  This paper establishes the continuity of the path delay operators for dynamic
network loading (DNL) problems based on the Lighthill-Whitham-Richards model,
which explicitly capture vehicle spillback. The DNL describes and predicts the
spatial-temporal evolution of traffic flow and congestion on a network that is
consistent with established route and departure time choices of travelers. The
LWR-based DNL model is first formulated as a system of partial differential
algebraic equations (PDAEs). We then investigate the continuous dependence of
merge and diverge junction models with respect to their initial/boundary
conditions, which leads to the continuity of the path delay operator through
the wave-front tracking methodology and the generalized tangent vector
technique. As part of our analysis leading up to the main continuity result, we
also provide an estimation of the minimum network supply without resort to any
numerical computation. In particular, it is shown that gridlock can never occur
in a finite time horizon in the DNL model.
