Message scheduling for tandem multi-hop wireless networks

Simplified tandem multi-hop wireless networks are considered where each of N nodes (connected in tandem) periodically generates a message every T time-slots. Each message can be transmitted on a wireless radio link from a node to an adjacent within each single time-slot, should be relayed in a store-and-forward manner from its source node to one of two gateways at the edges of the tandem within T time-slots, and then forwarded from the gateway to a central server via a reliable network. Our study is toward message transmission scheduling in which a static global time-slot assignment is designed to avoid conflicts among simultaneous transmissions on adjacent links, as well as dynamic message selection for proactive redundant transmissions with network coding are adopted to cope with lossy unreliable wireless links. In this present paper, as the first step of our study, we mainly focus on finding a good time-slot assignment.We analytically investigate, as a performance metric, the probability that all N generated messages are successfully relayed in a duration of T time-slots when a static time-slot assignment is accompanied by a static message selection for redundant transmissions, which can provide a baseline performance. To find a static time-slot assignment with static message selection that maximizes the metric, we successfully apply a mathematical optimization theory.