Stability of periodic polling system with BMAP arrivals

This paper considers the stability of BMAP/GI/1 periodic polling models with mixed service disciplines. The server attends the N stations in a repeating sequence of stages. Customers arrive to the stations according to batch Markov arrival processes (BMAPs). The service times of the stations are general independent and identically distributed. The characterization of global stability of the system, the order of instability of stations and the necessary and sufficient condition for the stability are given. Our stability analysis is based on the investigation of the embedded Markovian chains at the polling epochs, which allows a much simpler discussion than the formerly applied approaches. This work can also be seen as a survey on stability of a quite general set of polling models, since the majority of the known results of the field is a special case of the presented ones.