  We extend the measure-valued fluid model, which tracks residuals of patience
and service times, to allow for time-varying arrivals. The fluid model can be
characterized by a one-dimensional convolution equation involving both the
patience and service time distributions. We also make an interesting connection
to the measure-valued fluid model tracking the elapsed waiting and service
times. Our analysis shows that the two fluid models are actually characterized
by the same one-dimensional convolution equation.
