A State-Dependent Polling Model with Markovian Routing

TL;DR

This paper introduces a state-dependent polling model with Markovian routing, providing analytical results for the stationary distribution, ergodicity conditions, and performance metrics like queue length and waiting times.

Contribution

It generalizes classical Markovian polling models by incorporating state-dependent routing with two matrices and derives key performance and stability results.

Findings

Stationary distribution of server position derived

Ergodicity conditions established via dynamical system analysis

Average queue length and waiting times computed under symmetry

Abstract

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.