This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible Maximum Expected Delay: A New Metric to Analyse the Performance of Asynchronous Quorum-based Protocols in Wireless Sensor Networks Mahta Moezzi Department of Computer Engineering Technical and Vocational University (TVU) Alborz, Iran mahta.moezi73@gmail.com Parsa Emamdadi Department of Computer Engineering Technical and Vocational University (TVU) Tehran, Iran parsaemamdadi@gmail.com Abstract— Energy management is a crucial challenge in wireless sensor networks. To date, many techniques have been proposed to reduce energy consumption. Duty cycle methods reduce the energy consumption of wireless sensor networks since energy consumption declines in the sleep mode. Using quorum-based methods, sensors can stay in the sleep mode and be awaken periodically to send and receive data from adjacent nodes. In this paper, we review a subset of these methods called asynchronous quorum-based methods, independent of synchronization between nodes, and investigate their performances in different metrics. Then, we propose a new metric to investigate the latency of adjacent nodes in wireless sensor networks. Next, we study the performances of all discussed methods using the proposed metric. Finally, we introduce the best and worst methods based on different metrics. Keywords— Wireless Sensor Networks; power-saving protocols; quorum-based protocols; neighbor discovery; end to end delay; quorum systems. I. INTRODUCTION Today, billions of sensors are used to capture our surroundings. On a broad scale, these sensors are used to monitor and connect various devices in smart network systems [1-3]. A powerful and efficient addressing method is needed to connect various devices to effectively address things in the Internet of Things [4-10]. Wireless sensor networks (WSNs) consist of small sensors with short-range radio transmission, limited power source, limited computing power, and limited storage resources [11-12]. A limited power source unit is the main restriction in WSNs [13-14]. Given the impossibility of battery change in most WSN applications, designing a low consumption system with a great lifespan mounts a fundamental challenge. Hence, a commonly used method designed for wireless network protocols is a quorum-based system that increases the network lifespan. Quorum-based systems increase a network's lifetime by their typical behavior, switching between sleep and awake modes [15-20]. In the sleep mode, the energy consumption of active nodes can drop by more than 0.1. In quorum-based protocols, time is divided into equal shares known as quorum intervals. Every interval contains  equivalent separation during which a station can sleep or remain awake. Quorum-based systems determine a wakeup-sleep pattern in  consecutive length, where  is an integer number defining the system size. The strength of these protocols is in fact the stations that have to be awake in (√) out of  beacons, at least two stations are awake in every interval. Increasing the number of active slots known as quorum time slots increases the likelihood of active transmitter nodes during data transmission, which reduces transmission delays. Besides, the number of quorum time slots is negatively associated with the lifetime of nodes. A more detailed description of quorum-based protocols is given by [21]. In this paper, after reviewing related works, we study the connection of current methods with the system size and compare their performances in different aspects of the system size. The rest of the paper is organized as follows. The second section reviews related works. The third section introduces existing metrics used to evaluate suggested methods and presents a new latency-based evaluation metric. The fourth section compares existing methods with metrics like EQOS, active ratio, QER, and our proposed metric. Finally, the fifth section draws conclusions. II. RELATED WORKS For all quorum-based protocols (QBPs), time is divided into sections called QI, with every QI containing  equal time units. Every time unit in QI is a BI, and every BI is divided into three subdivisions, as shown in Fig. 1. There is a beacon window at the beginning of every BI that transmits beacons. The beacon packet contains simple information like node address and the node's timestamp. The following figure shows the MTIM window where the node keeps waiting to receive other nodes' ATIM packets. In the send/receive window, nodes can send and receive data packets. Both authors contributed equally to the paper.