ERGODICITY OF A POLLING NETWORK

The polling network considered here consists of a finite collection of stations visited successively by a single server who is following a M arkovian routing scheme. At every visit of a station a positive random number of the customers present at the start of the visit are served, whereupon the server takes a positive random time to walk to the stat ion to be visited next. The network receives arrivals of customer grou ps at Poisson instants, and all customers wait until served, whereupon they depart from the network. Necessary and sufficient conditions are derived for the server to be able to cope with the traffic. For the p roof a multidimensional imbedded Markov chain is studied.