| With the rapid development of urban rail transit, it has improved the status of the city, promoted economic growth along the subway lines, expanded the capacity of urban public transport and alleviated the traffic congestion of urban roads, etc. However, the urban rail transit is concentrated, instantaneous and the transport capacity cannot be stored. Currently, there appears a common phenomenon in several major domestic cities that subway stations are crowded and trains are often overloaded during the peak periods, while during the trough periods, the subway system suffers a sharp drop on passenger volume and high empty-loaded ratio for the vehicles. In order to alleviate overcrowding during the peak periods, it can be considered to adopt the time differential pricing strategy, by which to achieve the goal of shifting partial peak demands to off-peak periods. On the basis of exploring the feasibility of time differential pricing strategy, this paper takes Beijing subway for example to propose time differential pricing models for urban rail transit and provides scientific basis for the time differential pricing strategy of urban rail transit.Firstly, the effect of time differential pricing strategy that has been implemented in foreign metro systems is analyzed, such as Melbourne, Singapore, Washington, London, New York, etc. As the subway passenger volume is unbalanced and price elasticity of demand vary from peak to off-peak periods, the feasibility of time differential pricing strategy is explored based on congestion pricing and revenue management theory. In the meanwhile, the advantages and disadvantages of the most commonly used time differential pricing models are discussed, such as the Ramsey pricing model and the Bertrand Nash Equilibrium Model.Secondly, time differential pricing models are proposed. Beijing subway is taken for example and passengers’ travel characteristics during the weekdays’ peak and weekend’s off-peak period are analyzed respectively. For different purposes, two bi-level programming models are established for peak and off-peak period to achieve the balance between the two contradictory bodies:the urban rail transit enterprise and the passengers. The enterprise aims to achieve the maximum benefit competing with other travel modes while the passengers expect the minimum generalized travel costs. This paper also proposes a pricing method to shift partial peak demands of an interval in a subway line.Thirdly, particle swarm iterative algorithm is proposed to solve the morning peak period differential pricing bi-level programming model and Karush-Kuhn-Tucker Method is used to solve the off-peak period bi-level programming model. An example is presented for morning peak period differential pricing bi-level programming model, Beijing subway is taken for reference while setting the parameters, then the implementation effect of time differential pricing strategy is evaluated, which verifies the effectiveness and validity of the proposed model and algorithm.Finally, this paper provides a series of suggestions for implementing the time differential pricing strategy and points out the future direction of the study. |
