New stability results for adversarial queuing

We consider the model of "adversarial queuing theory" for packet networks introduced by Borodin et al. [J. ACM. 48 (2001). pp. 13-38]. We show that the scheduling protocol first-in-first-out (FIFO) can be unstable at any injection rate larger than 1/2 and that it is always stable if the injection rate is less than 1/d, where d is the length of the longest route used by any packet. We further show that every work-conserving (i.e., greedy) scheduling policy is stable if the injection rate is less than 1/(d + 1).