Day-to-day Traffic Assignment Model of Heterogeneous Travelers in Urban Road Network under MaaS Mode
To study the day-to-day routing behavior and traffic distribution evolution of heterogeneous users in urban road networks under the Mobility as a Service(MaaS)model,travelers are classified into platform users who select MaaS services and free users who make their own decisions.The travel behaviors of the two types of users are described as follows:(1)During the day-to-day decision-making process,users adjust whether to continue accepting platform scheduling,implying that user attributes change during the day-to-day deduction.(2)Free users seek to maximize their own travel utility and adjust their routes in day-to-day travel.(3)The platform plans and publishes the system path based on pre-trip input from users,ensuring the principle of System Optimal(SO).Under the MaaS model,heterogeneous users decide whether to change their travel mode and routes for the day based on the previous day's travel outcomes.The changes in user travel decisions lead to shifts in the final distribution state of network traffic,thereby influencing users'travel on the following day.Further-more,this paper calculates the average travel time for both platform users and free users across all routes and,based on the principle of bounded rationality,defines a threshold where the travel time saved by an alternative exceeds the tolerance level,at which point users may reconsider whether to join the MaaS platform.Thus,based on these tolerance levels,transition probabilities are calculated,a day-to-day adjustment model for the total number of both types of users are established.Similarly,a day-to-day transition model for free users'routes is developed based on the time saved and tolerance values.The day-to-day model distributes the total number of MaaS users to routes following the SO principle,and transforms the path impedance to establish a User Equilibrium(UE)model equivalent to SO.The model's Frank-Wolfe algorithm solution is also provided.The paper demonstrates the principle of flow conservation in the overall model and uses fixed point theory to analyze whether solutions to the model exist.Using the FOURSIX network as an example to validate the model,the following conclusions are reached:(1)At equilibrium,the travel times for different routes of the same origin-destination(OD)pair are not the same,and the difference in travel times between routes reflects the tolerance value of bounded rationality users.(2)The adjustment of the total travel time in the network gradually weakens from the initial intense state,and the network is not stable at an optimal state,mainly due to differences in individual user utilities and issues such as fairness during the allocation process,resulting in unstable route flows,with heterogeneous users still likely to reselect on the second day based on the utility they receive.(3)At equilibrium,the overall proportion of platform users in the network increases,indicating that MaaS travel services have certain advantages and attractions,but there is a need for corresponding strategies to retain users.(4)The total travel time in a network of heterogeneous users is always less than that of pure free users,indicating that MaaS travel services optimize the network by fully utilizing network facilities and reducing overall travel time.
mobility as a serviceday-to-day traffic assignment modelheterogeneous userssystem optimiza-tionbounded rationality
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