In this paper we propose a novel static traffic assignment model where the network loading component accounts for non-stationary residual queues as well as spillback effects by explicitly adding capacity and storage constraints. This is achieved by deriving a static version of the dynamic general link transmission model that describes average link inflow and outflow rates during a given time period under simplified temporal assumptions. The resulting model adopts the same concave fundamental diagram and first order node model used in state-of-the-art macroscopic dynamic network loading without the need to explicitly describe time. We show that our mathematical problem formulation is an extension of several other models described in the literature, including the traditional capacity restrained static modelling paradigm. The equilibrium problem is formulated as a variational inequality problem while the network loading problem can be formulated as a fixed point problem. We prove that a solution exists to each problem as long as all traffic is loaded onto the network (i.e., no queue spillback into an origin). The model is illustrated via numerical examples on several hypothetical transport networks.

在本文中，我们提出了一种新颖的静态流量分配模型，其中，网络负载组件通过显式添加容量和存储约束来解决非平稳残留队列以及溢出效应。这是通过推导动态通用链路传输模型的静态版本来实现的，该模型描述了给定时间段内在简化的时间假设下的平均链路流入和流出速率。最终的模型采用了最新的宏观动态网络加载中使用的相同的凹形基础图和一阶节点模型，而无需明确描述时间。我们表明，我们的数学问题公式是文献中描述的其他几种模型的扩展，包括传统的容量约束静态建模范例。平衡问题可以表述为变分不等式问题，而网络负载问题可以表述为不动点问题。我们证明只要所有流量都加载到网络上（即没有队列溢出到源），就可以解决每个问题。通过几个假设的运输网络上的数值示例说明了该模型。