  The problem of evaluation of Lyapunov exponent in queueing network analysis
is considered based on models and methods of idempotent algebra. General
existence conditions for Lyapunov exponent to exist in generalized linear
stochastic dynamic systems are given, and examples of evaluation of the
exponent for systems with matrices of particular types are presented. A method
which allow one to get the exponent is proposed based on some appropriate
decomposition of the system matrix. A general approach to modeling of a wide
class of queueing networks is taken to provide for models in the form of
stochastic dynamic systems. It is shown how to find the mean service cycle time
for the networks through the evaluation of Lyapunov exponent for their
associated dynamic systems. As an illustration, the mean service time is
evaluated for some systems including open and closed tandem queues with finite
and infinite buffers, fork-join networks, and systems with round-robin routing.
