynamics (with infinitesimal tokens). Then, we show that a counter function, measuring the deviation to the stationary regime, coincides with the value function of a semi-Markov decision problem. Then, we establish a finite time convergence result, exploiting the hierarchical structure of the Petri net. We obtain an explicit bound for the transience time, as a function of the initial marking and sojourn times. This is based on methods from the theory of stochastic shortest paths and non-linear Perron--Frobenius theory. We illustrate the bound on a case study of a medical emergency call center.
