  We present a novel calculation of the spectrum of electrons and positrons
from random sources, supernova remnants and pulsars, distributed within the
spiral arms of the Galaxy. The pulsar emissivity in terms of electron-positron
pairs is considered as time dependent, following the magnetic dipole spin-down
luminosity, and the temporal evolution of the potential drop is accounted for.
Moreover each pulsar, with the magnetic field and initial spin period selected
at random from the observed distribution, is considered as a source of pairs
only after it leaves the parent supernova due to its birth kick velocity (also
selected at random from the observed distribution). We show that (i) the
spectrum of electrons is characterized by a feature at $\gtrsim 50$ GeV that
proves that their transport is dominated by radiative losses. The flux
reduction at $E\gtrsim 1$ TeV is explained as a result of lepton transport from
sources in the spiral arms. (ii) The spectrum of positrons is very well
described by the contribution of pulsars and the rising positron fraction
originates naturally. The implications of pulsars as positron sources in terms
of positron fraction at very high energies are also discussed. (iii) The role
of fluctuations in the high-energy regime is thoroughly discussed and used to
draw conclusions on the possibility to single out the contribution of local
sources to the lepton spectrum with current and upcoming experiments.
