The polling network considered here consists of a finite collection of stations visited successively by a single server who is following a Markovian 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...

In an M/G/1 environment with finite waiting room, the server, for each new customer to be served, may choose any of k different service modes. Under a certain cost structure and certain assumptions about the different "speeds" of service it is shown that the search for an optimal policy can be...