论文标题
定时培养皿网的分段仿射动力学模型 - 申请紧急呼叫中心
Piecewise Affine Dynamical Models of Timed Petri Nets -- Application to Emergency Call Centers
论文作者
论文摘要
我们使用预选和优先路由研究定时的培养皿网。我们通过分段仿射动力学系统表示这些系统的行为。我们使用非专业映射理论中的工具来分析这些系统。我们在无优先流体的定时PETRI网和半马多夫决策过程之间建立了等效定理，从中我们将收敛性得出到周期性制度和吞吐量的多项式时间计算性。更普遍地，我们开发了一种受热带几何形状启发的方法，将拥塞阶段描述为多面体复合物的细胞。我们通过当前对巴黎地区紧急呼叫中心的绩效评估的应用来说明这些结果。我们表明，优先级可以导致矛盾的行为：在某些制度中，最先前的任务的吞吐量可能不是资源的增加功能。
We study timed Petri nets, with preselection and priority routing. We represent the behavior of these systems by piecewise affine dynamical systems. We use tools from the theory of nonexpansive mappings to analyze these systems. We establishan equivalence theorem between priority-free fluid timed Petri nets and semi-Markov decision processes, from which we derive the convergence to a periodic regime and the polynomial-time computability of the throughput. More generally, we develop an approach inspired by tropical geometry, characterizing the congestion phases as the cells of a polyhedral complex. We illustrate these results by a current application to the performance evaluation of emergency call centers in the Paris area. We show that priorities can lead to a paradoxical behavior: in certain regimes, the throughput of the most prioritary task may not be an increasing function of the resources.
