  This study advocates a mathematical framework of ''transport relations'' on a
network. They single out a subset of ''traffic states'' described by time,
duration, position and other traffic attributes (called ''monads'' for short).
Duration evolutions are non-negative, decreasing toward zero for incoming
durations, increasing from zero for outgoing durations, allowing the detection
of ''junction states'' defined as traffic states with ''zero duration''. A
''junction relation'' (crossroads, synapses, clearing houses, etc.) Is a subset
of the transport relation made of junction states? The objective is to
construct a ''transport regulator'' associating with traffic states a set of
''celerities'' that mobiles circulating in the network can use as velocities.
In other word, a network is regarded as a ''provider of velocity information''
to the mobiles for travelling from one departure state to an arrival state
across a junction relation (a kind of geodesic problem). This investigation
assumes that a system governs the evolution of monads in function of time,
duration and position using celerities as controls and provides the transport
regulator, a feedback from transport states to celerities. The proposed
mathematical framework can acclimate road or aerial networks, endocrine
(hormonal) or synaptic (neurotransmitters) networks, financial or economic
networks, which motivated this investigation. This framework could probably
accommodate computer and even social networks. This investigation is restricted
to junctions between two routes.
