基于极大代数理论的交通系统稳态性能分析

Analysis of the Steady State Performance of Traffic System Based on Max-plus Theory

为构建轨道交通系统优化调度方案,针对列车在轨道交通线网上的运行过程,通过将轨道交通系统视为一类离散事件动态系统,以及将单个列车视为一个批次,基于轨道交通系统调度规则和路网空间分布结构,在极大代数框架下建立了单区段和多区段轨道交通流开环和闭环控制模型,获取了系统输入变量、状态变量和输出变量之间的约束关系.从轨道交通系统输出演化过程出发,基于摄动分析法研究了不同列车排序形式对系统稳态周期性能的影响,以轨道交通系统过程的演化周期最短为优化目标,分析了多种列车排序方式的性能并获取了最优的系统调度方案.以保持系统演化周期稳态参量恒定为目标,进一步研究了单元素和多元素摄动情形下系统的鲁棒性.研究结果可为交通系统运行控制提供参考.

For the running process of the train in the rail transit line, the urban railway traffic system is regarded as a discrete event dynamic system. Based on the rail transit system dispatching rule and railway network space distribution structure, the single train is viewed as a batch in order to obtain the optimization scheduling scheme of rail transit system. Under the maximal algebraic framework, the open loop and closed loop control models of the single link and multi section traffic flow are established. Besides, the constraint relationship between the input variables, state variables and output variables is obtained. Starting from the state evolution of the rail transit system, the influence of different train scheduling forms on the system performance is studied based on the perturbation analysis method. The performance of several kinds of sorting methods and optimal system scheduling scheme are presented regarding rail transit system evolution process shortest period as optimization objective. Furthermore, the system robustness in the case of single element and multi element perturbation is put forward in order to maintain the steady state system evolution parameter. The research results can provide reference for the traffic system control.