  We propose a macroscopic modeling framework for a network of roads and
multi-commodity traffic. The proposed framework is based on the
Lighthill-Whitham-Richards kinematic wave theory; more precisely, on its
discretization, the Cell Transmission Model (CTM), adapted for networks and
multi-commodity traffic. The resulting model is called the Link-Node CTM
(LNCTM).
  In the LNCTM, we use the fundamental diagram of an "inverse lambda" shape
that allows modeling of the capacity drop and the hysteresis behavior of the
traffic state in a link that goes from free flow to congestion and back.
  A model of the node with multiple input and multiple output links accepting
multi-commodity traffic is a cornerstone of the LNCTM. We present the
multi-input-multi-output (MIMO) node model for multi-commodity traffic that
supersedes previously developed node models. The analysis and comparison with
previous node models are provided.
  Sometimes, certain traffic commodities may choose between multiple output
links in a node based on the current traffic state of the node's input and
output links. For such situations, we propose a local traffic assignment
algorithm that computes how incoming traffic of a certain commodity should be
distributed between output links, if this information is not known a priori.
