COMPARATIVE ANALYSIS OF RETRANSMISSION IN SYNCHRONOUS AND
ASYNCHRONOUS MEDIUM ACCESS CONTROL PROTOCOLS IN WIRELESS
SENSOR NETWORKS
Rohini Mittal * and Vidushi Sharma #
*
Department of Electronics and Communication Engineering,
Hindustan College of Science and Technology,
Farah, Mathura, India rohini.mittal1@gmail.com
# School of Information and Communication Technology,
Gautam Buddha University,
Greater Noida, India vidushi@gbu.ac.in
ABSTRACT
Wireless sensor networks (WSNs) are application specific and energy constrained.
So, for the fulfilment of the requirements of an application, an extended network lifetime is the major issue of concern. Duty cycled Medium Access Control (MAC) protocols are an approach to efficiently utilize constrained energy supplies as they put sensors to sleep periodically. Duty cycled MAC protocols can either be synchronous or asynchronous. Synchronous duty cycled
MAC protocols use ‘SYNC’ packet to synchronize all the nodes within a network. This causes the nodes to sleep and wake at the same time. Asynchronous MAC protocols are classified with arbitrary offset to start their sleep-wake up cycle. This removes the overhead caused due to synchronization packet unlike synchronous duty cycled MAC protocols. Since, wireless sensor networks are application specific, certain applications as event based demand that the packets are received whenever an event occurs. However, this is not always possible because network cannot be 100% efficient as the packets may drop due to collision or network saturation. To overcome this inefficiency, data packets need to be retransmitted to ensure that complete information reaches the destination node. This paper presents a two dimensional Markov queuing model and proposes an algorithm to support retransmission in duty cycle MAC protocols with application to SMAC (synchronous MAC protocol) and XMAC (asynchronous
MAC protocol). The paper discusses and comparatively analyses the effects of retransmission on synchronous and asynchronous MAC protocols for event driven applications in wireless sensor networks.
Key Words: Wireless sensor networks, Retransmission, Synchronous MAC protocols,
Asynchronous MAC protocols, SMAC, XMAC.
1. Introduction
Wireless Sensor Network (WSN) is analogous to an ad hoc network with selfpowered and self-configuring sensor nodes that collectively sense environmental data, perform data aggregation and actuation functions to ensure reliability, efficiency and accuracy. WSNs are largely employed in disaster relief, environment control, smart buildings, healthcare and many other applications (Mittal and Sharma, 2013). WSN cannot have generalized features as

they are application specific. In certain cases, like patient monitoring or disaster management systems, the objective is to raise an alarm whenever there is an indication of abnormal behavior. Here, packet delivery during this abnormality is of prime concern. Whereas, in applications like environment monitoring systems, energy is of major concern due to weak battery support and in systems which are fixed, sensor networks having constant energy supply may have delay as major concern. Hence, a single approach cannot suffice all the requirements.
Due to constrained energy supply, researchers have focused towards the development of energy saving techniques. MAC layer protocols are power aware and reduce collisions with neighbors’ broadcast (Akyildiz, et al., 2002). One such approach is duty cycled MAC layer protocols which reduce idle listening by forcing sensors to sleep periodically. Duty cycled
MAC protocols can either be synchronous or asynchronous. Synchronous duty cycled MAC protocols, such as SMAC (Sakya ad Sharma, 2013), PMAC, PCS-MAC, TMAC, etc. use
‘SYNC’ packet to synchronize all the nodes within a network. This causes the nodes to sleep and wake at the same time. Synchronization improves communication efficiency as both sender and receiver are in listen mode and can exchange data within same duration.
Asynchronous MAC protocols are classified with arbitrary offset to start their sleep-wake up cycle (Yang and Heinzelman, 2012a).This removes the overhead caused due to synchronization packet unlike synchronous duty cycled MAC protocols. XMAC (Buettner, 2006a), Speck-
MAC (Wong and Arvind, 2006), CMAC (Liu, et al, 2007), etc are some of the asynchronous duty cycle MAC protocols. In applications where data delivery is major concern, these asynchronous protocols fare well in terms of lesser delay but they cannot ensure 100% data delivery due to several reasons as collision, loss of packet during sleep state, RTS/ CTS failure, data packet queue overflow, processing delay, network saturation, network breakdown due to contention among the nodes to gain access to the medium, etc. In order to ensure that the packets reach their destined node successfully, retransmission is required.
We performed retransmission in Synchronous MAC or SMAC (synchronous duty cycled MAC protocol) and XMAC or short preamble MAC protocol (asynchronous duty cycled MAC protocol). XMAC (Buettner, 2006a) prevents overhearing by embedding target
ID so that non- target nodes can go off to sleep, a series of short preambles with alternate pauses so that if receiver wakes up during a pause, it can send an ACK packet within this pause interval and cut the preamble to start data reception. The data sent by the transmitter does not contain any preamble.
Several authors proposed mathematical models to study sleep/ wake-up patterns in duty cycled MAC protocols. Luo, et al. (2007) developed a finite FIFO queuing model using a continuous time Markov chain for sensor nodes to study the performance of contention-based sensor networks with synchronous wakeup patterns. The model was designed for a finite buffer queue with sensor node generating and relaying the packets at respective rates with an assumption that a node alternates between sleep and active state. Mathematical and analytical models have been proposed for different MAC protocols too such as TMAC (Dam and
Langendoen, 2003), OMAC (Zhang, et al., 2008), SMAC (Yang and Heinzelman, 2009a) and
XMAC (Yang and Heinzelman, 2010). Yang et al. (2012) proposed a 1-D Markov queuing model with finite queue capacity to analyse the throughput of SMAC and XMAC protocols and describe their behaviour during packet transmission. They also proposed a 2-D Markov queuing model to analyse the throughput of SMAC with finite queue capacity during retransmission (Yang and Heinzelman, 2009a). Literature study reveals that asynchronous
MAC protocols are better for applications requiring guaranteed data transmission as their data transmission rate is high and hence reduced delay. One can further enhance the reliability by introducing retransmission in such protocols.
2

In this paper, we have implemented the 2-D Markov queuing model for retransmission in asynchronous MAC protocols. We have considered slotted XMAC protocol and analysed its packet delivery ratio (PDR), delay and power consumption and compared its performance with that of SMAC protocol. The rest of the paper is organised as follows. Section
2 presents the 2-D Markov queuing model for retransmission in duty cycled MAC protocols.
Section 3 and 4 describe the media access rules of SMAC and XMAC protocols respectively.
Section 5 deals with formulation for calculation of performance metrics. Numerical illustrations and results are discussed in Section 6. Finally, Section 7 concludes the paper.
2. Mathematical Model for Retransmission In Duty Cycled MAC Protocols
We have considered SMAC and XMAC protocols for developing mathematical model for retransmission in synchronous and asynchronous MAC protocols.
Markov model for ‘RL’ retransmissions has been considered, realized by cascading
‘RL+1’ layers of 1-D Markov model (Yang and Heinzelman, 2012a). This will yield the model shown in Figure 1. The model has (QC+1) states horizontally, corresponding to ‘0’ packets
(empty queue) to ‘QC’ packets in the queue (full queue) and ‘RL+1’ retransmission stages. It, thus, has (QC (RL+1) +1) states. The index (0, QC) indicates the arrival of ‘QC’ packets at 0 th retransmission stage. The state of the node changes when a packet arrives in the queue. If a packet fails to be transmitted, it enters into adjacent higher retransmission stage. A packet can be discarded to its empty queue state if it reaches the highest retransmission limit. However, if the packet is successfully retransmitted at any retransmission stage, it moves back to the 0 th retransmission stage. The model assumes constant probabilities of success and failure (ps, pf).
The model assumes an ideal channel, a finite FIFO queue at each node, transmission and reception of single data packet per node per cycle. The related notations are shown in
Table 1.
P
(0,0)->(0,QC)
P
(0,0)->(0,QC-1)
P
(0,0)->(0,0)
0,0
P
P
P
(0,0)->(0,1)
(1,1)->(1,1)
1,1
P
(0,1)->(0,2)
>
P
(0,1)->(0,1)
P
(0,1)->(0,0)
0,1
P
(0,0)->(0,2)
P
(0,2)->(0,2)
P
(0,2)->(0,1)
1)
0,
>(
0,2
)-
P
(0
,1)
->
(1
,2)
P
(0,1),(0,QC-1)
P
(1
P
P
(0
,0
)->
(1
,1
)
P
(1,1)->(1,2)
P
(1,2)->(1,2)
P
(1,2)->(1,1)
1,2
P
(1,1),(1,QC-1)
P
(0,2)->(0,QC-1)
P
(0
,
QC-1)->((0,QC)
. . . . .
P
(0,QC-1)->(0,QC-1)
0,QC
-1
P
(0
,
QC)->(0,QC-1)
0,QC
P
(0,2)->(0,QC)
P
(0,1 P
)->(
1,Q
C-1
)
(0,2
)->
(1,Q
C-1
)
P
(1,2)->(1,QC-1)
. . . . .
P
(1,QC-1)->(1,QC-1)
)
-1
C
0,
Q
>(
P
)-
C
P
(0
,Q
C
-1
P
(1
(0,1)->(0,QC)
)->
(1
,Q
C
)
1,QC
-1
P
(1
,
QC-1)->(1,QC)
P
(1
,
QC)->(1,QC-1)
1,QC
P
(1,2)->(1,QC)
P
(1,1)->(1,QC)
….
….
….
….
P
(0,QC)->(0,QC)
P
(1,QC)->(1,QC)
P
(RL,1)->(RL,1)
P
(RL
,
QC-1)->(RL,QC)
P
(RL,1)->(RL,2)
P
(RL,2)->(RL,QC-1)
RL,1
P
(RL,2)->(RL,2)
P
(RL,2)->(RL,1)
RL,2
P
(RL,1),(RL,QC-1)
. . . . .
P
(RL,QC-1)->(RL,QC-1)
P
(RL,2)->(RL,QC)
P
(RL,1)->(RL,QC)
RL,
QC-1
RL,
P
(RL
,
QC)->(RL,QC-1)
QC
P
(RL,QC)->(RL,QC)
3

Figure 1 2-D Markov queuing model for retransmission in asynchronous MAC protocols
( Source: Yang and Heinzelman (2009a))
Table 1 Notations used
Symbol Meaning n
QC
RL
CL
λ
P
P x ps
≥x
Number of nodes in the network
Queue capacity
Retransmission limit
Cycle length
Data packet arrival rate at MAC layer
Probability that ‘x’ data packets arrive in a cycle
Probability that no less than ‘x’ data packets arrive in a cycle
Probability of successful transmission of data packet pf p = ps
+
pf
Π
(0,0)
Probability of failure of transmission of data packet
Probability of winning contention
Stationary probability of empty queue state
Packet Delivery Ratio PDR
DL
PC
Delay
Power Consumption
Eq. (1)-(13) (Yang and Heinzelman, 2009a) depict the state transition equations. The equations for transition probabilities from empty queue state are:
𝑃
(0,0)−(0.𝑥)
𝑃
(0,0)−(0.𝑄𝐶)
= 𝑃 𝑥
𝑥 = 0 … 𝑄𝐶 − 1
= 𝑃
≥𝑄𝐶
(1)
(2)
Considering the transitions within retransmission stages:
𝑃
(0,𝑦)−(0.𝑧)
𝑃
(0,𝑦)−(0.𝑄𝐶)
= 𝑝𝑠 ∗ 𝑃 𝑦−𝑧+1
= 𝑝𝑠 ∗ 𝑃
+ (1 − 𝑝) 𝑃
𝑄𝐶−𝑦+1 𝑧−𝑦
+ (1 − 𝑝) 𝑃
𝑦 = 1 … 𝑄𝐶 − 1, 𝑧 = 𝑦 … 𝑄𝐶 − 1
𝑄𝐶−𝑦
𝑦 = 1 … 𝑄𝐶 − 1
(3)
(4)
𝑃
(0,𝑦)−(0.𝑦−1)
𝑃
(𝑥,𝑦)−(𝑥.𝑧)
= 𝑝𝑠 ∗ 𝑃
0
𝑦 = 1 … 𝑄𝐶
= (1 − 𝑝) ∗ 𝑃 𝑧−𝑦
(5)
𝑥 = 1 … 𝑅𝐿, 𝑦 = 1 … 𝑄𝐶 − 1, 𝑧 = 𝑦 … 𝑄𝐶 − 1 (6)
𝑃
(𝑥,𝑦)−(𝑥.𝑄𝐶)
= (1 − 𝑝) ∗ 𝑃
≥𝑄𝐶−𝑦
𝑥 = 1 … 𝑅𝐿, 𝑦 = 1 … 𝑄𝐶 − 1, 𝑧𝑦 … 𝑄𝐶 − 1 (7)
Considering the transition from one retransmission stage to adjacent higher stage:
𝑃
(𝑥,𝑦)−(𝑥+1.𝑧)
𝑃
(𝑥,𝑦)−(𝑥+1.𝑄𝐶)
= 𝑝𝑓 ∗ 𝑃 𝑧−𝑦
𝑥 = 0 … 𝑅𝐿 − 1, 𝑦 = 1 … 𝑄𝐶 − 1, 𝑧 = 𝑦 … 𝑄𝐶 − 1
= 𝑝𝑓 ∗ 𝑃
≥𝑄𝐶−𝑦
(8)
𝑥 = 0 … 𝑅𝐿 − 1, 𝑦 = 0 … 𝑄𝐶 (9)
The transition probabilities from non-zero to zero retransmission stage are described as:
𝑃
(𝑥,𝑦)−(0.𝑧)
𝑃
(𝑥,𝑦)−(0.𝑄𝐶)
= 𝑝𝑠 ∗ 𝑃 𝑧−𝑦+1
𝑥 = 1 … 𝑅𝐿 − 1, 𝑦 = 1 … 𝑄𝐶 − 1, 𝑧 = 𝑦 − 1 … 𝑄𝐶 − 1 (10)
= 𝑝𝑠 ∗ 𝑃
≥𝑄𝐶−𝑦+1
𝑥 = 1 … 𝑅𝐿 − 1, 𝑦 = 1 … 𝑄𝐶 (11)
𝑃
(𝑅𝐿,𝑦)−(0.𝑧)
𝑃
(𝑅𝐿,𝑦)−(0.𝑄𝐶)
= 𝑝 ∗ 𝑃 𝑧−𝑦+1
𝑦 = 1 … 𝑄𝐶 − 1, 𝑧 = 𝑦 − 1 … 𝑄𝐶 − 1
= 𝑝 ∗ 𝑃
≥𝑄𝐶−𝑦+1
𝑦 = 1 … 𝑄𝐶, 𝑧 = 𝑦 − 1 … 𝑄𝐶
(12)
(13)
Solving equations (1) – (13) for known values of ‘QC’ and ‘RL’, transition matrix for
2-D Markov queuing model of order (QC*(RL+1) + 1) can be obtained. The obtained matrix
4

can then be used to find the values of ‘ps’,’ pf’ and ‘π
(0,0)
’ which are governed by the function shown in eq. (14) (Yang and Heinzelman, 2009a),
Π
(0,0)
= 𝑓(𝑝𝑠, 𝑝𝑓) (14)
Further, ps and pf will be governed by the function given in eq. (15) (Yang and Heinzelman,
2009a),
(𝑝𝑠, 𝑝𝑓) = [ℎ(Π
(0,0)
), 𝑔(Π
(0,0)
) − ℎ(Π
(0,0)
)] (15)
Solving eq. (14) and eq. (15) simultaneously, we can find the operating points of
XMAC (ps
*
, pf
* , π
(0,0)
*
). These operating points will be utilized to calculate the performance metrics of XMAC such as PDR, delay and power consumption.
3. Media Access Rules of SMAC Protocol
Solving equations (1) – (13) for fixed values of Q and R, transition matrix for 2-D
Markov queuing model can be obtained. The obtained matrix is used to find the values of ‘ps’,
‘pf’ and ‘π
(0,0)
’ which are governed by eq. (14). The probability of transmission failure is given as,
𝑝𝑓 = 𝑝 − 𝑝𝑠 = 𝑔(𝜋
(0,0)
) − ℎ(𝜋
(0,0)
) (16) where, ‘ps’ can be represented as, 𝑝𝑠 = ℎ(𝜋
(0)
) = ∑ 𝑁−1 𝑘=0
𝑀 𝑘
(𝜋
0
). 𝑝𝑠 𝑘 𝑝𝑠 𝑘
= ∑ 𝑊 𝑖=1
(
1
𝑊
) (
𝑊−𝑖
𝑊
) 𝑘 𝑘 = 0 … 𝑁 − 1
(17)
(18) where, ps k is defined as the probability of transmitting a data packet successfully. The solution of eq. (16) and eq. (17) forms a curve in the space (ps
* pf * π
(0,0)
). Solving eq. (14) and eq.
(15) simultaneously, we can find the operating points of SMAC (ps * , pf * , π
(0,0)
* ) which are utilized to calculate the performance metrics of SMAC.
4. Media Access Rules of XMAC Protocol
The media access rules of XMAC are described in eq. (19)-(25) (Yang and
Heinzelman, 2009a). When a node wakes up,
(a) queue can either be ‘empty’ (e) with probability π
(0,0) or ‘non empty’ (e’)
(b) channel can either be ‘free’ or ‘busy’
(c) probability of success (ps) and failure (pf) according to the Markov model can be defined as: 𝑝𝑠 = 𝑃𝑟(𝑋|𝑓𝑟𝑒𝑒, 𝑒’). 𝑃𝑟(𝑓𝑟𝑒𝑒|𝑒’)
𝑝𝑓 = 𝑃𝑟(𝑌|𝑓𝑟𝑒𝑒, 𝑒’). 𝑃𝑟(𝑓𝑟𝑒𝑒|𝑒’)
(19)
(20)
Where, ‘X’ is the event that the node is only single contention winner and ‘Y’ is the event that the node is one of the contention winners. The probabilities ‘ps’ and ‘pf’ can be obtained by determining Pr(X|free,e’), Pr(free|e’) and Pr(Y|free,e’).
If a node’s queue is non-empty and channel is free when it wakes up, then a data packet can be successfully transmitted if either no other nodes in the network wake up
5

simultaneously or some nodes wake up at the same time, but don’t have any packet to send.
Then,
Pr(X|free, e ’ ) = ∑ 𝐶𝐿 𝑡=1
1
𝐶𝐿
∑ n−1 i=0
( n−1 i
) (
π (0,0)
)
CL i (
CL−1
CL
) N−i−1
(21)
In other case, if a node’s queue is non empty and the channel is free when it wakes up, the node can encounter collision during packet transmission if some other node in the network wakes up and starts sending its packet simultaneously. Then,
Pr(Y|free, e’) = ∑ CL t=1
∑ n−1 i=1
( 𝑛−1 𝑖
1
)(
CL
) i (
𝐶𝐿−1
𝐶𝐿
) 𝑛−𝑖−1 𝑖
∑ (1 − π j
(0,0) 𝑗=1
) π i−j
(0,0)
(22)
The probability of a channel being free or busy is same in every time slot in XMAC as the node sends packets at an arbitrary offset. Thus,
Pr(free|e’) ≈ Pr(free) =
E(free)
(E(free)+ E(busy))
(23) where, E(free) is the average length of free channel between two busy channels and E(busy) is the average length of busy channel between two chunks of free channels (Yang and
Heinzelman, 2009a). E(free) is further defined by eq. (24) for a chunk of free channel (n*CL + t).
𝐸(𝑓𝑟𝑒𝑒) = ∑ ∞ 𝑛=0
∑ 𝐶𝐿−1 𝑡=0
(𝑚 ∗ 𝐶𝐿 + 𝑡) . 𝑃𝑓𝑟𝑒𝑒(𝑚, 𝑡) (24)
Pfree(m,t) is the probability of a channel to be free for ‘m’ cycles. Similarly, E(busy) can be represented by eq. (25),
𝐸(𝑏𝑢𝑠𝑦) = ∑ 𝐶𝐿−1 𝑡=0
∑ 𝐶𝐿−1 𝑡=0
(
𝐶𝐿
2
+ 𝐶𝐿(𝐷𝐴𝑇𝐴)) . 𝑝𝑠, 𝑏(𝑚, 𝑡) + 𝑇 . 𝑝𝑐, 𝑏(𝑚, 𝑡) (25)
The terms ps,b(m,t) and pc,b(m,t) represent the probability of successful transmission and probability of failure when the channel is free for ‘m’ cycles and ‘t’ slots respectively.
Substituting eqs. (24) and (25) in eq. (23), the probability of channel being free can be obtained. Substituting eqs. (21) and (23) in eq. (19) and eqs. (22) and (23) in eq. (20) will yield the probabilities ‘ps’ and ‘pf’ for XMAC protocol.
5. Performance Metrics
5.1 Packet delivery ratio (PDR)
PDR describes the level of data delivered to the destination successfully. It is defined as the ratio between the number of packets successfully delivered to the destination to the total number of packets transmitted by the sending node. The PDR of XMAC can be calculated according to eq. (23).
PDR = (1 − π
∗
(0,0)
) ps ∗ / (λ ∗ cl ∗ τ) (23)
5.2 Delay
Delay is defined as the average time taken by a data packet to reach from source to destination. The total delay (DL) is expressed as a sum of queuing delay (QD) and contending delay (CD) (Yang, 2011). Queuing delay is time spent by a data packet in the queue. While,
6

contending delay is the time taken by the data packet to win contention in the medium and leave the queue.
𝐷𝐿 = 𝑄𝐷 + 𝐶𝐷 (24)
CD can be expressed as a function of ps and pf. A node has probability ‘p’ of winning contention in a cycle. A node can overcome contention and successfully transmit a data packet with probability ‘ps’ and consecutively, a packet with probability ‘pf’ may drop due to collision. Hence, the contending delay for ‘R’ retransmissions can be given by the formula explained in (Yang, 2011).
𝐶𝐷 = 𝑇. 𝑝𝑠. ∑ 𝑅𝐿 𝑖=0
∑ ∞ 𝑗=0
( 𝑖+𝑗 i
)𝑝𝑓 𝑖 (1 − 𝑝𝑓) j
(25)
Queuing delay can be calculated as a function of contending delay (Yang and
Heinzelman, 2010a) and is given as:
𝑄𝐷 = 𝐶𝐷 . ∑
𝑄−1 𝑖=0 𝑚𝑎𝑥(0,𝑖−0.5).𝜋(𝑖)
(1−𝜋(𝑄))
(26)
Substituting the values obtained in eq. (25) and eq. (26) in eq. (24), total delay in
XMAC can be obtained.
5.3 Power consumption
Power consumption (PC) is an important aspect of XMAC as it is designed to consume less power like other asynchronous MAC protocols. Energy consumption in XMAC
(Yang and Heinzelman, 2009a) can be analysed under five different cases as described in eq.
(27)-(32):
Case I: Energy consumed when a node is the sender of successful data transmission (E ss
)
In this case, the probability of node becomes ((1- Π
(0,0)
) ps) and the average communication time is (CL/2+t d
). CL/2 period is used to send preamble packets and listen acknowledgement packets, while t d period is the duration of sending data packets. Hence, energy consumed in this case can be elaborated as:
𝐸 𝑠𝑠
= (1 − π ∗
(0,0)
). ps ∗ . τ [
CL
2
( t p t a
+t a
) . Ptx +
CL
2
( t p t a
+t a
) . Ptx + t d
. Prx ] (27)
Case II: Energy Consumed when a node is the destination of successful data transmission (E rs
)
In this case, a node receives the preamble during t p period, sends acknowledgement packet for t a period and receives data packet during t d
period with probability ((1- Π
(0,0)
) ps)
(Yang and Heinzelman, 2012). The destination node listens for duration (t p
+ t a
)/2 before receiving the complete preamble. Hence, energy consumed in this case can be elaborated as:
𝐸 𝑟𝑠
= (1 − π ∗
(0,0)
). ps ∗ . τ [( t p
+t
2 a
) . Prx + t p
. Prx + t a
. Ptx + t d
. Prx ] (28)
Case III: Energy Consumed when a node is the sender of unsuccessful data transmission (E sf
)
If more than one node starts sending preamble simultaneously, then no preamble packet can be received successfully. In this case, the probability of a node for being the sender of unsuccessful data transmission becomes ((1- Π
(0,0)
).pf) and the nodes continuously send
7

preamble packets and listen to the medium for entire cycle length (CL). The energy consumed
(Yang and Heinzelman, 2012) in this case can be given as:
𝐸 𝑠𝑓
= (1 − π
∗
(0,0)
). pf ∗ . τ [CL ( t p t p
+t a
) . Ptx + CL ( t a t p
+t a
) . Prx] (29)
Case IV: Energy Consumed when a node is the destination of unsuccessful data transmission
(E rf
)
This case occurs if node wakes up when colliding preamble packets are half way through transmission or when the colliding senders are listening to the media between two successive preamble packets (Yang and Heinzelman, 2012). In this case, the node is awake for the period (t p
+ t a
)/2 + t p
and energy consumption is given as:
𝐸 𝑟𝑓
= (1 − π ∗
(0,0)
). pf ∗ . τ [( t p
+t
2 a
) . Prx + t p
. Prx] (30)
Case V: Energy Consumed when a node is idle (E idle
)
In this case, the node can go to sleep and is not involved in packet transmission. The probability of a node to remain in idle state is 1 – 2 (1-Π
(0,0)
) . p. The energy consumed (Yang and Heinzelman, 2012) in this case is given as:
𝐸 𝑖𝑑𝑙𝑒
= 1 − 2(1 − π ∗
(0,0)
). p. τ. Prx[∑
tp [∑ 𝑇−1 𝑡=𝐴
𝑃𝑓𝑟𝑒𝑒(0, 𝑡) + ∑ ∞ 𝑛=1
𝐴−1 𝑡=0
∑
𝑃𝑓𝑟𝑒𝑒(0, 𝑡). (𝑡 + tp + ta/2)
𝑇−1 𝑡=0
𝑃𝑓𝑟𝑒𝑒(𝑛, 𝑡) ]𝐴]
+
(31)
On adding eq. (27) to eq. (31), total energy consumption (E) and power consumption (PC) of a node in a cycle can be obtained as:
𝐸 = 𝐸 𝑠𝑠
+ 𝐸 𝑟𝑠
+ 𝐸 𝑠𝑓
+ 𝐸 𝑟𝑓
+ 𝐸 𝑖𝑑𝑙𝑒
PC = E/T
(32)
(33)
The power consumed by a node in the network can be further used to find the lifetime of the network.
6. Numerical Illustration and Result Analysis
The proposed algorithm for retransmission in XMAC protocol employing 2-D
Markov queuing model was simulated in MATLAB 7.0.1. During simulation, input parameters used are shown in Table 2.
Table 2 Input Parameters
Parameter
Channel Sensing Time
Advertisement Period
Acknowledgement Period
Data Transmission Period
Queue Capacity
Number of Retransmission Stages
Number of Nodes
Packet Arrival Rate
Contention Window Size
Symbol
C t adv t a t d
QC
RL n
λ w
Value
1
3
1
5
5
1, 3, 5, 7, 9
10
1
128
Unit ms ms ms ms
-
-
- pkt/s
-
8

At different retransmission stages, simulation of 2-D Markov queuing model yields different value of p s
, p f and π
0 for SMAC and XMAC, which can be determined from Figure 2
(A)-(D). The blue curve represents simulation results obtained from 2-D Markov queuing model. While, the red curve depicts the simulation results due to media access rules of XMAC.
The point of intersection of these two curves yields the operating point ps*, pf *and π
0
*. For convenience, π
(0,0) is taken as π
0.
As the values of p s
, p f and π
0 vary according to retransmission stage (R) in SMAC and
XMAC, variations can be observed in performance metrics, such as PDR, delay and power respectively. As evident from Figure 3 (A) and (B) that PDR of XMAC is higher than that of
SMAC, which implies that for a given number of packets, XMAC is capable of transmitting more packets than SMAC successfully in a network at lower power. Besides, XMAC can transmit data packets with lower delay than SMAC at lower power consumption. This makes
XMAC a favourable energy efficient MAC protocol.
N=10 W=128 Q=5

=1pkt/s
0.6
0.4
1
0.8
1
0.8
0.6
0.4
0.2
0.2
0
1
0
1
1 1
0.5
pf
0.2
0 0
N=10 W=128 Q=5

0.4
(A) SMAC, R=1
0.6
0.8
0.5
pf
0.2
0
0
N=10 W=128 Q=5

=1pkt/s
(B) XMAC, R=1
0.4
ps
0.6
0.8
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
1
0
1
1
1
0.5
0.8
0.5
0.8
0.4
0.6
0.4
0.6
0.2
0.2
0
0
0
0 pf ps
(C) SMAC, R=9 pf ps
(D) XMAC, R=9
Figure 2(A) – (D) Determination of (p s
, p f
, π
0
) for 2-D Markov model in SMAC and
XMAC at different retransmission stages
9

PDR, Delay, Power Consumption vs.
No. of Retransmission Stages
PDR, Delay, Power Consumption vs.
No. of Retransmission Stages
10000
PDR
1000
PDR
1000
Delay
100
Delay
100
10
Power
Consumption
10
1
Power
Consumption
1
0,1
1 3 5 7 9 0,1
1 3 5 7 9
0,01
0,01
0,001
0,001
Retransmission Stage
0,0001
Retransmission Stage
(A) SMAC (B) XMAC
Figure 3 (A), (B) Effect of retransmission on PDR, delay and power consumption in (A)
SMAC and (B) XMAC
Figure 4 (A)-(D) represents the simulation results at varying packet arrival rate for
SMAC and XMAC at R=1, λ=1 and 5 to show the variation in p s
*, p f

*and π
(0,0)
* according to packet arrival rate.
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
1
0
1
0.5
0.4
pf
N=10 W=128 Q=5

=5pkt/s
0 0
0.2
(A) SMAC, R=1, λ=1 ps
0.6
0.8
1
0.5
pf
0.6
0.4
N=10 W=128 Q=5

0 0 ps
(B) XMAC, R=1, λ=1
0.8
1
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
1
0
1
0.5
0.4
0.2
pf
0 0 ps
(C) SMAC, R=1, λ=5
0.6
0.8
1
0.5
pf
1
0.8
0.6
0.4
0.2
0 0 ps
(D) XMAC, R=1, λ=5
Figure 4 (A) – (D) Determination of (p s
, p f
, π
0
) for 2-D Markov model in SMAC and
XMAC at R=1 for varying packet arrival rate
10

It can be seen in Figure 4 that as the packet arrival rate increases, the values of p s
, p f and π
0 change accordingly. These changes cause the values of PDR (eq. 23), delay (eq. 24) and power consumption (eq. 33) to change accordingly. In Figure 5 (A)-(D), the effect on PDR is studied for different packet arrival rates in SMAC and XMAC protocols at different retransmission stages.
0,2
PDR vs. Packet Arrival Rate at
R=1
0,2
PDR vs. Packet Arrival Rate at
R=3
0,15
SMAC
XMAC
0,15
SMAC
XMAC
0,1 0,1
0,05 0,05
0
0 2 4
Packet Arrival Rate at (pkt/s)
6
(A) R=1
0
0 2 4
Packet Arrival Rate (pkt/s)
6
(B) R=3
0,2
PDR vs. Packet Arrival Rate at R=7
0,2
PDR vs. Packet Arrival Rate at R=9
0,15
SMAC
XMAC
0,15
SMAC
XMAC
0,1
0,1
0,05
0,05
0
0 2 4
Packet Arrival Rate (pkt/s)
6
0
0 4
(C) R=7 (D) R=9
Figure 5 (A)–(D) Effect of packet arrival rate on PDR in SMAC and XMAC
6
PDR of XMAC is higher than SMAC at every retransmission stage. However, the
PDR of XMAC falls sharply with increasing ‘λ’ as the retransmission stage advances. While, the PDR of SMAC decreases up to λ=2 pkt/s, and then becomes almost constant.
Figure 6 (A)-(D) indicates that as λ increases, the delay increases in both SMAC and
XMAC at each retransmission stage. However, when compared at individual retransmission stage, the delay experienced by XMAC is lower than SMAC, which can be attributed to the asynchronous property of XMAC protocol.
Delay vs. Packet Arrival Rate at R=1
160
140
120
100
80
60
SMAC
XMAC
0 2 4
Packet Arrival Rate (pkt/s)
6
Delay vs. Packet Arrival Rate at R=3
360
260
SMAC
XMAC
160
60
0 2 4
Packet Arrival Rate (pkt/s)
6
11

(A) R=1
Delay vs. Packet Arrival Rate at
R=7
(B) R=3
Delay vs. Packet Arrival Rate at R=9
600
SMAC
XMAC
800
700
500
400
600
SMAC
XMAC
500
300
2 4
Packet Arrival Rate (pkt/s)
400
0 6
0 2 4
Packet Arrival Rate (pkt/s)
6
(C) R=7 (D) R= 9
Figure 6(A) – (D) Effect of packet arrival rate on delay in SMAC and XMAC
Figure 7 (A)-(D) discusses the effect of ‘λ’ on delay at different retransmission stages.
It is clear from Figure 7 that number of retransmissions does not affect power consumption of
SMAC and XMAC. Besides, it can be concluded that power consumed by XMAC is less than
SMAC protocol due to the absence of synchronization overhead. This makes XMAC, i.e., an asynchronous MAC protocol, a better option for data transmission due to its power efficiency.
Power Consumption vs. Packet
Arrival Rate at R=1
0,0016
0,0014
0,0012
0,001
0,0008
0,0006
0,0004
0 2 4
Packet Arrival Rate (pkt/s)
6
(A) R=1
Power Consumption vs. Packet
Arrival Rate at R=7
0,008
SMAC
XMAC
0,004
Power Consumption vs. Packet
Arrival Rate at R=3
0,003
0,002
0,001
0
1 2 3 4 5
Packet Arrival Rate (pkt/s)
(B) R=3
SMAC
XMAC
Power Consumption vs. Packet
Arrival Rate at 9
0,008
0,006
0,004
SMAC
XMAC
0,006 SMAC
XMAC
0,004
0,002
0,002
0
0
0 2 4 6
Packet Arrival Rate (pkt/s)
1 2 3 4 5
Packet Arrival Rate (pkt/s)
(C) R=7 (D) R=9
Figure 7(A) – (D) Effect of packet arrival rate on power consumption in SMAC and
XMAC
12

We also studied the performance of SMAC and XMAC by varying number of nodes
N=10 W=128 Q=5

=1pkt/s N=10 W=128 Q=5 =1pkt/s from 5 to 25. Figure 8 (A)-(D) represents the MATLAB simulation graphs for SMAC and
XMAC at R=1 and N=5, 25 to show the variation in p s
*, p f
*and π
(0,0)
*.
1
0.8
1
0.8
0.6
0.6
0.4
0.2
0.4
0.2
1
0.8
0.6
0.4
0.2
0
1
0
1
1
0.8
0.5
0.4
pf
N=25 W=128 Q=5
 0.2
0
0 ps
(A) SMAC, R=1, N=5
0.6
1
0.8
0.6
0.8
0.5
0.6
0.4
0.2
pf
0 0 ps
(C) SMAC, R=1, N=25
1
0.4
0.2
0
1
0
1
0.5
0.4
pf
N=25 W=128 Q=5

0.2
0
0
(B) XMAC, R=1, N=5 ps
0.6
0.5
0.4
0.2
pf
0 0 ps
(D) XMAC, R=1, N=25
0.6
0.8
0.8
1
1
Figure 8(A)–(D) Determination of (p s
, p f
, π
0
) for 2-D Markov model in SMAC and XMAC at R=1 for varying number of nodes
In Figure 8, the values of p s
, p f and π
0 decrease with an increase in ‘n’ at different retransmission stages and are greater for XMAC as compared to SMAC.
Figure 9 (A)-(D) studies the effect on PDR for increasing number of nodes in SMAC and XMAC protocols at different retransmission stages.
No. of Nodes vs. PDR at R=1 No. of Nodes vs. PDR at R=3
0,4
0,35
0,3
0,25
0,2
0,15
0,1
0,05
0
SMAC
XMAC
0,5
0,4
0,3
0,2
0,1
0
SMAC
XMAC
5 10 15 20 25
No. of nodes
(A) R=1
5 10 15 20 25
No. of Nodes
(B) R=3
13

No. of Nodes vs. PDR at R=7 No. of Nodes vs. PDR at R=9
0,4
0,4
0,3
SMAC
XMAC
0,3
0,2
0,2
0,1
0,1
0
5 10 15
No. of Nodes
20 25
0
5 10 15
No. of Nodes
20 25
(C) R=7 (D) R=9
Figure 9(A) – (D) Effect of number of nodes on PDR in SMAC and XMAC
SMAC
XMAC
We know that PDR decreases with increasing number of nodes as the retransmission stage advances due to collisions in the network. It is clear from Figure 9 that PDR of XMAC is higher than SMAC as the number of nodes exceed beyond 10. It implies that XMAC is able to transmit more data packets successfully within the network for large number of nodes as compared to SMAC.
In Figure 10 (A)-(D), the effect on delay is studied at different retransmission stages for increasing number of nodes.
No. of Nodes vs. Delay at R=1
No. of Nodes vs. Delay at R=3
170
150
130
110
90
70
SMAC
XMAC
300
250
200
510
460
410
360
310
5 10 15 20 25
No. of nodes
(A) R=1
No. of Nodes vs. Delay at R=7
5 10 15 20 25
No. of nodes
(C) R=7
SMAC
XMAC
150
5 10 15 20 25
No. of nodes
(B) R=3
No. of Nodes vs. Delay at R=9
650
600
550
500
450
400
5 10 15 20 25
No. of Nodes
(D) R=9
SMAC
XMAC
SMAC
XMAC
Figure 10(A) – (D) Effect of node variation on delay in SMAC and XMAC
14

It is evident from Figure 10 that delay experienced by SMAC is more than that by
XMAC at each retransmission stage. It is also noticeable that delay in SMAC increases with the number of nodes during R=1 and 3 and then starts reducing with nodes at R= 7 and 9.
While, XMAC being asynchronous, avoids delay due to synchronization overhead, thus, leading to lower values of delay.
It can be inferred from Figure 11 (A)-(D) that power consumption of XMAC is lower than SMAC. This is due to the fact that synchronization overhead is removed in asynchronous
MAC protocols, thus, making XMAC a power efficient protocol. Besides, the power consumed by SMAC increases with number of nodes. While, power consumption is almost constant in
XMAC.
No. of Nodes vs. Power Consumption at
R=1
No. of Nodes vs. Power Consumption at R=3
0,0014
0,0034
0,0009
SMAC
XMAC 0,0024
SMAC
XMAC
0,0014
0,0004
5 10 15 20 25
No. of nodes
(A) R=1
0,0004
5 10 15 20 25
No. of nodes
(B) R=3
No. of Nodes vs. Power Consumption at R=7
No. of Nodes vs. Power Consumption at R=9
0,0074
0,0064
0,0054
0,0044
0,0034
0,0024
SMAC
XMAC
0,0084
0,0064
0,0044
0,0024
SMAC
XMAC
0,0014
0,0004
0,0004
5 10 15 20 25
5 10 15 20 25
No. of nodes No. of Nodes
(C) R=7 (D) R=9
Figure 11(A) – (D) Effect of varying number of nodes on power consumption in SMAC and XMAC
7. Conclusion and Future Work
The results are analysed for retransmission in synchronous and asynchronous MAC protocols with application to SMAC and XMAC. During simulation, we studied the impact of retransmission on performance of SMAC and XMAC. Our performance metrics included PDR, delay and power consumption. We analysed the behaviour of SMAC and XMAC protocols under different retransmission stages, varying packet arrival rate and number of nodes. It is concluded that under every scenario, XMAC outperforms SMAC. It is due to the absence of
15

synchronization overhead that XMAC experiences lower delay than SMAC. Lower delay implies timely data transmission, thus, lower energy consumption.
Although, SMAC is a low duty- cycled MAC layer protocol with low energy consumption, yet it experiences high delay, latency, etc. In WSN, in critical applications, delay is not acceptable during retransmission of information (data packets). This degrades the quality of service of SMAC protocol. This proves that asynchronous MAC protocols give better performance than their synchronous counterparts during retransmission.
Our work can be extended to study retransmission in other asynchronous MAC protocols. The methodology to determine (p s
*, p f
*, π
(0,0)
*) will remain the same except for media access rules of the concerned protocol in Step 6. Besides, the model can be extended to practical channels and transmission of multiple data packets per node in a cycle.
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