Oscillatory Traffic Flow Patterns Induced by Queue Spillback in a Simple Road Network

We study in this paper some consequences of queue spillback in a simple road network with a steady demand and provide exact formulas for traffic flow patterns. This one origin-destination pair, two-route network contains a diverge and a merge, and the interaction of queues formed at the merge produces several interesting traffic flow patterns, of which two types of oscillatory solutions are of particular interest. One of the oscillatory solutions is decaying, and the other is perfectly periodic. The latter resembles the stop-and-go pattern found in real-world traffic. Because a general road network usually contains many components like the simple network studied here, interaction of queues at junctions provides an alternative explanation to the formation of stop-and-go traffic.