## 2 Related Work
### Analysis of IEEE 802.15.6 CSMA/CA  
Several research studies on performance analysis of the IEEE 802.15.6 are based on Discrete Time Markov Chain (DTMC). [PERSON] et al. proposed an early probabilistic model for this standard, which evaluates the effects of access phase periods over network performance [13]. By considering saturated and non-ideal channel conditions, they observed that the IEEE 802.15.6 CSMA/CA perform poorly for high traffic loads. The authors of [14] proposed a DTMC to evaluate throughput, delay and power consumption of IEEE 802.15.6 CSMA/CA for an error-prone channel. The proposed DTMC considers the delay of a node by taking into account the acknowledgement time after the packets are transmitted. Under a saturated traffic scenario, the authors analyzed the performance for different user priorities and concluded that five user priorities are enough to satisfy the network requirements. In another study [15], the authors proposed a Markov chain for all user priorities defined in the standard and concluded that high priority nodes have unfair access to the channel, thus degrading throughput of low priority nodes. The authors of [16] reached to the same conclusion for an ideal channel. They modeled the backoff process of the IEEE 802.15.6 CSMA/CA using a Markov chain, and analyzed the effects of traffic loads, modulation and coding, and different user priorities on saturated throughput and access delay. The author of [17] proposed an adaptive priority method that decreases the number of retransmission by considering the channel environment of IEEE 802.15.6 networks. [PERSON] et. al. improved the IEEE 802.15.6 standard by proposing an adaptive medium access control protocol [18]. The proposed protocol adjusts superframe and access phase lengths according to the nodes generating traffic. By considering three user priorities, the proposed protocol outperforms the IEEE 802.15.6 in terms of network delay and power consumption. In [19], the authors proposed a time-saturation model for IEEE 802.15.6 CSMA/CA by considering the effects of lost packets, which were ignored in the above-mentioned works. The authors observed that network throughput converges according to the system values, thus changing the time-saturation model to either saturated or non-saturation models. In [20], the authors introduced a novel and prioritized Fibonacci backoff scheme in IEEE 802.15.6 CSMA/CA to decrease node waiting time and number of collisions on the channel. By using a Markov chain, the authors observed that the proposed backoff scheme performs better than that of IEEE 802.15.6 in terms of throughput, power consumption, and head of line delay. The authors of [21] utilized a multi-beam directional antenna in the IEEE 802.15.6 CSMA/CA to extend network reliability and lifetime. In [22], the authors proposed a power-enabled priority scheme that reduces the number of retransmissions of packets. They concluded that the proposed scheme outperforms the IEEE 802.15.6 CSMA/CA in terms of bandwidth efficiency, energy consumption, throughput, and delay. The random transmission delay of the IEEE 802.15.6 CSMA/CA is analyzed in [23], where the authors used a probabilistic model for asynchronous duty-cycling networks. The authors concluded that the proposed model achieves better performance in terms of expectations and variance of the delay.