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Transactions on Vehicular Technology
1
Medium Access for Concurrent Traffic in Wireless
Body Area Networks: Protocol Design and Analysis
Rongrong Zhang, Hassine Moungla, Jihong Yu, Ahmed Mehaoua
Abstract—Wireless Body Area Networks (WBANs) have been
deployed to monitor the health condition of patients. In these
applications, multiple sensors are required to report the real-
time data to the sink such that a physician can diagnose
accurately, especially for intensive care patients, which boosts the
convergecast traffic load and increases the collision probability.
However, the existing protocols cannot operate effectively under
such concurrent traffic load. To bridge this gap, we present a
novel two-phase receiver-initiated MAC protocol for Concurrent
traffic based on asynchronous duty cycling, called C-MAC.
Technically, C-MAC in the first phase employs the Carrier Sense
Multiple Access with Collision Avoidance (CSMA/CA) of IEEE
802.15.6 standard and designs an ordering-based communication
algorithm to effectively avoid collisions. Moreover, C-MAC en-
ables sensor nodes to switch to Standby Mode (SBM) to avoid idle
listening and overhearing in the second phase. Furthermore, the-
oretically, we explicitly formulate the mathematical expressions
of the random delay and energy consumption of C-MAC. Finally,
we conduct the extensive numerical analysis and simulation to
demonstrate the correctness of theoretical results and the better
effectiveness and efficiency of C-MAC than that of RI-MAC and
A-MAC in terms of transmission delay and energy consumption.
I. INT ROD UC TI ON
A. Background
Wireless Body Area Networks (WBANs) typically consist
of a collection of low-power, miniaturized, lightweight sensor
nodes that can be implanted in or on the human body to
monitor the real time physiological parameters [1]. Equipped
with such sensor nodes, WBANs have emerged as a promising
alternative to traditional wired medical network and improved
patients’ quality of life. But the limited battery of sensor nodes
raises a number of challenges on the design of Medium Access
(MAC) protocols [2].
Generally, the energy is consumed mostly for idle listening,
collision and overhearing [3]. Specifically, in idle listening,
a node keeps its radio on to listen to an idle channel for
receiving possible packets even though no packets have been
sent. The collision happens when more than one senders
communicate with the same destination simultaneously, re-
sulting in corrupted, discarded or retransmitted events. The
overhearing problem occurs when a node receives a packet not
Copyright (c) 2015 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
R. Zhang, H. Moungla and A. Mehaoua are with Lab. Informatique Paris
Descartes (LIPADE), Univ. Paris Descartes, Sorbonne Paris Cit´
e 45 rue des
saints p`
eres, 75006, Paris, France E-mail: {rongrong.zhang; hassine.moungla;
ahmed.mehaoua}@parisdescartes.fr.
J. Yu is with Lab. Recherche Informatique (LRI-CNRS UMR 8623), Univ.
Paris-Sud, 91405 Orsay, France, E-mail: jihong.yu@lri.fr.
originally for it. To reduce the energy waste and prolong the
lifetime of sensor nodes, in recent years, many energy-efficient
MAC protocols [4] have been designed from the perspective
of reducing idle listening, collision and overhearing.
Duty cycling, an effective energy saving technique in Wire-
less Sensor Networks (WSNs) [5], is employed in most of
these solutions. By duty cycling, each node periodically turns
on/off its radio to alternate between active and sleep states.
Based on the synchronization requirement, the existing duty
cycling MAC protocols can be roughly categorized into two
types: synchronous and asynchronous.
In synchronous protocols such as T-MAC [6], RMAC [7],
Mix-MAC [8] and iA-MAC [9], neighbor nodes exchange
control message to schedule transmissions, which greatly
reduces idle listening, but periodic time synchronization incurs
much extra overhead. In addition, it is inefficient in handling
variable rate traffic to use fixed duty cycle period.
In contrast, asynchronous duty cycling protocols that do
not require synchronization allow nodes have their individual
duty cycles. Depending on which end of a communication link
initiates a transfer, the asynchronous protocols may be further
classified as either sender-initiated (e.g., B-MAC [10], X-
MAC [11]and WiseMAC [12]) or receiver-initiated (e.g., RI-
MAC [13], A-MAC [14], PW-MAC [15] and RC-MAC [16])
(cf. Sec.II for detailed discussion).
B. Problem statement and contributions
Although duty cycling-based approaches can remarkably
save energy, they will also lead to the significant latency
in packet delivery, since the senders have to wait until the
receiver wakes up to transmit packets. Despite some existing
protocols attempt to mitigate the additional latency, they only
work effectively under light traffic load. However, a WBAN
could often experience bursty or concurrent traffic, especially
in health monitoring applications, where multiple sensors
will send their reports to the sink concurrently, boosting the
convergecast traffic load and increasing the channel contention
among multiple active sensors which leads to severe collisions.
In this case, the existing protocols will become less efficient
in delay and energy efficiency, because this concurrent traffic
in the latency-sensitive applications is ignored in their design.
Motivated by the observations and based on our previous
work [17], in this paper we present an asynchronous duty
cycling MAC protocol for concurrent traffic load, called C-
MAC. C-MAC attempts to avoid collisions of concurrent flows
to reduce the packet transmission delay and conserve energy,
i.e., ensuring that multiple detected physiological parameters
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Transactions on Vehicular Technology
2
can accurately and timely be received by the sink to the
maximum extent such that the actuator can make the accurate
diagnoses in the medical applications.
Definitely, C-MAC exploits the receiver-initiated approach,
which removes the pressure on the battery from the sensor
nodes to the sink, considering the characteristics of WBANs
that the sink is more powerful than sensor nodes, such as the
operability of recharge or replacement.
Moreover, differing from the existing MAC protocols, C-
MAC focus on handling collisions, idle listening and over-
hearing problems in medical applications with the concurrent
traffic load. Therefore, the main contributions of this paper are
articulated as follows:
•Firstly, we propose a two-phase asynchronous duty cy-
cling MAC protocol, called C-MAC. In the first phase, the
Carrier Sense Multiple Access with Collision Avoidance
(CSMA/CA) mechanism is employed to avoid collisions
among the control messages exchanges. Moreover, an
ordering-based communication algorithm is designed to
sequence data packet transmissions. In the second phase,
we introduce StandBy Mode (SBM) which nodes are
allowed switch to, in order to resolve the idle listening
and overhearing among data packet transmissions.
•Secondly, we explicitly derive the mathematical formu-
las of the random delay and the normalized energy
consumption for C-MAC. Subsequently, we validate the
correctness of theoretical analysis in terms of the mean
and variance by simulation and numerical results.
•Finally, we conduct extensive simulation to evaluate the
performance of C-MAC by comparing with RI-MAC
and A-MAC. The simulation results demonstrate that
C-MAC significantly conserves energy and reduces the
transmission delay, especially under concurrent traffic.
To the best of our knowledge, we believe that this is the
first effort to address the concurrent traffic in the medical
applications of WBANs by designing an IEEE 802.15.6 C-
SMA/CA and ordering-based receiver-initiated asynchronous
duty cycling MAC protocol.
C. Paper organization
The remainder of this paper is organized as follows. Sec-
tion II gives a brief overview of related work in duty cycling
MAC protocols. In Section III, we introduce IEEE 802.15.6
CSMA/CA mechanism. In section IV, we detail C-MAC
protocol and then develop the theoretical analysis of delay and
energy consumption of C-MAC in Section V and Section VI,
respectively. In Section VII, we evaluate the performance of
C-MAC. Finally, we conclude our paper in section VIII.
II. RE LATE D WO RK
Due to the efficiency of duty cycling on the energy conserva-
tion, a number of MAC protocols have recently been proposed
in [10]-[16] which will be briefly reviewed in this section.
Sender-initiated protocols. B-MAC [10] and X-MAC [11]
are primary sender-initiated asynchronous duty cycling proto-
cols. The Low Power Listening (LPL) mechanism is exploited
in B-MAC and X-MAC, in which, the sender with pending
packets first transmits a long preamble or a series of short
preambles to the receiver before data transmission. When the
receiver wakes up and detects the preamble, it will remain
awake to receive the subsequent packets. This approach can
achieve high energy efficiency under light traffic load. The
energy efficiency and channel utilization, however, degrades
as the traffic load increases.
Subsequently, a prediction-based mechanism is proposed
in WiseMAC [12] to save energy and improve the channel
utilization by learning duty cycle of the receiver. But the
hidden terminal problem and persistent collisions will often
happen as the nodes maintain the same fixed duty cycles.
Due to the drawbacks of sender-initiated protocols, re-
searchers turn their attentions to receiver-initiated approach
which can handle hidden terminal problem and support low
duty cycles.
Receiver-initiated protocols. In RI-MAC [13], the receiver
immediately broadcasts a beacon after its wakeup. Upon the
beacon reception, the sender transmits its packet immediately.
If a collision is detected, the receiver sends another beacon
with increased backoff window to request the senders to do
a backoff before their next transmission attempts in order to
avoid repeated collisions.
Differently, the sender needs to send back an auto-ACK
after receiving a probe from the receiver and then transmits its
packet after a random backoff delay in A-MAC [14]. Whereas,
once the ACKs or packets collide, the receiver transmits
another probe with an explicit contention window to request
the senders to retransmit packets. However, the efficiency of
RI-MAC and A-MAC degrades under the concurrent traffic
load as the collision avoidance has not been considered in
advance, and the overhearing problem cannot be resolved.
An efficient prediction-based retransmission mechanism is
designed in PW-MAC [15]. When a node recognizes the failure
of its transmission, it switches to sleeping state and wakes up
at the next predicted receiver wakeup time to retransmit the
packet, thereby minimizing the energy consumption spending
on waiting for the receiver. However, for the sake of accurate
prediction, PW-MAC requests the nodes to persistently learn
and update the prediction state of its neighbors, which needs
more memory and increases message overhead.
Recently, a Receiver-Centric MAC (RC-MAC) protocol is
presented in [16]. RC-MAC takes advantage of the data gather-
ing tree structure and multichannel technique to improve the
throughput. However, the overhead and energy consumption
are very heavy as each node needs to periodically update the
beacon offset of all its neighbors to obtain link information.
It is worth noticing that all the aforementioned MAC proto-
cols cannot be directly applied in WBANs with bursty or con-
current traffic. The main reason is that the collision probability
is very high when multiple nodes concurrently communicate
with the same destination, however, the collision avoidance has
not been considered in advance in prior protocols, which can
resulting in the persistent collisions among nodes and increase
the energy consumption and the transmission delay.
In contrast, C-MAC exploits the IEEE 802.15.6 CSMA/CA
mechanism to avoid collisions in control message exchange
phase. And the design of ordering-based communication can
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Transactions on Vehicular Technology
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achieve contention-free data packets transmission in the sec-
ond phase. Moreover, the idle listening and overhearing can
be essentially resolved by the introduction of SBM. Therefore,
C-MAC has the potential to handle concurrent traffic load for
WBANs, more effectively and efficiently.
III. OVERVIEW OF IEEE 802.15.6 CSMA/CA
In this section, we briefly introduce the CSMA/CA mecha-
nism specified in IEEE 802.15.6 standard [18], which will be
used in the follow-up design and analysis of C-MAC protocol.
To meet the MAC needs of low-power and short-range
WBANs, the CSMA/CA scheme has been developed and
employed in IEEE 802.15.6 standard. In the scheme, a node
maintains three variables for each transmission attempt: NB,
CW and BC, where NB is the number of backoff times, CW is
the value of contention window, and BC is the backoff counter.
First, after sensing the channel is idle for a Short Inter-
Frame Spacing (SIFS) time interval for an arbitrary node, it
initializes its BC to a random integer uniformly distributed
over the interval [1, CW], where C W ∈(CWmin,C Wmax ).
The values of CWmin and CWmax depend on the priority
of a user. Subsequently, the node decreases BC by one for
each idle CSMA/CA slot. Otherwise, the node locks the BC
until the channel is idle again. Once the BC reaches zero and
the channel is idle, the node can send its packet. Meanwhile,
the number of NB increases by one for each access attempt.
If the contention fails, CW is doubled for even number of
failures, and remains unchanged for odd number of failures.
If the doubling CW exceeds the C Wmax , the node sets the
CW to C Wmax . Then, the node will select a new BC over
new [1, CW] and repeat the backoff procedure in the following
slots until the packet is transmitted successfully or it reaches
the maximum number of backoff NBmax . Note that the initial
CW is generally set to C Wmin .
IV. C- MAC DESIGN
In this section, we first introduce the application scenarios
and system model. Then, the C-MAC design is described.
A. Application scenarios and system model
Typical medical applications of WBANs are to monitor the
different physiological data such as electrocardiogram (ECG),
electroencephalogram (EEG), electromyogram (EMG), glu-
cose level, blood pressure and temperature, etc.. When the
status of a patient changes, different physiological data will
concurrently converge from multiple sensor nodes to the sink,
which boosts the traffic load suddenly and thus increases
the collision probability. In this case, to accurately detect
the patient’s health condition, the physician needs the real-
time data from sensors and comprehensively analyze the
data. Therefore, it is essential to design a MAC protocol to
accommodate this concurrent traffic in medical applications.
In these scenarios, we consider a popular single-hop star
WBAN network of a sink and multiple sensor nodes. The
“sensor node” is referred to as “node” in the rest of this paper.
In duty cycling protocols, the sink and each node alterna-
tively stay in two major states, i.e.,
•Active state: the sink and the node turn on their radio and
stay awake to transmit or receive packets.
•Sleep state: the sink and the node completely shut down
to conserve energy.
Sink
Node
SBM Active Sleep
Fig. 1. State transition relationship
Moreover, in order to avoid idle listening and overhearing
for the nodes during data packet transmission, inspired by [19],
we further introduce SBM, i.e.,
•Standby mode: all the operations of the node are stopped
except the system clock thus the node can save energy and
also promptly switch to active state to transmit packets.
Fig.1 illustrates the transition relationship among these states.
Note that only the node can switch between the active state
and the SBM.
B. C-MAC description
The C-MAC consists of two phases: the control message
exchange phase and the data packet transmission phase. Fig. 2
illustrates an example of the operation of C-MAC.
O-ACK
Wake up
ACK
2
N
ACK
ACK
G-ACK
Node active
Receive Transmit Collision StandBy
Mode
With transmission order
ACK
Packet
arrival
1
N
G-ACK
3
N
ACK
G-ACK
Phase 1 Phase 2
G-ACK
ACK
ACK
G-ACK G-ACK
G-ACK
G-ACK
O-ACKO-ACK O-ACK
With inform. of received ACKs
ACK
Fig. 2. Illustration of C-MAC
1) Phase 1-Control message exchange: After turning on
its radio, the sink broadcasts a preamble, announcing that it
is awake and ready to receive packets. For the nodes with
pending packets, they stay silent to wait for the preamble from
the sink. Upon receiving a preamble, the nodes will respond
ACKs following the IEEE 802.15.6 CSMA/CA mechanism.
If receiving ACKs, the sink realizes the success of its pream-
ble transmission, while instead of replying with an I-ACK
(Immediate-ACK) it waits for all probable ACKs from the
other active nodes triggered by the same event and sends a G-
ACK (Group-ACK) with the information of received ACKs
after a timeout. Otherwise, the sink will transmit another
preamble with random backoff until it receives ACKs suc-
cessfully or it reaches the maximum number of the preambles
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Np. Note that the G-ACK’s role is twofold: On one hand, it
reports the correct receipt of ACKs of which nodes, and it
informs the nodes whose ACKs were collided to resend their
ACKs subsequently, on the other hand.
After the reception of G-ACK, each node firstly checks
whether its ACK has been received successfully. If so, the
node will wait for O-ACK (Organized-ACK); otherwise, it
will retransmit its ACK and wait for G-ACK. If there is
no incoming ACK in a timeout after transmitting a G-ACK,
the sink regards itself having received all ACKs successfully
and executes the ordering-based communication algorithm
subsequently described in Algorithm 1 to sequence all nodes’
data packet transmissions and broadcasts an O-ACK with
nodes’ communication order. Specifically, the O-ACK can
acknowledge all ACKs and also notice the start of the data
packet transmission phase. If there is not any feedback after
the Np-th preamble transmission, the sink realizes that there
is no incoming packet and switches to sleep state.
2) Phase 2-Data packet transmission: Once receiving O-
ACK, each node will compute its accurate transmission time
according to its order. Thus, it can decide to remain active to
transmit packet or switch to the SBM until just before its due
transmission time. If the node does not find its communication
order in O-ACK, it will sleep immediately. Once the O-ACK
is lost, the sink will retransmit until O-ACK is successful or
it reaches the maximum transmission times No.
Under the concurrent traffic load, C-MAC significantly re-
duces the transmission delay resulted from persistent collisions
by combining IEEE 802.15.6 CSMA/CA and ordering-based
communication algorithm. Moreover, the design of G-ACK
and O-ACK enables that the sink can receive concurrent
packets as many as possible in one duty cycle and resolve the
early sleep problem [20] that the sink goes to sleep when some
other active nodes still have packets to transmit. Furthermore,
C-MAC dramatically reduces the energy consumption incurred
by the idle listening and overhearing by the design of SBM.
C. Ordering-based communication algorithm
We here elaborate the ordering-based communication algo-
rithm executed by the sink.
As shown in Algorithm 1, with the inputs of the timeout
Tout, the maximum number of preambles Np, G-ACKs Na,
O-ACKs No, respectively, the sink initializes the time counters
Cs,Cd, the corresponding current numbers kp,ka,koand the
sets of received ACKs and data packets Sack,Sdata . Then, the
sink receives probable ACKs and adds them to the set Sack in
aTout as line 2-4. If Sack is not empty, the sink sends back a
G-ACK, resets the counter Csand repeats the procedures 2-4
to further receive ACKs from nodes. If there is no incoming
ACK when Tout expires, the sink then sequences the data
packet transmissions and sends an O-ACK. Subsequently, if
the sink does not receive any data packet within TSIF S +Tdata
and ko< No, it repeats 14-17. Otherwise, the sink continues
to receive packets from the others. If Sack is empty and kp
does not reach to Np, the sink transmits a new preamble in
order to receive possible ACKs. Then, the sink returns to the
initialization and repeats lines 2-31. If not receiving any ACK
after sending Nppreambles, the sink turns off its radio and
switches to sleep state.
Algorithm 1 Ordering-based communication algorithm
Input: Tout,Np,Na,No.
1: Initialization: counters Cs=0,Cd=0, and kp,ka,ko, sets
of received ACKs and data packets Sack=∅,Sdata =∅.
2: while Cs< Tout do
3: Receive ACK,Sack =Sack ∪ACK
4: end while
5: if |Sack| ≥ 1then
6: Nack =|Sack|
7: if ka< Nathen
8: Send G-ACK, ka++
9: reset Cs= 0 and repeat 2-4
10: if |Sack|> Nack then
11: Repeat 6-9
12: else
13: Sequence the data packet transmission
14: Send O-ACK
15: while Cd< TSI F S +Tdata do
16: Receive DAT A,Sdata=Sdata ∪DAT A
17: end while
18: if |Sdata|==0 then
19: ko++
20: if ko< Nothen
21: Repeat 14-17
22: else
23: Turn off the radio
24: end if
25: else
26: Continue to receive data packets
27: end if
28: end if
29: else
30: Execute 14-28
31: end if
32: else if kp< Npthen
33: Send another preamble, kp++
34: Execute 1-31
35: else
36: Turn off the radio
37: end if
V. DE LAY ANA LYSI S
In this section, we explicitly formulate the mathematical
expression of the delay Tdwhich is the duration between the
packet arrival at a node and its successful reception by the sink.
For deriving Td, we need calculate the following components:
•T1: random delay spent by the sink to accomplish a
successful preamble transmission.
•Tw: random delay spent by the node from the instant of
packet arrival until a successful reception of preamble.
•To: random delay spent by the node from the reception
of a preamble until the reception of O-ACK.
•Tc: random delay spent by the node from the O-ACK
reception until the transmission of a packet.
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TABLE I
MAI N SYM BO LS
Symbols Descriptions
Ton Active duration of the sink in one duty cycling period
TsSleep duration of the sink in one duty cycling period
TdTransmission delay spent by a node from the instant of packet arrival until its reception successfully by the sink
T1Random delay spent by the sink before transmitting a preamble
TwRandom delay spent by the node from the instant of waking up until a successful reception of preamble
ToRandom delay spent by the node from the reception of a preamble until the reception of O-ACK
TcRandom delay spent by the node from the O-ACK reception until the transmission of a packet
Tout Maximum time that the sink waits for ACKs after having sent a preamble
Tack Random delay spent by the node to send back an ACK to the sink
TaRandom time spent by the node to wait from its wakeup to the wake-up instant of the sink as the event Bis true
TbTime interval from the wake-up moment of the sink until the node succeeds in receiving one preamble as Bis true
T0
aTime interval between the wake-up instants of the sink and nodes given that the event Bis false
T0
bRandom delay spent by the sink from its wake-up moment until a successful reception of one preamble as Bis false
TpMaximum time duration spent by the sink to transmit preambles
Tdata Delay to transmit a packet
ENmEnergy consumption spent by the node Nmto transmit a packet to the sink sucessfully
Esink Energy consumption spent by the sink during its active duration
NbMaximum number of backoffs of a preamble
NpMaximum number of preambles that can be sent by the sink
NaMaximum number of G-ACK that can be sent by the sink
NoMaximum number of O-ACK that can be sent by the sink
SbUnit backoff time used by the CSMA/CA algorithm
αProbability of busy channel
tp,k,j Random backoff time before the jth attempt to transmit a preamble as the event Akhappens
AkEvent that the channel is busy for k−1times and free at the kth time
BEvent that the sink is sleeping when the nodes wake up and intend to transmit packets
CkEvent that the sink has to send kpreambles before being received and the ACK is sent back before timeout
PjEvent that a preamble or an ACK is lost at time index jdue to collisions
DkEvent that the sink transmits kpreambles before expiration of Tp
FkEvent that an ACK is transmitted successfully before timeout of the sink in case that Dkis true
NkEvent that the k−1th preamble is sent but the nodes are sleeping
EkEvent that the kth preamble is sent and the nodes have waken up
RnEvent that the sink has to send nG-ACKs until no ACK from nodes is received
QlEvent that the lth O-ACK is received successfully by the nodes
O-ACK
ACK ACK
m
N
O-ACK
a
T
b
T
1
T
out
T
o
T
w
T
c
T
d
T
ack
T
G-ACK G-ACK
Fig. 3. An illustration of delay Td
As shown in Fig. 3, the delay for an arbitrary node Nmto
successfully send a data packet is thus Td=Tw+To+Tc.
Next, we formally derive these delay components in sequence.
Note that Table I lists the main symbols used in the paper.
A. Modeling of T1
Assume that the mechanism to transmit a preamble for
the sink is the same with an ACK message transmission
for nodes as specified in IEEE802.15.6 CSMA/CA. Let α
be the probability of busy channel which is approximately
independent at each attempt for each node [21]. Let Nbbe the
maximum number of backoffs of a preamble, i.e., to access
the channel the sink can transmit at most Nbpreambles.
Let tp,k,j be the random backoff time before the jth attempt
to transmit a preamble for the case where the channel is busy
for k−1times and free at the kth time. It follows that tp,k,j has
a uniform distribution over the interval [1, CWk,j ]·Sb, where
Sbis a unit backoff time used by the CSMA/CA mechanism.
Denote by Akthe event that the channel is busy for k−1times
and free at the kth time, and by Athe event that a preamble
is transmitted with at maximum Nbbackoffs. Thus, random
delay T1spent by the sink before transmitting a preamble
within Nbattempts can be expressed as
T1=
Nb
X
k=1 k
X
j=1
tp,k,j !1Ak|A=
Nb
X
k=1
Σk1Ak|A,(1)
where 1(·)is the indicator function (1(·)= 1 if the argument
is true, and 1(·)= 0 otherwise) and Σk=Pk
j=1 tp,k,j is
the random variable describing the time spent for the kth
random backoff. Note that the primitive backoff for the first
preamble first attempt is set to 0, i.e., tp,1,1= 0 in this paper.
Consequently, we can obtain the probabilistic characteristics
of T1as stated in the following lemma 1.
Lemma 1. The mean and variance of T1are
µT1=E[T1] =
Nb
X
k=1
µΣk
αk−1
ΣNb
j=1αj−1,
σT1=E[T1−E[T1]]2=
Nb
X
k=1
σ2
Σk
αk−1
ΣNb
j=1αj−1,
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where E[·]defines the mean of a random variable and
(µΣk=E[Σk] = Pk
j=1 µtp,k,j ,
σ2
Σk=E[Σk−E[Σk]]2=Pk
j=1 σ2
tp,k,j ,
where µtp,k,j and σ2
tp,k,j denote the mean and variance of the
random variable tp,k,j .
Proof: Since Akis the event that the channel is busy for
k−1times and free at the kth time, the probability of this
event is Pr(Ak) = αk−1(1 −α). The probability of the event
Ais then derived as
Pr(A) = Pr Nb
X
j=1
Aj!=
Nb
X
j=1
Pr(Aj)
where the equality comes from that the events Aj,
j=1, . . . , Nbare mutually exclusive. It thus also holds that
Pr(Ak|A) = Pr(AkPNb
j=1 Aj)
Pr(A)=Pr(Ak)
PNb
j=1 Pr(Aj)
=αk−1
PNb
j=1 αj−1
Since Σkis the sum of independent uniformly distributed
random variables, its mean can be given by µΣk=E[Σk] =
Pk
j=1 µtp,k,j , where µtp,k,j =(CWk,j −1)Sb/2[21], and its
variance thus equals the sum of the variance of tp,k,j, i.e.,
σ2
Σk=E[Σk−E[Σk]]2=Pk
j=1 σ2
tp,k,j , where σ2
tp,k,j =(CWk,j −
1)2S2
b/12. By using µΣkand σ2
Σkand the properties of the
expectation operator, the lemma 1 follows.
Remark. Since T1is the weighted sum of uniform random
variables with different mean and variance, no closed-form
expression is available for the probability mass function. How-
ever, a Gaussian distribution can approximate the probability
mass function of T1.
In addition, since the ACK message is transmitted with
the same backoff mechanism of the preamble, the random
delay Tack spent by one node to send back sucessfully an
ACK message to the sink can be approximated by a Gaussian
distribution with mean and variance given as
µTack =
Nb
X
k=1
µΣk
αk−1
PNb
k=1 αk−1, σ2
Tack =
Nb
X
k=1
σ2
Σk
αk−1
PNb
k=1 αk−1.
B. Modeling of Tw
In this subsection we model Twthat the random delay
between the wakeup moment of a node and the reception mo-
ment of a successful preamble followed by an ACK message
which is sent back successfully to the sink before timeout. Due
to the implementation of asynchronous duty cycling protocol,
we proceed to derive Twin the following two cases:
Tw=(Ta+Tb, Case1 : Sink is sleeping,
T0
b−T0
a, Case2 : Sink is awake.(2)
Case 1: The sink is sleeping when the node wakes up
and intends to transmit data packet. The aforementioned Fig.3
shows an illustration for an arbitrary node.
First, denote by Tathe random time for the node to wait
from its waking up moment to the instant of the sink waking
up. Ta= 01¯
B+T21B, where the event Boccurs when the
sink is sleeping at the moment that the node has data packet
to transmit, and T2is the random time to wait for the wakeup
of the sink given that the event Bis true. Consequently, the
probabilities of Band ¯
Bare
Pr(B) = Ts
Ton +Ts
,Pr( ¯
B)=1−Pr(B),
where Tsand Ton are the duration of the sleep and activation
of the sink during one duty cycling period, respectively. As
the definition, that Pr(Ta= 0) = Pr( ¯
B). Furthermore, since
T2has a uniform distribution in the range [0, Ts], thus the
probability of Tafor 0< Ta≤Tsis give by
Pr(Ta) = Pr(T2) Pr(B) = Pr(T2)Ts
Ton +Ts
.
Therefore, the probability mass function of Tais
Pr(Ta) = (1
Ton+Ts0< Ta≤Ts,
Ton
Ton+TsTa= 0.
We then define Tbas the time interval from the wakeup
moment of the sink until one preamble is received successfully
by the node given that the event Bis true, as shown in
Fig.3. In order to avoid that the sink spend much energy on
transmitting preambles as there is no incoming packets for
long time, the maximum number of preambles that the sink
can transmit is restrained as Np. Furthermore, define Ckas
the event that the sink has to send kpreambles before being
received and the corresponding ACK is sent back and received
before the timeout of the sink. Thus, the random delay of Tb
can be formulated as
Tb=
Np
X
k=1 k
X
j=1
T1,k,j + (k−1)Tout!1Ck|C,(3)
where T1,k,j is the random delay of the transmission of the jth
preamble when the kth preamble with the distribution given in
Eq.(1) is received successfully by the nodes. Tout is defined as
the maximum time for the sink to wait for ACKs after having
sent a preamble. And Cis the event that the sink receives
ACKs within Nppreambles. We next present the probabilistic
characteristics of Tbin lemma 2.
Lemma 2. The mean and variance of Tbare
µTb=
Np
X
k=1
(kµT1+ (k−1)Tout )Pr(Ck)
PNp
j=1 Pr(Cj),
σ2
Tb=
Np
X
k=1
σ2
Tb,k
Pr(Ck)
PNp
j=1 Pr(Cj),
where σ2
Tb,k is the variance of Pk
j=1 T1,k,j + (k−1)Tout, and
Pr(Ck) = [Pr (kT1+ (k−1)Tout ≤Tp) (1 −Pr(Tack ≤Tout ))
×Pr(Tack ≤Tout) Pr( ¯
P1)] + [Pr (kT1+ (k−1)Tout ≤Tp)
×Pr(Tack ≤Tout)2Pr(P1) Pr( ¯
P2)].
where Tpis the maximum time duration to transmit Np
preambles for the sink.
Proof: The proof is based on expressing the mean and
variance of Tbin terms of Pr(Ck). According to the expression
of Tbin Eq.(3), its mean and variance can be presented as
(µTb=PNp
k=1 (kµT1+ (k−1)Tout ) Pr( Ck|C),
σ2
Tb=PNp
k=1 σ2
Tb,k Pr(Ck|C).
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Using the fact that the events Cj,j= 1, . . . , Npare mutually
exclusive, we have
Pr(C) = Pr
Np
X
k=1
Ck
=
Np
X
k=1
Pr(Ck),
and then
Pr(Ck|C) =
Pr CkPNp
j=1 Cj
Pr(C)=Pr(Ck)
PNp
j=1 Pr(Cj),
which completes the proof.
Next, the key step is to find the expression for Pr(Ck).
To that end, we firstly define τas the probability of nodes
attempting to transmit in a randomly chosen time slot. And
denote by Pjthe event of losing a preamble or an ACK at
time index jdue to collisions. Thus Pr( ¯
Pj)=1−(1−τ)M−1
is the probability that at least one of the remaining nodes
attempts to transmit in the same time slot, where Mis the
total number of nodes in once concurrent traffic load. As the
size of a preamble and an ACK is much smaller, we assume
that these probabilities are independent at each attempt.
Furthermore, let Dkas the event that the sink transmits k
preambles before the expiration of Tp. Denote by Fkas the
event that an ACK message is transmitted successfully before
timeout of the sink in case that Dkis true. Let Ωbe the certain
event. Now we ready to determine Pr(Ck)in lemma 3.
Lemma 3. Following the definition of Ck, it holds that
Ck= (Dk−1¯
Fk−1+Dk−1Fk−1P1)DkFk¯
P2(4)
where
D0= Ω,Dk= (kT1+ (k−1)1(k−1)≥0Tout )≤Tp),
¯
F0= (Tack > Tout),Fk= ( Tack ≤Tout |Dk),
¯
Fk−1= (Tack > Tout |Dk−11(k−1)≥0).
Proof: From the definition of Ck,Ckconsists of two
events: 1) the event C1,k =Dk−1¯
Fk−1DkFk¯
P2occurs when
the k−1th preamble was sent but the nodes were not able
to send back an ACK before the timeout of the sink; and 2)
the event C2,k =Dk−1Fk−1P1DkFk¯
P2occurs when the
k−1th preamble was sent and an ACK was sent back before
timeout but it was collided. As C1,kC2,k =φ, we thus have
Pr(Ck) = Pr(C1,k) + Pr(C2,k ).(5)
Subsequently, we derive the probabilities of C1,k and C2,k.
By considering that the event of Fkand Pjare independent
of the others, the probability of C1,k is given as
Pr(C1,k) = Pr(Dk−1Dk) Pr( ¯
Fk−1Fk) Pr( ¯
P2).
for Dk−1Dk=Dk. Since ¯
Fk−1and Fkare independent, and
Pr( ¯
Fk−1)=1−Pr(Fk−1)=1−Pr(Tack ≤Tout), we have
Pr(C1,k) = Pr(Dk) Pr( ¯
Fk−1) Pr(Fk) Pr( ¯
P2)
= Pr (kT1+ (k−1)Tout ≤Tp) (1 −Pr(Tack ≤Tout ))
×Pr(Tack ≤Tout) Pr( ¯
P2).
(6)
Furthermore, since Dk−1Dk=Dkand Fk−1is indepen-
dent of Fk, it holds that
Dk−1Fk−1P1DkFk¯
P2=Fk−1P1DkFk¯
P2.
As a consequence, we can derive that
Pr(C2,k) = Pr(Fk−1) Pr(Dk) Pr(Fk) Pr(P1) Pr( ¯
P2)
= Pr (kT1+ (k−1)Tout ≤Tp)
×Pr(Tack ≤Tout)2Pr(P1) Pr( ¯
P2).
(7)
Thus, substituting Eq.(6)-(7) into Eq.(5) yields Pr(Ck).
As a result, the random delay in case 1 is Tw=Ta+Tbas
shown in Fig.3.
Case 2: The sink is awake when the node has a packet to
transmit, as shown in the Fig.4.
O-ACK
m
N
ACK
ACK
O-ACK
b
T
a
T
w
T
o
T
c
T
G-ACK G-ACK
Fig. 4. The sink is awake when the nodes wake up
Inspired by the analysis in case 1, let T0
abe the time interval
between the wakeup instants of the sink and the node. From
the definition of event B, it holds that T0
a= 01B+T31¯
B,
where T3is the random time spent by the sink on waiting
for the wakeup of the node given that the event Bis false.
Since T3has a uniform distribution in the range [0, Tp], the
probability mass function of T0
ais
Pr(T0
a) = (Ton
Tp(Ton+Ts)0< T 0
a≤Tp,
Ts
Ton+TsT0
a= 0.
Correspondingly, let T0
bdenote the random delay spent by
the sink from its wakeup moment until a successful reception
of one preamble given that the event ¯
Bis true. Referring to
the derivation of Tb,T0
bcan be formulated as
T0
b=
Np
X
k=1 k
X
j=1
T1,k,j + (k−1)Tout!1Ck|C,(8)
Note that the occurrence of Ckoccurring in case 2 is different
with that in case 1 since the sink does not know when the
node wakes up. Although the expression of T0
bis the same
with Tb, the expression of Pr(Ck)in case 2 differs from that
in case 1, as shown in the following lemma 4.
Lemma 4. In case 2, Pr(Ck)is derived as
Pr(Ck) = (Pr(NkDk)−Pr( ¯
Ek)) Pr(Fk) Pr( ¯
P2)
+ (Pr(Dk)−Pr(NkDk)) Pr( ¯
Fk−1) Pr(Fk) Pr( ¯
P2)
+ (Pr(Dk)−Pr(NkDk)) Pr(Fk−1) Pr(Fk) Pr(P1) Pr( ¯
P2),
where
Pr( ¯
Ek) = P1T0
a−(k−1)Tout
k,
Pr(Dk) = P1Tp−(k−1)Tout
k,
Pr(Nk) = P1T0
a−(k−2)Tout
k−1,
Pr(NkDk) = Pr(Dk) (1 −Pr(T1≤Tp−T0
a−Tout))
+ Pr(Nk) Pr(T1≤Tp−T0
a−Tout).
Proof: Let Nkdefine the event occurring when the k−1th
preamble is sent but the node is sleeping. And event Ekoccurs
when the kth preamble is sent and the node has waken up.
Recall the definitions in case 1, we then have Ck=(Nk+
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Transactions on Vehicular Technology
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Ek−1Dk−1¯
Fk−1+Ek−1Dk−1Fk−1P1)EkDkFk¯
P2, where
(Nk= ((k−1)1(k−1)≥0T1+ (k−2)1(k−2)≥0Tout ≤T0
a)
Ek= (kT1+ (k−1)1(k−1)≥0Tout > T 0
a).
In case 2, a preamble fails in three situations, which follows
that Ck=C1,k +C2,k +C3,k, where C1,k =NkEkDkFk¯
P2
is the event that the node is sleeping when the sink sent the
k−1th preamble; C2,k =Ek−1Dk−1¯
Fk−1EkDkFk¯
P2is the
event occurring when the k−1th preamble was sent but the
corresponding ACK is not sent back before the timeout; and
C3,k =Ek−1Dk−1Fk−1P1EkDkFk¯
P2is the event that the
k−1th ACK sent back before timeout was collided. For C1,k,
C2,k and C3,k are mutually exclusive, we have
Pr(Ck) = Pr(C1,k) + Pr(C2,k ) + Pr(C3,k ).(9)
Hence, the key is to derive Pr(C1,k),Pr(C2,k)and Pr(C3,k ).
For the mutual independence of the event Fkand Pj, the
probability of C1,k is given by
Pr(C1,k) = Pr(NkEkDk) Pr(Fk)¯
P2.
Following the total probability theorem, we have
Pr(NkDk) = Pr(NkEkDk) + Pr(Nk¯
EkDk),
and it holds that Nk¯
EkDk=¯
EkDk=¯
Ek, such that
Pr(NkEkDk) = Pr(NkDk)−Pr( ¯
Ek).(10)
Rewriting Nkas Nk=kT1+ (k−1)Tout ≤T0
a+T1+
Tout, we have NkDk=(Dkif Tp≤T0
a+T1+Tout
Nkotherwise and
Pr(NkDk)= Pr(Dk)(1−Pr(T1≤Tp−T0
a−Tout))+Pr(Nk)Pr
(T1≤Tp−T0
a−Tout). Combining this with Eq.(10) yields
Pr(C1,k) = (Pr(NkDk)−Pr( ¯
Ek)) Pr(Fk) Pr( ¯
P2).(11)
We next compute Pr(C2,k), because Ek−1Ek=Ek−1=¯
Nk
and Dk−1Dk=Dk, we have Ek−1Dk−1¯
Fk−1EkDkFk¯
P2=
Ek−1Dk¯
Fk−1Fk¯
P2. Moreover, ¯
Fk−1and Fkare indepen-
dent, so it holds that
Pr(C2,k) = Pr( ¯
NkDk) Pr( ¯
Fk−1) Pr(Fk) Pr( ¯
P2)
= (Pr(Dk)−Pr(NkDk)) Pr( ¯
Fk−1) Pr(Fk) Pr( ¯
P2).(12)
Similarly, we have
Ek−1Dk−1Fk−1P1EkDkFk¯
P2=Ek−1DkFk−1P1Fk¯
P2.
Correspondingly, we can derive that
Pr(C3,k) = Pr( ¯
NkDk) Pr(Fk−1) Pr(P1) Pr(Fk) Pr( ¯
P2)
=(Pr(Dk)−Pr(NkDk))
×Pr(Fk−1) Pr(Fk) Pr(P1) Pr( ¯
P2).(13)
We thus get Pr (Ck)in case 2 by merging Eq.(11)-(13).
Consequently, the delay in case 2 is Tw=T0
b−T0
aas shown
in Fig.4. In summary, since Twis given by the weighted sum
of Gaussian distributed variables, it follows that Twcan also
be approximated by a Gaussian random variable.
C. Modeling of Toand Tc
In this section we analyze Toand Tc, which are defined as
the random delay spent by the node from the reception of a
preamble until the reception of the O-ACK and from the O-
ACK reception until the transmission of a packet, respectively.
We assume that concurrent traffic load comes from Mnodes,
and Nmrepresents the node that mthly sends data packet.
In order to receive all probable ACKs from concurrent active
nodes, the sink needs to send G-ACK to the nodes multiple
times. Let Naand Nobe the maximum numbers of G-ACK
and O-ACK that can be sent by the sink, respectively. Denote
by Rnas the event that the sink has to send nG-ACKs until
no ACK from nodes is received. And denote by Qlas the
event that the lth O-ACK is received successfully by the nodes.
According to the aforementioned analysis on Tband T0
b, we
can formulate the random delay of Toas
To=
Np
X
k=1 Na
X
n=1 n
X
i=1
(Tout +Tgack,n,i ) + Tout
+
No
X
l=1
l
X
j=1
(Toack,l,j +TSI F S )1Ql|Q!1Rn|R!1Ck|C,
(14)
where Tgack,n,i is the random delay to transmit the ith G-ACK
when the O-ACK is sent after the nth G-ACK transmission.
And Ris the event that the sink receives all ACKs within Na
transmissions of G-ACK. Correspondingly, Toack,l,j is the de-
lay to transmit the jth O-ACK when the lth O-ACK is received
successfully by the nodes. And Qis the event that the O-ACK
is received successfully within Notransmissions. TSIF S is
the short interframe space interval among the separated data
packet transmission. Note that the probabilities of Rnand Ql
can be calculated by the same method as that of Ck. In the
sake of the limited space, the probabilistic characteristics of
Toare omitted, which can refer to lemma 2.
Then, the delay to accomplish the data transmission for the
node Nmcan be approximated as
Tcm=
Np
X
k=1
Na
X
n=1
No
X
l=1
m·(TSI F S +Tdata)1Ql|Q1Rn|R1Lk|C,
where Tdata is the delay to transmit one packet, i.e.,
Tdata=Lp/Rs+Thr , where Lpis the payload of one packet
in bits and Rsis data rate in bits/s as in IEEE 802.15.6 [18],
and Thr is the time taken by the hardware platform to
process the packet and propagate it. In fact, Tcmconsists of
(m−1)(TSI F S +Tdata )when the node stays in SBM and
one (TSI F S +Tdata)when the node sends a data packet.
Therefore, the delay for the successful communication be-
tween the sink and a node is given by Td=Tw+To+Tc, which
can be approximated by a Gaussian distribution with mean
µTd=µTw+µTo+µTcand variance σ2
Td=σ2
Tw+σ2
To+σ2
Tc.
D. Accuracy evaluation
In this section, we evaluate the accuracy of the theoretical
analysis. The numerical and simulation parameters are listed
in Table II.
Fig.5 and Fig.6 illustrate the analytic and emulational expec-
tation and variance of the transmission delay Tdfor a network
with 10 nodes and traffic arrival rate λ= 0.02 as a function
of the sleep time Tsand active time Ton, respectively. As
shown in figures, the theoretical results match well with the
simulation results, verifying the accuracy of the theoretical
analysis. Moreover, a good linear relationship between delay
and the sleep time can be inferred from Fig.5, especially in
the case that Ton ≤Ts, since the packet transmission time
and the active time are very short compared to the sleep time.
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Transactions on Vehicular Technology
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0.5 11.5 2
0
0.2
0.4
0.6
0.8
1
1.2
The Sleep Time Durat ion T
s
(s)
The Average Delay (s)
sim,T
on
=6ms
sim,T
on
=60ms
sim,T
on
=250ms
sim,T
on
=0.5s
sim,T
on
=1s
ana,T
on
=6ms
ana,T
on
=60ms
ana,T
on
=250ms
ana,T
on
=0.5s
ana,T
on
=1s
Fig. 5. The expectation of Td
0.5 11.5 2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
The Sleep Time Duration T
s
(s)
The Variance of Delay (s
2
)
sim,T
on
=6ms
sim,T
on
=60ms
sim,T
on
=250ms
sim,T
on
=0.5s
sim,T
on
=1s
ana,T
on
=6ms
ana,T
on
=60ms
ana,T
on
=250ms
ana,T
on
=0.5s
ana,T
on
=1s
Fig. 6. The variance of Td
And this trend is similar to that reported in [22]. Moreover,
the average delay decreases as the active duration increases.
VI. EN ER GY CO NS UM PT IO N ANALYSIS
In this section, we formulate the total normalized energy
consumption of the network under C-MAC protocol.
A. Modeling of energy consumption
Since the energy consumed per unit time is rather low in
the sleep state, we thus focus on the energy consumption spent
in the active state. As a result, the total normalized energy
consumption of the network per unit time is given by
Etotal =
M
X
m=1
ENm
Tdm
+Esink
Ton
(15)
where ENmand Tdmare the energy consumption and random
delay spent by the node Nmto successfully transmit a packet
respectively, and Esink is the energy consumption spent by the
sink in its whole active state. The energy components ENm
and Esink are formulated in the following lemma 5.
Lemma 5. According to the delay analysis in section V, the
total energy consumption for the sink and the node Nmare
upper bounded as
Esink ≤
Np
X
i=1 i
X
n=1
En
tx,T1+ (i−1)ETout +ETo
+MErx,Tdata !1Ci+ Np
X
n=1
En
tx,T1+NpETout !1¯
C(16)
ENm≤Erx,p +ETo+ESB M +Etx,Tdata (17)
where ¯
C=TNp
i=1 ¯
Ciand
En
tx,T1=
Nb
X
k=1
k
X
j=1
Prx ·tp,k,j +Ptx ·Sp
1Ak,(18)
ETout =Prx ·Tout,(19)
ETo≤max(Ptx, Prx )To,(20)
Erx,Tdata =Prx (TSI F S +Tdata ),(21)
Etx,Tdata =Ptx(TS IF S +Tdata),(22)
Erx,p ≤Prx Tw+PrxSp,(23)
ESBM = (m−1)Ps(Tdata +TS I F S ),(24)
where Psis the power consumed in SBM, Ptx and Prx are the
energy dissipated to transmit and receive packet respectively.
And Spis the preamble packet duration.
Proof: The upper bound of Esink is the sum of two main
components: one corresponding to the case that data packet
transmissions are successful, and the other corresponding to
the case that no data packet transmission is successful.
The ith term in the first component corresponds to the case
where the ith preamble is successfully transmitted and the
corresponding ACKs are received from nodes, i.e., 1Ci= 1.
In this case, the energy consumption consists of four parts.
•For the first part, the energy spent for the preamble
transmission is given by the sum from the 1st preamble
to the ith preamble, i.e., Pi
n=1En
tx,T1. Recall the analysis
of T1in subsection V-A, the energy consumption spent
by the sink on backoff and the transmission of the nth
preamble can be expressed as Eq.(18).
•For the second part, the energy consumption to wait for
the ACKs after each preamble transmission is defined as
ETout , given in Eq.(19). Thus, the energy wastage during
the timeout periods for the first i−1preambles can be
calculated as (i−1)ETout .
•For the third part, the energy used to receive the cor-
responding ACKs and broadcast the G-ACKs and O-
ACKs is great difficult to give a closed form expression,
as it depends on the actual transmission numbers of G-
ACKs and O-ACKs. We thus provides a upper bound
of ETogiven in Eq.(20) following the analysis of Toin
section V-C to simply the analysis.
•For the fourth part, the energy dissipated to receive the
subsequent Mpackets are MErx,Tdata , where Erx,Tdata
is shown in Eq.(21) .
The second component corresponds to the case where all
the preambles are not received successfully, thus, the energy
consumption in this case equals to the energy spent transmit-
ting Nppreambles and waiting for Nptimeouts.
Furthermore, for the node Nm, the upper boundary of the
energy consumption is derived as in Eq.(17), which is also
composed of four parts. Note that the part of ETohere is the
same with that of the sink. Denote by Erx,p the energy used
for successfully receiving a preamble from the sink, we bound
Erx,p upwards as in Eq.(23) following the modeling of Tw
in subsectionV-B. Moreover, ESBM is the energy dissipation
during the SBM state which can be expressed as Eq.(24).
Besides, Etx,Tdata , defining the energy spent by the node on
transmitting a packet, is formulated in Eq.(22).
0018-9545 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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Transactions on Vehicular Technology
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Remark. Because the node has to listen to the channel
status during the backoff and timeout duration, the power
consumption is assumed to equal to Prx.
Since the events involved in the calculation of Esink and
ENmare highly cross correlated, it is very difficult to model
the accurate characteristics of Etotal. But we can compute the
upper bound of Etotal by using Eq.(15) and Lemma 5.
B. Accuracy evaluation
In this section, we validate the correctness of theoretical
normalized energy consumption by comparing the analytical
results with simulation results in different duty cycles.
0.5 11.5 2
-5.4
-5.3
-5.2
-5.1
-5
-4.9
The Sleep Time Duration T
s
(s)
The Normalized Eenergy Consumption (dB)
sim,T
on
=6ms
sim,T
on
=60ms
sim,T
on
=250ms
sim,T
on
=0.5s
sim,T
on
=1s
ana,T
on
=6ms
ana,T
on
=60ms
ana,T
on
=250ms
ana,T
on
=0.5s
ana,T
on
=1s
Fig. 7. The analytical and simulation results of Etotal
Fig.7 shows the analytical and simulation results of the total
normalized energy consumption in dB as a function of Tsand
Ton for a network with 10 nodes and traffic arrival rate λ=
0.02. This figure shows a good matching of the analysis results
with simulations, which further demonstrates the correctness
of the mathematical analysis.
VII. PER FO RM AN CE EVALUATIO N
In the previous sections, we have formulated the delay and
energy consumption and validated the analysis accuracy by
numerical and simulation results. In this section, we further
evaluate the performance of C-MAC protocol by comparing
with two receiver-initiated protocols: RI-MAC [13] and A-
MAC [14].
A. Simulation settings
The parameters in the simulation are set in accordance with
the data sheet of CC2420 radio chip [23] and the specifications
in the IEEE 802.15.6 standard [18] at 2.4 GHZ. We summarize
the parameters in Table II. Moreover, each simulation result
is computed by the average of 100 independent experiments.
TABLE II
SIM ULATI ON SETTINGS
Parameter Value Parameter Value Parameter Value
Rs242.9 kbps Thr 1µsC Wmin 2
Sp88bits/RsTSI F S 75µsCWmax 8
Lp255bytes Lack 11bytes Nb5
Prx 96.6mW Sb125µsNp10
Ptx 86.2mW Ps1.6mW Na,No10,10
B. Simulation results and analysis
In this section, we present the simulation results and eval-
uate the performance of C-MAC.
1) Delay:Here, we show the average delay of each node
in Fig.8 and Fig.9.
In order to better assess the impact of the concurrent traffic
on the delay, we plot the average delay of each node with
the number of nodes M= 5,10 and the traffic arrival rate
λ= 0.02,0.2, respectively in Fig.8. As shown in these figures,
the average delay of C-MAC is much smaller than that of RI-
MAC and A-MAC in every case, especially for the later nodes.
Moreover, a quantitative comparison can be made from Fig.8
(a) and (b) that C-MAC can reduce 18.12% and 22.54% of
the average delay of RI-MAC, and 14.94% and 19.11% of
that of A-MAC as packet arrival rate λ= 0.02 and λ= 0.2,
respectively. Similarly, as shown in Fig.8 (c) and (d), C-MAC
outperforms RI-MAC over -26.76% and -31.11%, and A-MAC
over -22.11% and -27.43% in average delay.
12345
0.05
0.06
0.07
0.08
(a) N
m
Delay (s)
M=5, λ=0.02
RI-MAC A-M AC C-MAC
1 2 3 4 5
0.05
0.06
0.07
0.08
M=5, λ=0.2
(b) N
m
Delay (s)
2 4 6 8 10
0.06
0.08
0.1
0.12
M=10, λ=0.02
(c) N
m
Delay (s)
246810
0.06
0.08
0.1
0.12
M=10, λ=0.2
(d) N
m
Delay (s)
Fig. 8. The average delay with different traffic load
The reason for the high delay of RI-MAC and A-MAC is
that they do not take preventive measures to avoid collisions.
Due to the numerous collisions under concurrent traffic load,
data packets in RI-MAC and A-MAC are retransmitted fre-
quently, resulting in the large delay. In contrast, C-MAC em-
ploys CSMA/CA mechanism, which can tremendously reduce
the collision probability in advance. Moreover, sequencing
data packet transmission can completely eradicate the collision
in the second phase. Thereby, C-MAC can greatly reduce the
additional delay caused by the collisions.
In addition, we can find that C-MAC can achieve high
adaptivity for dynamic concurrent traffic load in WBANs. For
example, when the traffic arrival rate increases from 0.02 to
0.2, the delay of RI-MAC and A-MAC increases by 7.17% and
8.17% while that of C-MAC only increases by 0.79%. Note
that the same conclusion can also be drawn for the different
number of nodes.
In order to better evaluate the influence of the duty cycle
on the delay, Fig.9 shows the simulation results of C-MAC,
A-MAC and RI-MAC with respective to different percentages
of Ton, i.e., about 10%, 20%, 30% and 50% for a WBAN with
10 nodes and traffic arrival rate λ= 0.02.
As depicted in Fig.9, C-MAC can achieve much smaller
delay than RI-MAC and A-MAC in every case. Specially, the
enhancement of C-MAC can reach to at least about 15.31%,
0018-9545 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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Transactions on Vehicular Technology
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2 4 6 8 10
0.25
0.3
0.35
(a) N
m
Delay (s)
T
on
=0.06s, T
s
=0.6s
RI-MAC A-MAC C- MAC
2 4 6 8 10
0.7
0.8
0.9
T
on
=0.5s , T
s
=2.1s
(b) N
m
Delay (s)
2 4 6 8 10
0.3
0.35
0.4
0.45
T
on
=0.5s , T
s
=1.1s
(c) N
m
Delay (s)
246810
0.15
0.2
0.25
0.3
0.35
T
on
=1.0s , T
s
=1.1s
(d) N
m
Delay (s)
Fig. 9. The average delay with different duty cycle
20.84%, 32.64% and 46.13% over RI-MAC and A-MAC,
respectively, by comparing Fig.9 (a), (b), (c) and (d).
In other words, with the increase of the proportion of
Ton, the improvement of C-MAC becomes more and more
significant. Furthermore, even under light traffic load, the
C-MAC can also outperforms RI-MAC and A-MAC, which
further verifies the adaptivity of C-MAC.
Consequently, C-MAC shows better delay performance than
RI-MAC and A-MAC.
2) Energy Consumption:We here show the energy con-
sumption of C-MAC.
Since A-MAC is more energy-efficient than RI-MAC, for
the sake of clarity, we just compare C-MAC with A-MAC
temporally. Fig.10 presents the total normalized energy con-
sumption of the whole network with M= 5 and λ= 0.02.
We can see that C-MAC is more energy-efficient than A-MAC,
especially, as the sleep duration Tsis small. The lower energy
consumption of C-MAC can be attributed to its great capacity
of reducing collisions, idle listening and overhearing.
00.5 11.5 2
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
The Sleep Duration T
s
(s)
The Total Normalized Energy Consumption (J)
A-M AC,T
on
=6ms
A-M AC,T
on
=60ms
A-M AC,T
on
=250ms
A-M AC,T
on
=0.5s
A-M AC,T
on
=1s
C-MAC,T
on
=6ms
C-MAC,T
on
=60ms
C-MAC,T
on
=250ms
C-MAC,T
on
=0.5s
C-MAC,T
on
=1s
Fig. 10. The normalized energy consumption of the whole network
Moreover, in order to better understand the energy con-
sumption of C-MAC, we further plot the normalized energy
consumption for each node in Fig.11. Note that for the limited
space in subgraphs, the Normalized Energy Consumption is
abbreviated as NEC.
We can obtain two main observations from Fig.11. First,
the NEC of each node in C-MAC is much smaller than that in
RI-MAC and A-MAC. Second, the energy budget to transmit
a packet in C-MAC is almost the same for each node, while
the later transmission for a node, the more energy budget in
RI-MAC and A-MAC. The main reasons are two-fold. First,
in RI-MAC and A-MAC, the nodes must keep active until its
packet is transmitted successfully. Thus, the later nodes need
persistently to listen to the channel and may overhear other
nodes’ packets, wasting much energy. Second, in C-MAC, they
can switch to SBM until their individual turn, avoiding idle
listening and overhearing.
Furthermore, A quantitative comparison can be made from
Fig.11 that C-MAC mostly outperforms RI-MAC and A-MAC
over 90.42%, 89.46%, 87.88% and 84.85% in every duty cycle,
respectively. Therefore, we can conclude that C-MAC not only
reduces the energy consumption of the netwrok but also lowers
and balances the energy budget for each node.
1 2 3 4 5 6 7 8 9 10
0
0.01
0.02
(a) N
m
NEC (J)
T
on
=0.06 s, T
s
=0.6s
C-MAC A-M AC RI-MAC
1 2 3 4 5 6 7 8 9 10
0
5
x 10
-3
T
on
=0.5s, T
s
=2.1s
(b) N
m
NEC (J)
1 2 3 4 5 6 7 8 9 10
0
0.005
0.01
0.015
T
on
=0.5 s, T
s
=1.1s
(c) N
m
NEC (J)
12345678910
0
0.01
0.02
T
on
=1.0s,T
s
=1.1s
(d) N
m
NEC (J)
Fig. 11. The normalized energy consumption
However, the improvement in energy consumption of each
node is at the cost of the more energy consumption of the
sink, as shown in Fig.12. The main reason is that C-MAC is
a receiver-initiated protocol that the preambles must be sent
periodically by the sink as it wakes up. Besides, the sink must
persistently listen to the channel after transmitting a preamble
to detect if there are incoming packets. In addition, in order
to receive all probable ACKs from nodes, the sink has to send
G-ACKs multiple times.
12345678910
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
Number of Nodes
The Eenergy Cons umption (J)
RI-MAC,
λ
=0.02
A-MAC,
λ
=0.02
C-MAC,
λ
=0.02
RI-MAC,
λ
=0.2
A-MAC,
λ
=0.2
C-MAC,
λ
=0.2
Fig. 12. The normalized energy consumption of the sink
Furthermore, as in Fig.12, the energy consumption of the
sink is almost not influenced by traffic arrival rate, which
further demonstrates the strong adaptiveness of C-MAC to the
concurrent traffic load.
From all these results, we can conclude that C-MAC is able
to effectively and efficiently reduce delay and conserve energy,
especially under concurrent traffic.
0018-9545 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2016.2573718, IEEE
Transactions on Vehicular Technology
12
VIII. CON CL US IO N
This paper addressed the delay and energy consumption un-
der concurrent traffic in the medical applications of WBANs.
To that end, we designed and analyzed a two-phase receiver-
initiated asynchronous duty cycling protocol, called C-MAC.
In the first phase, C-MAC employed the IEEE 802.15.6 CS-
MA/CA mechanism to avoid collisions and sequenced the data
packet transmission of different nodes to resolve collisions in
the second phase. Moreover, C-MAC enabled nodes to switch
to SBM in the second phase, which dramatically reduces the
idle listening and overhearing. Subsequently, we derived the
mathematical expressions of delay and energy consumption
and further verified their correctness by the numerical analysis
and simulation. Furthermore, extensive simulations results
demonstrated that the performance of C-MAC outperforms RI-
MAC and A-MAC, especially for concurrent traffic.
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RongrongZHANG received the B.Eng and M.Eng
degrees in communication and information systems
from Chongqing University of Posts and Telecom-
munications, Chongqing, China, in 2010 and 2013,
respectively, and is currently pursuing the Ph.D.
degree in Computer Communication in the Faculty
of Mathematics and Computer Science at the Univer-
sity of Paris Descartes, France. Her research interests
focus on Wireless Area Body Networks (WBANs)
for healthcare.
Hassine MOUNGLA is Associate Professor at
the University of Paris Descartes and a member
of the Paris Descartes Computer Science Labora-
tory (LIPADE) since October 2008. He was a re-
searcher at INRIA until 2008 and research fellow at
CNRS-LIPN laboratory of the Paris Nord University
until 2007. His research interests lie in the field
of Wireless Area Body Networking (WBAN) for
medical and health applications, Wireless Sensor
Networking, QoS in WSN, Middleware for 5G Mo-
bile and Sensor Networks. He participated and still
participates to several national and international research projects. He is on
the technical program committee of different ACM and IEEE conferences,
including Globecom, ICC, WCNC, PIMRC, IWCMC and chaired some of
their sessions. He is also reviewer on a regular basis for major international
journals. Dr. Moungla is a member of IEEE and IEEE Communication Society.
Jihong YU received the B.E degree in communica-
tion engineering and M.E degree in communication
and information systems from Chongqing University
of Posts and Telecommunications, Chongqing, Chi-
na, in 2010 and 2013, respectively, and is currently
pursuing the Ph.D. degree in computer science at the
University of Paris-Sud, Orsay, France. His research
interests include wireless communications and net-
working and RFID technologies.
Ahmed MEHAOUA received the M.Sc. and
Ph.D.degrees in computer science from the Universi-
ty of Paris, in 1993 and 1997, respectively. He is cur-
rently a Full Professor of Computer Communication
in the Faculty of Mathematics and Computer Science
at the University of Paris Descartes, France. He is
also the Director of the Multimedia Networking and
Security Department at the LIPADE. He currently
researches on security and resource optimization in
Wireless Sensor Networks for Healthcare.
