## 1 Introduction  
Machine-to-machine (M2M) communications are one of the fastest growing segments in information and communication technologies [1; 2]. M2M networks will facilitate new and promising applications that will create a revolution in the way we run industries, cities, _etc_. However, the technology faces several significant challenges that need to be solved in order to get all of the potential of M2M. Among others, energy efficiency is crucial in the design of communication protocols for M2M networks that must operate for long periods of time with very limited access to energy sources and without human intervention. In this paper, we focus on wireless M2M area networks [3], where a large group of hundreds or thousands of end-devices sense physical parameters from the environment and transmit the sensed information to a data concentrator, e.g., a gateway. Examples of such applications are: smart metering, where electricity, gas or water meters periodically transmit readings to a data-collector; asset tracking, where a radio frequency identification (RFID) reader sends requests to the tags, and they respond with their location and identification; and video surveillance, where a group of video cameras deployed in a building transmit still images every few minutes. In all of these data collection scenarios, end-devices remain in sleep mode for certain periods of time to save energy and wake up to transmit a burst of data packets when they are requested by the gateway. Therefore, the network changes abruptly from idle into saturation when all end-devices wake up to transmit simultaneously; this has been referred to in the literature as the delta traffic condition or batch arrival [4]. The contention process of a delta traffic condition starts when the gateway sends a request and finishes when all of the end-devices have succeeded in transmitting data. On the contrary, in steady-state conditions, it is assumed that end-devices generate data traffic following a given random distribution. Due to its mathematical tractability, stationary Poisson processes have been used in the past to model traffic generation. However, new applications and new communication scenarios, particularly posed by the Internet of Things, require a revision of existing models, including traffic generation models and their impact in communication protocols. Since the total number of end-devices that may attempt to simultaneously get access to the channel can be potentially large under a delta traffic condition, an energy-efficient medium access control (MAC) protocol is needed to manage this traffic and to minimize the delay and energy waste due to collisions among end-devices and to idle listening periods devoted to carrier sensing. While time division multiple access (TDMA) allows every end-device to transmit without collisions, thus minimizing energy consumption, TDMA is not optimal in M2M networks with a large and dynamic number of end-devices, due to the delay and energy required to update the knowledge of the network topology and to create, maintain and distribute the network schedule. Contrarily, the simplicity and distributed operation of random access protocols [5; 6], e.g., ALOHA or carrier sense multiple access (CSMA), make them ideal for simple and low-cost devices in M2M area networks with an unknown and dynamic number of end-devices. Many standards for wireless communications rely on random access protocols, such as the IEEE 802.15.4 [7] for low-rate wireless personal area networks, the wireless Meter-Bus (M-Bus) [8] for smart metering, the IEEE 802.11 [9] for wireless local area networks and the ISO/IEC18000-7 [10] for asset tracking. The frame slotted ALOHA (FSA) protocol has been identified in the past as a good approach to handle the delta traffic in data collection scenarios due to its simplicity and good performance when optimally configured (e.g., [11; 12; 13; 14]). As an example, FSA was adopted in the ISO/IEC 18000-7 standard, which is targeted at active RFID systems.