**报告人****/Speaker****：****Prof. M. Kolonko**，Clausthal University of Technology, Germany

**报告题目****/Title****: **Modelling Delay Propagation in Railway Networks Using Closed Families of Distributions

**时间****/Date & Time****：**Sep. 11 (Monday) , 2017, 14:00-15:30

**地点****/Location****：北京科学与工程计算研究院**（理科楼M八层）843会议室

Conference Room, M844, BISEC, Scientific Research Building M

**报告摘要****/Abstract****：**In railway networks, small delays seem to be inevitable in the every-day operation of trains. These source delays may accumulate and propagate throughout the network leading to larger delays, missed connections and a poor system performance. In this talk we develop a model that allows to determine the distributions of the propagated delays at all stations given the distribution of the source delays. This may e.g. be used to evaluate the robustness of a given time-table against typical delays or to compare different types of waiting time rules ("wait at most ten minutes for a delayed feeder"). The accumulation, propagation and reduction of delays is modelled by corresponding operations on distribution functions (cdf) of the random delays. If we restrict the cdf to certain (large) families of parametrized distributions, these operations can be efficiently performed with sufficient precision. In most cases, the event-activity-network that models the real network will contain cycles. In order to obtain a stable operation, the delay distributions within these cycles must converge. We give simple conditions, borrowed from queueing theory, that guarantee the existence of equilibrium distributions in cycles. The validity of this approach is shown on a simple network where we compare our analytical results to a Monte Carlo simulation which is very precise but also extremely time-consuming.

**报告人简介****/About the speaker: ****Prof. Dr. Michael Kolonko** received his Diploma degree in Mathematics in 1976, and his PhD with a thesis on stochastic dynamic programming in 1979 from Bonn University (Germany). Then, he did his Habilitation for mathematics at Karlsruhe University from 1979 to 1983. After that, he joined Siemens Corporation for software research and development. Since 1987, he became a full Professor for Computer Science and Applied Mathematics at Hildesheim University. Since 1996, he led the stochastic optimization group at Clausthal University of Technology, Germany. His research interests are stochastic modelling and heuristic optimization, modelling of public transport, and simulating particle systems in material science. Up to now, he has published numerous articles in these fields, and did a lot of relevant projects granted by industries.