Universal Routing in Multi-hop Radio Networks

In this article we introduce a new model to study stability in multi-hop wireless networks in the framework of adversarial queueing. In such a model, a routing protocol consists of three components: a transmission policy, a scheduling policy to select the packet to transmit form a set of packets parked at a node, and a hearing control mechanism to coordinate transmissions with scheduling. For such a setting, we propose a definition of universal stability that takes into account not only the scheduling policies (as in the standard wireline adversarial model), but also the transmission policies. First, we show that any scheduling policy that is unstable in the classical wireline adversarial model remains unstable in the multi-hop radio network model, even in scenarios free of inter- ferences. Then, we show that both SIS and LIS (two well-known universally stable scheduling policies in the wireline adversarial model) remain stable in the multi-hop radio network model, provided a proactive hearing control is used. In contrast, such scheduling policies turn out to be unstable when using a reactive hearing control. However, the scheduling policy LIS can be enforced to be universally stable provided ties are resolved in a permanent manner. Such a situation doesn't hold in the case of SIS, which remains unstable regardless of how ties are resolved. Furthermore, for some transmission policies which we call regular, we also show that all scheduling policies that are universally stable when using proactive hearing control (which include SIS and LIS) remain universally stable when using reactive hearing control.