  This article mediates an mathematical insight to the theory of vehicular
headways measured on signalized crossroads. Considering both, mathematical and
empirical substances of the socio-physical system studied, we firstly formulate
several theoretical and empirically-inspired criteria for acceptability of
theoretical headway-distributions. Sequentially, the multifarious families of
statistical distributions (commonly used to fit real-road headway statistics)
are confronted with these criteria, and with original experimental
time-clearances gauged among neighboring vehicles leaving signal-controlled
crossroads after a green signal appears. Another goal of this paper is,
however, to decide (by means of three completely different numerical schemes)
on the origin of statistical distributions recorded by stop-line-detectors.
Specifically, we intend to examine whether an arrangement of vehicles is a
consequence of traffic rules, driver's estimation-processes, and
decision-making procedures or, on contrary, if it is a consequence of general
stochastic nature of queueing systems.
