### Significance of the Contribution  
The main contribution of this work is the analytical modeling and comprehensive assessment of the energy consumed by the SNs of a WSN that deploys the PSA-MAC protocol. In the proposed model, SNs have different loads, MAC parameters, and access priorities and may use the SPT or APT schemes.  
The model is based on two two-dimensional Discrete-Time Markov Chains (2D-DTMC). We propose comprehensive closed-form expressions based solely on the stationary probability distribution of the two previous DTMCs. These expressions allow the determination of the average energy consumed by SNs in a cycle of operation in network scenarios that consider the coexistence of different SN classes, priority assignments, and all the additional above-mentioned features of the PSA-MAC protocol.  
SNs deploying the PSA-MAC protocol perceive the time as partitioned into cycles, and each cycle is further divided into three parts (_periods_): _sync_ (synchronization), _data_ and _sleep_. In addition, the PSA-MAC protocol considers _normal_ and _awake_ operating cycles. In _normal_ cycles, an active SN willing to transmit a packet enters the _sleep_ period after transmitting a packet, either with success or failure or when it senses a busy medium before its backoff timer expires. Active SNs are those with packets to send. In _awake_ cycles, SNs do not enter the _sleep_ mode but stay awake, listening to the transmission of possible synchronization (_SYNC_) packets from neighboring SNs until the cycle ends. _SYNK_ packets are used by SNs to update their synchronization calendar and, in this way, synchronize their cycle initiation instants.  
The current traffic model is mainly based on the model presented in [23]. However, in the current study, a significant extension is proposed to compute the energy consumed by an SN along the entire operation cycle. While, in the previous model only the _data_ period of a cycle was considered. Here, we also include the _sync_ and _sleep_ periods.  
The total energy a SN consumes is computed as the summation of different terms: (i) the energy consumed during _normal_ cycles; (ii) the energy consumed during _awake_ cycles; (iii) the energy consumed during _data_ periods; and (iv) the energy consumed during _sync_ periods that occur at the beginning of each cycle. Please note that _normal_ cycles repeat more frequently than _awake_ cycles.  
The aggregate packet transmission (APT) feature that was proposed in [24] is also integrated into the current model. However, in [24], the full operation cycle was not considered, while it is considered in the new model.  
The stationary probability distribution elements are the key terms that form part of the expressions that allow the determination of the average energy consumed by SNs. In the new model, the complexity of these expressions increases as the model takes into account the energy consumed during the different periods of a cycle, as well as in _normal_ and _awake_ cycles.  
The design of the new energy computation methodology has been quite challenging, as it must take into account the heterogeneity among SNs. A heterogeneous scenario needs to consider the multiple combinations of states in which the SNs of the network might be at each operation cycle. This highlights the importance of the contribution presented in Section 4, where expressions are defined to represent the multiple contributions that are required to determine the average energy consumed by an SN of any class along a cycle.  
Finally, it is important to highlight that the methodology to compute the energy consumed by SNs proposed here is considerably more systematic than those in previously proposed approaches. Also, as shown in Section 5.5, the new energy computation methodology is very accurate.