We analyze Gittins' Markovian model, as generalized by Varaiya, Walrand and
Buyukkoc, in discrete and continuous time. The approach resembles Weber's
modification of Whittle's, within the framework, of both multiparameter pro
cesses and excursion theory. It is shown that index-priority strategies are
optimal, in concert with all the special cases that have been treated prev
iously.