# DDS: A Delay-Constrained Duty-Cycle Scheduling Algorithm in Wireless Sensor Networks
## 1 Introduction  
Wireless sensor networks (WSNs) are widely used in various fields for practical applications, such as environmental monitoring, vehicle tracking, surveillance, and healthcare [1]. In WSNs, a large number of sensor nodes are deployed in a region to collect information, e.g., tracking and identifying the location of miners and roof falls in underground mine environments, or detecting a vehicle accident using monitoring cameras in vehicles [2; 3]. Since the primary power source of sensor nodes is a battery with limited capacity, reducing the power consumption to prolong network lifetime is a crucial challenge in WSNs. One of the most effective solutions for saving energy is the duty cycling mechanism [4; 5] in which a node's radio is switched on for an active period and off for the rest of the duty cycle interval. Because sensor nodes only occasionally transmit and receive data packets in practice, having the sensor's radio continuously turned on is not necessary. Because sensor nodes consume low energy with a large duty cycle interval, a long network lifetime can be achieved by maximizing the duty cycle interval. However, a large duty cycle interval also leads to a long end-to-end (E2E) delay [6], which is the latency from packet generation time at the source node to reception time at the sink. As the duty cycle interval increases, nodes wake up less frequently. Therefore, the transmitters' waiting time for potential forwarding candidates to wake up becomes longer, which results in a longer E2E delay. From those two aspects of the duty cycling mechanism, consideration of a balanced performance between energy consumption and E2E delay is desired, since a lot of applications in WSNs require a certain E2E delay bound, as well as low energy consumption. For example, in a fire warning system, because a long E2E delay can have serious consequences, packets may be required to reach the sink within a given delay bound at a certain probability. Although a lot of studies [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19] attempted to address long E2E delays in WSNs, they focused on simply reducing E2E delays, instead of taking the delay bound requirement into account. As a result, it is hard for them to achieve a balanced performance between E2E delay and energy consumption. We also note that a few studies [20; 21; 22] considered both the delay bound requirement and energy consumption. However, those works required additional information or certain assumptions. For example, nodes have to synchronize wake-up schedules among other nodes in the network [20; 21; 22]. In order to address the limitations of existing work, we propose a delay-constrained duty-cycle scheduling (DDS) algorithm with the objective of achieving low energy consumption while satisfying the delay bound requirements in duty-cycled WSNs. DDS does not require time or wake-up schedule synchronization. Moreover, no specific node deployment strategy is required, i.e., sensor nodes can be placed inside buildings or outdoors, following a deterministic or nondeterministic deployment layout depending on user application demands. In the considered WSNs, data packets are required to reach the sink within a given time; i.e., the E2E delay of packets is bounded by an application-specific demand. For example, an application may require 95% of transmitted packets to arrive at the sink within 30 s [21; 23]. More formally, in this work, a deadline success ratio (DSR) is defined as the ratio between the number of packets delivered to the sink within the given delay bound and the total number of transmitted packets (e.g., the application may require a 95% DSR with a delay bound of 30 s). Under DDS, after sensor nodes are deployed, they are assigned a group number based on the hop distance to the sink. To deliver data packets to the sink, sensor nodes in a group forward their packets to the first awake node from among potential forwarders that belong to a group closer to the sink.