In this work, we elaborate on the entropy argument for the trip-chain distribution and derive the unconstrained gravity model. From the most probable trip-chain configurations under the global constraints of the mean trip-chain length as well as the cost, the resulting flow is shown to follow the gravity law. We apply the model to assess the passenger flow in Seoul public transportation system. With the trip-chain cost taking into account the loss from trip time as well as the gain from visiting, the flow is estimated well from the numbers of departing and arriving passengers. It is thus concluded that the gravity model in general can be rationalized through the single paradigm of maximal entropy.

在这项工作中，我们详细阐述了绊链分布的熵论证，并推导了无约束重力模型。在平均行程链长度以及成本的全局约束下，从最可能的行程链配置中，得出的流量显示遵循重力定律。我们应用该模型评估首尔公共交通系统中的客流。考虑到行程链的成本，要考虑到行程时间的损失以及来访所带来的收益，因此从出发和到达的旅客人数中可以很好地估计客流。因此得出结论，一般而言，重力模型可以通过最大熵的单个范式来合理化。