Stability of the max-weight routing and scheduling protocol in dynamic networks and at critical loads

We study the stability of the Max-Weight protocol for combined routing and scheduling in communication networks. Previous work has shown that this protocol is stable for adversarial multicommodity traffic in subcritically loaded static networks and for single-commodity traffic in critically loaded dynamic networks. We show: ? The Max-Weight protocol is stable for adversarial multicommodity traffic in adversarial dynamic networks whenever the network is subcritically loaded. ? The Max-Weight protocol is stable for fixed multicommodity traffic in fixed networks even if the network is critically loaded. The latter result has implications for the running time of the Max-Weight protocol when it is used to solve multicommodity flow problems. In particular, for a fixed problem instance we show that if the value of the optimum solution is known, the Max-Weight protocol finds a flow that is within a (1 - )-factor of optimal in time O(1/) (improving the previous bound of O(1/2 )). If the value ...

• Type: Conference
• Year: 2007
• Where: STOC
• Authors: Matthew Andrews, Kyomin Jung, Alexander L. Stolyar
• Keywords: Adversarial Dynamic Networks, Adversarial Multicommodity Traffic, Algorithms, Multicommodity Flow Problems, STOC 2007