Equilibrium Analysis And Fare Reward Scheme For Transit Morning Commute Considering The Random Delay

Since the classical bottleneck model was proposed,it has been widely used in the study of commuting problems including private car commuters and public transport commuters.Most studies use deterministic bottleneck models to analyze commuting scenarios without considering randomness.However,there are various kinds of randomness in the transportation system,including the randomness of road capacity and passenger travel demand.Accordingly,the random bottleneck model is constructed to describe the commuting scenario considering randomness.This paper presents a bottleneck model for subway commuting considering random delay.It is assumed that subway commuters need to transfer to the ground bus to get to work place after taking subway,and the ground bus has random delay.This paper discusses the impact of random delay of ground bus on the travel behavior of subway commuters in the morning rush hour,and then studies the fare-reward scheme.This paper assumes that the random delay time that commuters may encounter after transferring to ground buses is T,and T is uniformly distributed within the range of),0(b.In equilibrium,it is assumed that the expected costs of commuters are equal.Our study indicates that,with the constant increase of b value,the whole rush hour commuters appeared in three states.The travel behavior of commuters in these three states is analyzed respectively and the analytic solutions of total cost expectation of system and total cost expectation of individual travel are given.Next,the fare reward scheme proposed by Yang and Tang in 2018 is analyzed based on the difference of random delay fluctuation amplitude.How to set the charging range and how to determine the charging ratio are studied.The study found that when random delays fluctuated widely,FRS results in an optimal reward ratio up to 50%,and the total time cost of the system and the total cost of individual travel were reduced at most by less than 5%.In the case of moderate fluctuation of random delay,the closed form solution of the maximum charge ratio can not be obtained,but the effect of FRS is much better,the total time cost of the system is reduced by 12%,and the total cost of personal travel is reduced by nearly 11%.FRS worked best with small fluctuations in random delays,reducing total time costs by up to 25% and total personal travel costs by up to nearly 19%.At the same time,when the delay fluctuation tends to zero,the charge ratio tends to 50%,which is consistent with the result of the certainty model.The research results can provide scientific basis for proposing reasonable traffic management and control measures to reduce the cost of subway commuting in rush hours.