## 1 Introduction  
A Wireless Sensor Network (WSN) consists of sensor nodes with limited power supply, restricted communication range, and constrained computational capability [1]. To overcome these limitations, various routing protocols have been proposed, and in particular the multipath routing protocol is exploited to provide fault-tolerant routing, congestion control, and Quality of Service (QoS) support [2, 3, 4]. Namely, multipath routing could improve load balancing and reliability of packet delivery. However, if a node participates in multiple paths, that is, parts of multiple paths overlap, the above advantages may be lost. To prevent the path overlap problem and achieve the above-mentioned purpose of a multipath, the source node that detected some event transmits a path construction message to the sink node. In the process of message relay, the nodes which received the construction message are chosen as members of the path. After the construction of one path, if the member nodes receive a path construction message to construct another path, the nodes ignore the message. The message is transmitted to a non-member node, and it is chosen as the member node of another path. Through these processes, a node is prevented from participating in different paths. The routing protocol exploiting a multipath constructed by these processes is called a node-disjoint multipath routing protocol [5, 6, 7, 8]. The node-disjoint multipath routing protocol is suitable for load balancing to deal with the congestion control. However, since each path is adjacent, it is difficult to transmit packet exploiting multipaths simultaneously to improve end-to-end transmission success ratio due to collisions and interference between adjacent nodes. Therefore, multipaths are constructed at a certain distance between each path to avoid collisions and interference that may occur between nodes. This certain distance is usually determined by the transmission range of a node, and it is called a guardband. Since each path transfers a packet with the guardband in between, unlike nodes in the node-disjoint multipath routing protocol, it is not affected by collision and interference [9; 10; 11]. However, traditional multipath routing protocols should construct the paths before packet transmission to the sink node, and even if a part of the path is broken, a new path should be constructed. This phenomenon adversely affects end-to-end transmission success ratio and transmission time, which are important factors in WSNs. Therefore, in this paper, we propose a cluster-disjoint real-time and reliable packet transmission scheme. In the proposed scheme, the network is divided into a grid cluster of a certain size according to the transmission range at the network initialization phase. In the phase, each cluster is numbered by an (x,y)-coordinate. After the initialization phase, the protocol operates as follows:  
* When any source node detects an event, the source node delegates the packet to the cluster head to which it belongs. The cluster head transmits the packet to the next cluster closest to the sink node according to the cluster information calculated in the network initialization phase. * The node inside the next cluster that received the packet delegates the packet to its cluster head, and the cluster head transmits the packet to its next cluster. In this process, each cluster head caches information on the cluster selected as the next cluster. Through this process, one shortest path is constructed. * If more than one path is required, the cluster head repeats the above process by selecting the next cluster closest to the sink node, and additional clusters according to the number of paths are required. That is, since the cluster to which the packet is transmitted is determined simultaneously with packet transmission, no additional time to construct a path is required.