Large deviations rate function for polling systems (Q1605044)

A polling system with one server, Markovian routing and exponential service times and walkover times is considered. Let \(Q_t\) be the state vector of the system at time \(t\). A sample path large deviations principle is established for \(\{Q_{nt}/n\}_{t\geq 0}\) as \(n\to\infty\) and certain information on the form of the rate function is given. Key tools in the analysis are a so-called local generator, obtained by considering only subsets of the states and neglecting the positivity restrictions on the process, and fluid limits. The example of cyclic polling is considered and the connection to large deviations theory for Jackson networks is discussed.