# An Energy-Efficient Fail Recovery Routing in TDMA MAC Protocol-Based Wireless Sensor Network
## 2 Network Topology and Energy Model  
### Network Topology with Time Division Multiplexing  
This section describes the network topology, scheduling and routing schemes of the proposed method. Energy-efficient data aggregation is often considered as the primary goal of many WSNs. In conventional sensor networks based on simplistic CSMA, as each sensor's data travels through multi-hop paths, its data is duplicated and transmitted by the nodes along the paths. Such duplicate transmissions, however, often cause excessive energy consumption. In this paper, we consider a more energy-efficient data forwarding method, a TDMA-based aggregate-and-forward method with convergent network topology. In this forwarding method, each node receives sensing data packets from all its child nodes in different time slots, and sends at once an aggregated data packet to its parent node in another time slot. In the network topology considered in this paper, we assume that all the nodes wake up together at a pre-scheduled sensing period, while they stay in a long sleep period in order to save energy. In [27], the authors proposed a multi-channel TDMA scheduling where each sensor node has a single radio and selects one channel from a set of RF channels. We also consider a similar TDMA scheduling method in this paper. The scheduling process is conducted after the routing process. In the routing process, each child node selects its parent considering the transmission distance. In the scheduling process, each selects a time slot while satisfying the constraint that the time slot of a parent node \(p_{i}\) is higher than all child nodes \(c_{i}\). This allows all nodes to aggregate and forward the sensing data from leaf nodes towards the final destination, the sink node. For example, Figure 2a illustrates a network with TDMA time slots and channels selected by the above routing and scheduling process for each node. This example is cited from [27]. In this network scenario, a sensor node first selects its parent node, and then schedules its transmission in the time slot that is earlier than the slot of the selected parent. Employing different RF channels allows concurrent time slots for large-scale networks. It also mitigates the interference between the nodes that are using identical slots in the zone of interference. In Figure 2, node n31 and n33 select the same time slot. Since they use different channels, their concurrent transmission does not cause collision. Although each sensor node has a single radio to communicate, it can bridge the child nodes that use various RF channels with the sink node. Initially, it tunes the RF channel of the child node who is allotted with the earliest slot. Then, it switches to other channels according to the sequence of the slots assigned to child nodes. The time consumed for switching from one channel to another is negligible [27]. For instance, in Figure 2, node n11 receives data from the child nodes using channel 1 and 2. Then, it forwards the aggregated data to the sink node. The process of data forwarding in various time slots is depicted in Figure 2b. The scheduling process ensures another constraint that multiple nodes can share the same time slot only when their channel is different. Figure 2b shows the result of time-slot scheduling. It uses eight time-slots and three channels to complete the aggregate and forward process from all nodes to the sink node n0. Shaded boxes denote each node-allocated time slot, while the colors of the boxes indicate the different channels selected. The dotted arrows represent the forwarding path from a child to its parent node. The objective of the routing and scheduling algorithm is to minimize the energy consumption by minimizing the number of time slots without exceeding the specified number of channels. If the network forwards all data using fewer time slots, all its nodes can switch back to sleep mode early, leading to less active energy.