Cost-Delay Tradeoffs for Two-Way Relay Networks

We consider two sources in a wireless network exchanging stochastically varying traffic using an intermediate relay. Each relay use incurs some cost, which, for example, could be transmission energy. This cost is shared between the sources when packets from both are transmitted simultaneously by the relay using network coding. If the relay transmits a packet originating from one source only, the cost is incurred by that source only. In this setting, we study transmission policies that tradeoff the average cost with the average packet delay. We first present the cost-delay tradeoff for a centralized scheme using Lyapunov stability arguments. Next, we consider a distributed policy, where each source aims to optimize its own cost-delay tradeoff. We determine the Nash equilibrium of the resulting non-cooperative game and show that it performs worse than the centralized algorithm. To overcome this limitation, we introduce a pricing mechanism at the relay, which is shown to achieve the centralized performance. These algorithms, though oblivious to the arrival statistics, do require global knowledge of queue backlogs. Lastly, we consider distributed algorithms that overcome this requirement. Among those, we observe that simple queue-length threshold algorithms perform remarkably well.