Research On Rescheduling Optimization Model With Train Delay In Urban Rail Transit

Train delay are becoming common in the daily operation of urban subway.Under the influence of multi-line network operation,the transitivity of train delay will affect the normal operation of the whole system.At the same time,the variety of passenger behavior choices under train and network complexity make it difficult for train rescheduling.This paper aims to analyze passenger dynamic path choices and passenger impatience time under the condition of train delay.Train rescheduling model is proposed in order to provide a scientific basis for emergency management strategy in urban subway.A space-time subway network is proposed to describe passenger schedule based path choices when they face train delay.Passenger waiting time,train running time,transfer time are mainly considered.Three scenarios under train delay are considered as follows: keep the planned path choice;choose other alternative path to avoid train delay;give up their planned trips.With objective of minimizing the passenger total travel time,a schedule based searching algorithm is proposed to obtain the passenger dynamic path choice from arbitrary origin to destination.At the same time,the relationship between the effect of train delay to the passenger path choice and spatial distribution of the corresponding OD is obtained.Distribution of passenger impatience time under the condition of train delay is studied in this paper based on the actual survey data from subway passengers.And the function relation between impatience time and the total travel time is obtained.The law of diminishing marginal utility in microeconomics is used to concluded that the added value of passenger impatience time will reduce gradually with the increase of total travel time.The fitted function based on the data of questionnaire survey is used to verify the law of diminishing marginal utility between impatience time and the total travel time.On the basis of that,the condition of passenger giving up the planned trips due to train delay is quantified.With the objective of minimizing the weighted combination of travel time cost and the cost of giving up the planned trips,train rescheduling model is used for lines which are interconnected with delayed line in this research.Train stopping times and arrival times are chosen as the decision variables to minimize the effects of train delay,with the consideration of train stopping time,arrival time,headway constraints under train delay.Finally,the proposed train rescheduling model is implemented using genetic algorithm,and further examined through numerical experiments of Beijing urban subway train timetabling test.The optimization results show that the weighted combination of travel time cost and the cost of giving up the planned trips has been reduced by the proposed train rescheduling model,which clearly demonstrates the effectiveness of proposed train rescheduling model.At the same time,it provides the scientific and theoretical basis for passenger flow emergency management strategy in urban subway.