  We consider an integro-differential equation model for traffic flow which is
an extension of the Burgers equation model. To discuss the model, we first
examine general settings for integrable integro-differential equations and find
that they are obtained through a simple residue formula from integrable
eqations in a complex domain. As demonstration of the efficiency of this
approach, we list several integrable equations including a difference equation
with double singular integral and an equation with elliptic singular integral.
Then, we discuss the traffic model with singular integral and show that the
model exhibits interaction between free flow region and congested region
depending on the parameter of non-locality.
