Applications of Stochastic Semigroups to Queueing Models

Abstract

Non-markovian queueing systems can be extended to piecewise-deterministic Markov processes by appending supplementary variables to the system. Then their analysis leads to an infinite system of partial differential equations with an infinite number of variables and non-local boundary conditions. We show how one can study such systems by using the theory of stochastic semigroups.

Keywords

• stochastic semigroup
• invariant density
• piecewise deterministic Markov process
• queueing systems
• 47D06
• 60J25
• 60K25
• 90B22