1 research outputs found
Analysis of loss networks with routing
This paper analyzes stochastic networks consisting of finite capacity nodes
with different classes of requests which move according to some routing policy.
The Markov processes describing these networks do not, in general, have
reversibility properties, so the explicit expression of their invariant
distribution is not known. Kelly's limiting regime is considered: the arrival
rates of calls as well as the capacities of the nodes are proportional to a
factor going to infinity. It is proved that, in limit, the associated rescaled
Markov process converges to a deterministic dynamical system with a unique
equilibrium point characterized by a nonstandard fixed point equation.Comment: Published at http://dx.doi.org/10.1214/105051606000000466 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org