Incorporation of non-persistent delays at signalised intersections in the link transmission model

Abstract

In macroscopic dynamic traffic assignment, traffic flows are allocated to a transport network by means of a dynamic network loading model, with travel time being a primary output. Dynamic network loading not only determines the flows on roads, facilitated by a link model, but also governs flows passing through intersections by means of a node model. Notably, in urban settings, most travel time delays arise due to queue formations at intersections. These intersection delays can be categorised into persistent and non-persistent delays. Contemporary flow-based models – such as link transmission models (LTM) – account for persistent delays through boundary conditions imposed by the node model. Non-persistent delays are absent in most existing LTM formulations unless green and red phases are explicitly simulated at a more detailed microscopic level. In this work, we propose a novel methodology to directly integrate non-persistent delays into the LTM formulation in which the effects of traffic lights are averaged without violating the First-In-First-Out (FIFO) principle this model relies on. To achieve this, one or more virtual links are implicitly considered in an augmented link model representation, wherein Webster’s uniform delay is reformulated as a hypocritical branch of an associated fundamental diagram. Augmented algorithms for networks are provided for the cases of link-specific or movement-specific exit capacities and numerical examples are provided to illustrate the new approach. The proposed methodology results in a more realistic depiction of traffic dynamics by directly embedding non-persistent delay in the network loading propagation scheme. In doings so, enhanced accuracy in travel time and traffic flow predictions compared to existing best-practice in macroscopic dynamic network loading can be achieved.