## 1 Introduction
In FSA, time is organized into frames divided into access slots. Each end-device randomly selects one slot of a frame to transmit data. The works in [11; 12; 13] show that the energy consumption of the RFID tags grows exponentially with the number of tags. The work in [14] also shows that there is an optimal frame length (_i.e._, number of slots per frame) that minimizes the delay to collect data and the energy consumption of the entire network. This optimal frame length is equal to the number of end-devices. Unfortunately, those works consider that every end-device has just one data packet (e.g., identification, measurement, _etc._) to transmit to the reader or data-collector. However, some other M2M data-collection applications, such as smart metering and video surveillance, for example, will require the transmission of longer messages from each end-device in every data collection round. These messages will be fragmented into smaller parts, which may require a new channel invocation to be transmitted. The reservation FSA protocol (RFSA) was proposed in [15] to improve the performance of FSA when devices generate long messages with packet fragmentation. In RFSA, when an end-device succeeds in transmitting the first packet of a message in a given slot, that slot is reserved for that end-device in subsequent frames until the last packet of the message is sent. A number of research works have proposed the use of RFSA in satellite communications [16; 17; 18; 19] and inter-vehicle communication [20; 21; 22]. As discussed into more detail later in Section 2, previous works focus on the throughput analysis of RFSA, assuming that the network is in steady-state conditions and consider that end-devices generate long messages following a given random distribution. Results show that RFSA outperforms FSA in terms of throughput. However, existing analytical models of RFSA do not evaluate the delay and energy consumption required to resolve the contention under delta traffic. Therefore, the analysis of RFSA under delta traffic conditions remains an open research question, which deserves attention for its application in data-collection scenarios. This is the main motivation for the work presented in this paper, which aims at filling this gap with the following contributions:  
1. We formulate an accurate theoretical model to calculate the average delay and the average energy consumption required to resolve the contention using RFSA in M2M networks under delta traffic and with fragmentation of long data messages. We validate the theoretical model with extensive computer-based simulations. 2. We perform a comprehensive analysis and performance evaluation of RFSA and FSA to optimize delay and energy consumption. For this particular performance evaluation, we have considered radio transceivers in compliance with the IEEE 802.15.4 standard [7]. Results show better performance of RFSA for its application in low-complexity M2M data-collection networks. The remainder of this paper is organized as follows. In Section 2, we describe the related work in order to motivate the contribution presented in this paper. In Section 3, we describe the system model and the operation of FSA and RFSA in data collection scenarios. In Section 4, we present the probabilistic analysis of RFSA based on absorbing Markov chains. Section 5 is devoted to the formulation of the analytical models to calculate the average delay and energy consumption for RFSA. In Section 6, we validate the models through computer simulation and evaluate the performance of both protocols in terms of delay and energy consumption. Finally, Section 7 concludes the paper.