A State-Dependent Polling Model with Markovian Routing

Guy Fayolle (1) , Jean-Marc Lasgouttes (1)

1 MEVAL - Methods, algorithms and software in automatic control

A state-dependent 1-limited polling model with N queues is analyzed. The routing strategy generalizes the classical Markovian polling model, in the sense that two routing matrices are involved, the choice being made according to the state of the last visited queue. The stationary distribution of the position of the server is given. Ergodicity conditions are obtained by means of an associated dynamical system. Under rotational symmetry assumptions, average queue length and mean waiting times are computed.

Mots clés: Polling systems; ergodicity

Domaines: Probabilités [math.PR]

Guy Fayolle, Jean-Marc Lasgouttes. A State-Dependent Polling Model with Markovian Routing. Frank P. Kelly and Ruth R. Williams. Stochastic networks, 71, Springer-Verlag, pp.283-312, 1995, The IMA Volumes in Mathematics and its Applications, 0-387-94531-8. ⟨hal-00717705⟩