  We consider a one-body spin-less electron spectral problem for a resonance
scattering system constructed of a quantum well weakly connected to a
noncompact exterior reservoir, where the electron is free. The simplest kind of
the resonance scattering system is a quantum network, with the reservoir
composed of few disjoint cylindrical quantum wires, and the Schr\"{o}dinger
equation on the network, with the real bounded potential on the wells and
constant potential on the wires. We propose a Dirichlet-to-Neumann - based
analysis to reveal the resonance nature of conductance across the star-shaped
element of the network (a junction), derive an approximate formula for the
scattering matrix of the junction, construct a fitted zero-range solvable model
of the junction and interpret a phenomenological parameter arising in Datta-Das
Sarma boundary condition, see {\cite{DattaAPL}, for T-junctions. We also
propose using of the fitted zero-range solvable model as the first step in a
modified analytic perturbation procedure of calculation of the corresponding
scattering matrix.
