Optimum Equilibrium Passenger Flow Control Strategies with Delay Penalty Functions under Oversaturated Condition on Urban Rail Transit

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When passengers are oversaturated in the urban rail transit system and a further increase of train frequency is impossible, passenger flow control strategy is an indispensable approach to avoid congestion and ensure safety. To make the best use of train capacity and reduce the passenger waiting time, coordinative flow control is necessary at each station on a line. In most published studies, the equilibrium of passenger distributions among different stations and periods is not considered. As a result, two issues occur making it hard to implement in practical. First, a large number of passengers are held up outside a small number of stations for very long time. Second, there is a large variation of controlled flows for successive time intervals. To alleviate this problem, a single-line equilibrium passenger flow control model is constructed, which minimizes the total passenger delay. By applying different forms of the delay penalty function (constant and linear), flow control strategies such as independent flow control and equilibrium flow control can be reproduced. An improved simulated annealing algorithm is proposed to solve the model. A numerical case is studied to analyze the sensitivity of the functions, and the best parameter relationship in different functions could be confirmed. A real-world case from Batong Line corridor in Beijing subway is used to test the applicability of the model and algorithm, and the result shows that the solution with linear delay penalty functions can not only reduce the total passenger delay but also equilibrate the number of flow control passengers on spatial and temporal.