## 1 Introduction  
Wireless Sensor Networks (WSNs) have attracted increasing interest in recent years [1]. Normally, a WSN consists of a very large number of wireless network nodes integrating many capacities like sensing, computation and communication. In order to monitor a field of interest, these WSN nodes collect data from its surrounding environment and transport the data to the sink node collaboratively via multi-hop communication. WSNs have been successfully applied to structural health monitoring [2], localization of an object [3], breeding behavior on Great Duck Island [4] and many other application domains. Their wide application implies their potential future in various fields. However, WSNs are typically characterized by constrained energy due to their energy recharging difficulty in many applications. This feature makes them more challenging in real applications and needs further research efforts.  
In this paper, we consider a series of applications of WSNs, where the nodes are all stationary. All of these nodes sample their environment information simultaneously and periodically, and then transmit the data to a sink node through multi-hop communication. These applications could cover structural health monitoring, location of objects and other applications. The WSN in this paper is based on a contention network, whose use has been increasing in popularity. Normally, in a contention network idle listening wastes most of the energy [1, 5]. Packet retransmission also wastes energy because it not only consumes much energy on retransmission, but also makes back-off times longer, which results in much more energy being wasted in the idle state. We propose herein a family of collaborative distributed scheduling approaches (CDSAs) for the purpose of reducing the energy consumption of WSNs, which are based on the discrete time Markov chain (DTMC). The CDSAs enable nodes to learn the behavior of their environment, and estimate the working features of their child nodes and parent node through collaboration. The CDSAs integrate sleep scheduling with packet transmission scheduling together to reduce energy consumption. Only when a node estimates that all its child nodes are not transmitting packets and its parent node can successfully receive its data packet, it schedules transmission of its data packet to its parent node. It can also schedule itself to a sleep state when it has transmitted all its data packets or when the serious collisions exist. We analyze the adaptability and practicability of the CDSAs. We also validate the CDSAs based on the CSMA/CA protocol through simulation and evaluate them on a WSN testbed. The results show that the proposed approaches can save energy effectively.  
The rest of this paper is organized as follows. In Section 2, we describe the background and elaborate our contributions. In Section 3, we present the network model. In Section 4, we present the family of CDSAs, describe the one-step collaborative distributed approach (O-CDSA) and the two-step collaborative distributed approach (T-CDSA) in detail. In Section 5, the adaptability and practicality of the two approaches are discussed. In Section 6, some experiments are carried out to evaluate the performances of CDSAs, and the experimental results are further discussed. In the last section, we conclude this paper and suggest some future research topics.