  This paper presents a macroscopic fundamental diagram model with volume-delay
relationship (MFD-VD) for road traffic networks, by exploring two new data
sources: license plate cameras (LPCs) and road congestion indices (RCIs). We
derive a first-order, nonlinear and implicit ordinary differential equation
involving the network accumulation (the {\it volume}) and average congestion
index (the {\it delay}), and use empirical data from a 266 km$^2$ urban network
to fit an accumulation-based MFD with $R^2>0.9$. The issue of incomplete
traffic volume observed by the LPCs is addressed with a theoretical derivation
of the observability-invariant property: The ratio of traffic volume to the
critical value (corresponding to the peak of the MFD) is independent of the
(unknown) proportion of those detected vehicles. Conditions for such a property
to hold are discussed in theory and verified empirically. This offers a
practical way to estimate the ratio-to-critical-value, which is an important
indicator of network saturation and efficiency, by simply working with a finite
set of LPCs. The significance of our work is the introduction of two new data
sources widely available to study empirical MFDs, as well as the removal of the
assumptions of full observability, known detection rates, and spatially uniform
sensors, which are typically required in conventional approaches based on loop
detector and floating car data.
