A two-queue polling model with a threshold service policy

We consider a model of two M/M/1 queues, served by a single server. The service policy for this polling model is of threshold type: the server serves queue 1 exhaustively, and does not remain at an empty queue if the other one is non-empty. It switches from queue 2 to queue 1 when the size of the latter queue reaches some level T. All switches are instantaneous. We determine the joint queue length distribution, both using analytic techniques and using the power series algorithm. The results are used to obtain further insight into the quality of threshold policies for polling models.< >