In this paper we introduce and study functionals of the intensities of
random measures modulated by a stochastic process ξ, which occur in
applications to stochastic models and telecommunications. Modulation of a
random measure by ξ is specified for marked Cox measures. Particular
cases of modulation by ξ as semi-Markov and semiregenerative processes
enabled us to obtain explicit formulas for the named intensities. Examples
in queueing (systems with state dependent parameters, Little's and
Campbell's formulas) demonstrate the use of the results.