# Optimizing Retransmission Threshold in Wireless Sensor Networks
## 2 Related Works  
The real-time performance of packet delivery is a fundamental factor in sensor networks, and many efforts have been made to design efficient real-time routing protocols in WSNs. Most of the existing works addressed the following two challenges. First, it is essential to design the metric, which measures the forwarding quality, such as node forwarding quality [9], link quality [10], data aggregation [2] and energy efficiency [12]. Approximate aggregation for tracking quantiles and range countings is presented in [2], where a dynamic binary tree based deterministic tracking algorithm is proposed. Based on the actual number of data transmissions, link-Quality of Forwarding (QoF) and node-QoF metrics are proposed in [9]. A data-driven-basedlink quality prediction approach is provided in [10], which combines the packet reception ratio and the physical-layer information. Considering queuing delay, the Weighted End-to-End Delay (WEED) metric is introduced in [11]; the work focuses on selecting the path with the minimum expected end-to-end delay. In multi-hop wireless networks, the routing decision takes spatial reusability into account to improve the end-to-end throughput [16]. The authors in [17] utilize the expected available bandwidth to capture the logical intra-flow and inter-flow interference, and an isotonic metric of expected delay is proposed. Dependence among links was revealed recently. By exploiting the low correlated forwarding links, link-correlation Opportunistic Routing (OR) is given in [18]. Facing the uncertainties in wireless communication, the multi-timescale adaptation routing protocol is provided in [6], which can adapt to _in situ_ delay conditions in routing delay.  
To provide real-time packet delivery, QoS provisioning protocols and transmission scheduling protocols have also been extensively studied. The literature [13] studies geographic opportunistic routing protocol for multi-constrained QoS provisioning in WSNs, and the problem is formulated as a multi-objective multi-constraint optimization problem. By differentiating the priorities of user-level applications, the author in [19] develops an optimization tool for balancing the system resources and presents a cluster-based routing protocol. Under the constraints of delay and load balancing requirements, a centralized heuristic algorithm for selecting the path with minimal cost is provided in [20]. To separate the packet of different QoS requirements, a virtual hybrid potential field is introduced in [21]. Considering capacitated multicast routing problem, the work [22] provides the approximation algorithms for multicast k-path routing and multicast k-tree routing. By supporting slot rescheduling, the segmented slot assignment-based method for improving retransmission efficiency is proposed in [23]. [PERSON] _et al._[24] formulate joint routing and scheduling into an optimization problem and solve the problem with a column generation method. To route around the dead end relay node, the authors in [25] propose the cross-layer protocol, which integrates geographic routing with the contention-based MAC protocol. The author in [26] map the scheduling of data flow to multiprocessor scheduling and prove an upper bound of the end-to-end communication delay.  
There exist limited studies on optimizing the retransmission threshold [5; 14]. A distributed route maintenance framework is proposed in [5], which enables the link to adjust the retransmission number. However, the proposed heuristic method cannot provide the reliability guarantee theoretically. In our previous work [14], a greedy-based algorithm for finding optimal retransmission thresholds is proposed, which overlooks the impact of queue length on the forwarding quality. To overcome the shortage of the method, we investigate the problem of finding optimal retransmission thresholds in this paper.