定时Petri网的分段仿射动力学模型——应用于紧急呼叫中心
Piecewise Affine Dynamical Models of Timed Petri Nets -- Application to Emergency Call Centers
AI总结：
本文通过分段仿射动力系统建模定时Petri网，利用非扩张映射和热带几何分析，建立了与半马尔可夫决策过程的等价性，并应用于巴黎紧急呼叫中心，发现优先级可能导致吞吐量悖论。
摘要：
我们研究了具有预选择和优先级路由的定时Petri网。我们将这些系统的行为表示为分段仿射动力系统。我们利用非扩张映射理论中的工具来分析这些系统。我们在无优先级的流体定时Petri网与半马尔可夫决策过程之间建立了一个等价定理，由此推导出周期状态的收敛性以及吞吐量的多项式时间可计算性。更一般地，我们开发了一种受热带几何启发的分析方法，将拥塞阶段表征为多面体复形的胞腔。我们通过当前应用于巴黎地区紧急呼叫中心性能评估的实例来展示这些结果。我们表明，优先级可能导致一种悖论行为：在某些状态下，最高优先级任务的吞吐量可能不是资源的递增函数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
