  The S-ALOHA (i.e. slotted-ALOHA) protocol is recently regaining interest in
Lower Power Wide Area Networks (LPWAN) handling M2M traffic. Despite intensive
studies since the birth of S-ALOHA, the special features of M2M traffic and
requirements highlight the importance of analytical models taking into account
performance-affecting factors and giving a thorough performance evaluation.
Fulfilling this necessity is the main focus of this paper: we jointly consider
the impact of capture effect, diversity of transmit power levels with imperfect
power control. We propose a low-complexity but still accurate analytical model
capable of evaluating S-ALOHA in terms of packet loss rate, throughput,
energy-efficiency and average number of transmissions. The proposed model is
able to facilitate dimensioning and design of S-ALOHA based LPWAN. The
comparison between simulation and analytical results confirms the accuracy of
our proposed model. The design guides about S-ALOHA based LPWAN deduced from
our model are: the imperfect power control can be positive with capture effect
and and appropriate transmit power diversity strategy. The transmit power
diversity strategy should be determined by jointly considering network charges
level, power control precision and capture ratio to achieve optimal performance
of S-ALOHA.
