Computer-Aided Civil and Infrastructure Engineering 23 (2008) 86–103 A Polymorphic Dynamic Network Loading Model Yu (Marco) Nie ∗ Department of Civil and Environmental Engineering, Northwestern University & Jingtao Ma & H. Michael Zhang † Department of Civil and Environmental Engineering, University of California, Davis, CA, USA Abstract: A polymorphic dynamic network loading (PDNL) model is developed and discretized to integrate a variety of macroscopic traffic flow and node models. The polymorphism, realized through a general node-link interface and proper discretization, offers several promi- nent advantages. First of all, PDNL allows road facilities in the same network to be represented by different traf- fic flow models based on the tradeoff of efficiency and realism and/or the characteristics of the targeted prob- lem. Second, new macroscopic link/node models can be easily plugged into the framework and compared against existing ones. Third, PDNL decouples links and nodes in network loading, and thus opens the door to parallel computing. Finally, PDNL keeps track of individual ve- hicular quanta of arbitrary size, which makes it possible to replicate analytical loading results as closely as desired. PDNL, thus, offers an ideal platform for studying both an- alytical dynamic traffic assignment problems of different kinds and macroscopic traffic simulation. 1 INTRODUCTION Dynamic network loading (DNL) is an underlying com- ponent of many dynamic network problems in which path costs depend on temporal path flows in ways gov- erned by traffic propagation and interaction. In the past † CKS Professor, Tongji University, Shanghai, China. ∗ To whom correspondence should be addressed. E-mail: y-nie@ northwestern.edu. two decades, DNL has been extensively studied owing to the needs of simulating urban traffic and solving dy- namic traffic assignment (DTA) problems. In this article we are concerned with the following DNL problem: Definition 1 (Dynamic Network Loading): The DNL problem determines, on a congested network and over a fixed time period, link cumulative arrival/departure curves (hence time-dependent link/path travel times) cor- responding to a given set of temporal path flow rates. In other words, DNL represents a mapping from path inflows to experienced travel times on the paths. Ac- cording to how they model traffic propagation and inter- action, existing DNL models may be classified into three groups: macroscopic, microscopic, and mesoscopic mod- els. Providing a complete list of all existing DNL mod- els/packages is difficult. Table 1 attempts to cover the best-known works in each of the three categories. 1 Although microscopic models provide the most de- tailed representation of traffic, they share two major limitations: the curse of high computational overhead, which often prohibits large-scale applications, and the analytical intractability often inherited from the Monte Carlo nature of the models. We are not suggesting, how- ever, that macroscopic models can solve the DNL prob- lem “analytically.” Indeed, even with the simplest as- sumptions, the mapping from path flow to path cost still cannot be cast in a closed form for general net- works. Nevertheless, for macroscopic models, analytical formulas for such a mapping may be obtained for spe- cial networks (e.g., with a single or two tandem links). C  2008 Computer-Aided Civil and Infrastructure Engineering. Published by Blackwell Publishing, 350 Main Street, Malden, MA 02148, USA, and 9600 Garsington Road, Oxford OX4 2DQ, UK.