Delay optimal control of multi-hop networks remains a challenging problem even in the simplest scenarios. In this paper, we consider delay optimal control of a two-hop half-duplex network with independent identically distributed ON-OFF fading. Both the source node and the relay node are equipped with infinite buffers and have exogenous bit arrivals. We focus on delay optimal link selection to minimize the average sum queue length over a finite horizon subject to a half-duplex constraint. To solve the problem, we introduce a new approach, whereby an actual discrete time system (ADTS) is approximated using a virtual continuous time system (VCTS).
We obtain an asymptotically delay optimal policy in the VCTS. Using the relationship between the VCTS and the ADTS, we obtain an asymptotically delay optimal policy in the ADTS. The obtained policy has both a priority feature and a safetySTOCK feature. It offers good design insights for wireless relay networks. In addition, the obtained policy has a closed-form expression, does not require knowledge of arrival statistics, and can be implemented online. Finally, using renewal theory and the theory of random walks, we analyze the average delay resulting from the asymptotically delay optimal policy.