基于分层时间Petri网的应急呼叫中心暂态边界计算
Computing Transience Bounds of Emergency Call Centers: a Hierarchical Timed Petri Net Approach
摘要：
紧急呼叫中心分析的一个基本问题是估计在大量呼叫到达的不寻常事件后返回无故障状态所需的时间。呼叫中心通常可以用具有层次结构的时间Petri网来表示，其中几层描述了呼叫处理的连续步骤。我们研究了连续近似的Petri网动态（与无穷小令牌）。然后，我们表明，计数器功能，测量的偏离平稳政权，符合半马尔可夫判定问题的价值函数。然后，我们建立了一个有限时间收敛的结果，利用Petri网的层次结构。我们得到了一个明确的界限的瞬态时间，作为一个功能的初始标记和逗留时间。这是基于随机最短路径理论和非线性Perron-Frobenius理论的方法。我们说明了一个医疗急救呼叫中心的案例研究的界限。
英文摘要：
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.
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