Configuring optimization of wireless sensor networks, which can improve the network performance such as utilization efficiency and network lifetime with minimal energy, has received considerable attention in recent years. In this paper, a cross layer optimal approach is proposed for multisource linear network and grid network under Rayleigh blockfading channels, which not only achieves an optimal utility but also guarantees the endtoend reliability. Specifically, in this paper, we first strictly present the optimization method for optimal nodal number N*, nodal placement d* and nodal transmission structure p* under constraints of minimum total energy consumption and minimum unit data transmitting energy consumption. Then, based on the facts that nodal energy consumption is higher for those nodes near the sink and those nodes far from the sink may have remaining energy, a cross layer optimal design is proposed to achieve balanced network energy consumption. The design adopts lower reliability requirement and shorter transmission distance for nodes near the sink, and adopts higher reliability requirement and farther transmission distance for nodes far from the sink, the solvability conditions is given as well. In the end, both the theoretical analysis and experimental results for performance evaluation show that the optimal design indeed can improve the network lifetime by 2050%, network utility by 20% and guarantee desire level of reliability.
1. Introduction
W
ireless Sensor Networks (WSNs) have captured considerable attention recently due to their enormous potential for environmental monitoring, surveillance operations, and industrial automation
[1

3]
. Configuring optimization, as it can improve the network performance, has been well discussed in many WSN applications
[4

5]
. In order to prolong the network lifetime, several optimization measures have been proposed, e.g., Zhang et al.
[6]
show that the network performance can be significantly improved by optimizing network parameters including the deployed nodal number
N
^{*}
, the nodal placement
d
^{*}
and the nodal transmission structure
P
^{*}
. In order to achieve the optimal transmission range in physical layer, Chen et al.
[7]
define the optimal onehop length for multihop communications, which not only minimizes the total energy consumption but also analyzes the influence of channel parameters on the optimal transmission range in a linear network. In
[8]
, a BitMeterperJoule metric is proposed, which enables us to receive the effects of the network topology, the nodal density and the transceiver characteristics on the overall energy expenditure. Regarding the utility based optimization, Chen et al.
[9]
introduce a performance measure of utilization efficiency defined as network lifetime per unit deployment cost. In addition, a separate tradeoff between network lifetime and the endtoend delay is addressed in
[10]
.
Different from the above configuring optimization, in this paper, we would like to propose a crosslayer optimal approach for multisource linear network and grid network in WSNS, which not only achieves an optimal utility but also guarantees the endtoend reliability. Specifically, the main contributions of this paper are threefold:
(1) It is proved strictly from mathematics that there exist optimal nodal number
N
^{*}
, nodal placement
d
^{*}
and nodal transmission structure
P
^{*}
which can meet minimum in not only total energy consumption for data collection but also unit data transmitting energy consumption.
(2) A cross layer optimal design is proposed, which can improve dramatically lifetime without increasing network cost. Based on the network energy consumption feature, i.e., the energy consumption near the sink is high, while energy consumption far from the sink is low, we can know that in regions near the sink, energy consumption is inadequate, while energy consumption is excess in regions far from the sink. Therefore, two measures are adopted to address this problem. Firstly, we decrease nodal transmission distance for nodes near the sink and increase nodal transmission distance for nodes far from the sink in order to balance the nodal energy consumption in the network. Secondly, we adopt the strategy on lower reliability requirement for nodes near the sink while higher reliability requirement for nodes far from the sink to decrease the nodal energy consumption near the sink and improve the nodal energy consumption far from the sink.
(3) Extensive theoretical analyses and simulation evaluations are conducted, and the results demonstrate that the design of both utilization performance and reliability can be achieved simultaneously.
The rest of this paper is organized as follows. In Section 2, the system model and problem statement are described. In Section 3, optimizations for network and channel are presented. In Section 4, we present the analysis and comparison of experimental results. In Section 5, we conclude the paper.
2. The System Model and Problem Statement
 2.1 Energy Consumption Model
According to
[9]
, the energy consumption for transmitting one packet
E_{p}
is composed of three parts: the energy consumed by transmitter
E_{t}
, receiver
E_{r}
and the acknowledgment packet exchange
E_{ACK}
, i.e.:
The energy model for transmitters and receivers are given respectively by:
where
P_{t}
is the transmission power,
N_{head}
is the number of bit in the overhead of a packet for the synchronization of physical layer,
R_{code}
is the code rate. The other parameters are described in
Table 1
.
Some parameters in the transceiver energy consumption
Some parameters in the transceiver energy consumption
The energy expenditure model of an acknowledgment is given by:
In
[6]
, the energy model for each bit is:
Put (1)–(4) into (5), we have
and
 2.2 Realistic Unreliable Link Model
The realistic unreliable link model is also the same as that in literatures
[6
,
11]
. The unreliable radio link probability (
pl
) is defined as the packet error rate (PER)
[6]
:
where
is the distance between node
x
and
x’, λ
is the wavelength,
R_{5}
is the symbol rate. Other parameters are the same as those in
Table 1
. Note that
R_{b}
=
R_{s}
·
b
, where
b
is the modulation order. The unreliable link models are approximated to Rayleigh block fading channels as follows
[9]
.
where
α_{m}
and
β_{m}
rely on the modulation type and order, e.g., for Multiple Quadrature Amplitude Modulation (MQAM) am
and
β_{m}
= 3log
_{2}
(
M
)/(
M
1) . For BPSK,
α_{m}
= 1 and
β_{m}
= 2.
 2.3 Problem Statement
(1) The total energy consumption for each source node transmitting one bit data to the sink is defined as
E_{tot}
.
(2) Energy consumption rate
ξ
is defined as transmitting one bit data to the sink with energy consumption
E_{tot}
divided by the number of nodes (
n
) participating in transmission, i.e.,
3) Network lifetime
ℓ
is defined as the average amount of time until any sensor runs out of energy (the first failure)
[9
.
13]
. Utilization efficiency
η
is defined as network lifetime
ℓ
divided by the number of deployed sensors (
N
), i.e.,
Utilization efficiency (
η
) indicates the rate at which network lifetime (
ℓ
) increases with the number of nodes (
N
). It causes the tradeoff between network lifetime and deployment cost.
The design goal is to find the optimal node number
N
^{*}
, sensor placement
d
^{*}
, and transmission structure
P^{*}
which can minimize
E_{tot}
and
ξ
, while maximizing utilization efficiency
η
:
At the same time, the network has to ensure the endtoend reliability to meet the minimum requirements of the application, such as
C
, i.e..
In summary, the optimization goal of this paper is shown as follows:
3. Scheme Design
 3.1 Multisource Linear Network
The multisource linear network is that each node in the network is deployed to monitor the surrounding environment and generates a sensed data in each cycle. Such linear networks are widely applied into applications such as roads, oil pipelines and border detection. Many routes such as shortest route, HEED route which are widely used in twodimensional network can also be considered in a linear network. Thus, this research has an important significance and is referred as a multisource linear network in this paper. As shown in
Fig. 1
, there are
n
nodes linearly deployed in the network, each node generates one data in a data collection round (cycle), and then transmits it to the sink. For
S
_{1}
nearest to the sink, the data load is
n
data packets, and for
S
_{2}
, it is
n
1 data packets, ..... for
S_{n}
, the data load is one data packet.
Illustration of the line network of each node as source
First, we discuss on how to decrease
d_{hop}
for nodes near the sink and increase
d_{hop}
for nodes far from the sink. As shown in
Fig. 2
, the nodal data load is much higher for nodes near to the sink, therefore the transmission distance can be decreased in order to reduce the energy consumption for unit data transmission.
Illustration of the unequidistant linear network
Theorem 1
: The total energy consumption is minimal when nodes are equidistantly deployed.
Proof
: Assuming the number of equidistantly deployed nodes is
n
, then the energy consumption for node
i
is:
First, when nodes are equidistant, the total energy consumption is as follows:
subject to
nd_{hop}
=
D
.
Proof (16): Assuming the distance between any two nodes is
d_{hop}
, then data is sent to the sink via
D/d_{hop}
hops. To meet reliability (more than or equal to
C
), the following should be ensured.
Put (9) into (17) we can derive :
Put (18) into (8), we have:
Where
γ
is the S/N (signaltonoise ratio),
P_{t}
is the transmission power, and
pl_{g}(γ)
is the reliability. Therefore
Put (20) into (15), we get (21).
While if the nodes are not equidistant, there is:
Put the above formula into (15),we get:
subject to
d
_{1}
+
d
_{2}
+ ... +
d_{n}
=
D
.
The following need to be proved:
That is, we need to prove:
Reorganize the above, we get:
Then, we prove (23):
Set
F
=
E
_{1}
+
E
_{2}
+ ... +
E_{n}
+
λ
(
d
_{1}
+
d
_{2}
+ ... +
d_{n}

D
), where
λ
≠ 0 is Lagrange multiplier. According to Lagrange multipliers:
(24) shows that when
∂E
_{1}
/
∂d
_{1}
= ... =
∂E_{n}
/
∂d
_{n}
= 
λ
, the minimum
F
can be obtained, since nodes are all the same in linear network, so we define
E_{i}
=
d_{i}^{α}
(
n
+1
i
), therefore
Then it is clear that when
α
> 2, if the above formula is bigger than 0, then
∂E
/
∂d_{i}
= is a function with
d_{i}
which is strictly monotonically increasing, and then (24) is solvable,
d
_{1}
=
d
_{2}
= ... =
d_{n}
=
D/n
. Thus,
So far, (23) is proved. As can be seen from previous proof, (22) is correct. Thus, the total energy consumption is the minimum when nodes are equidistantly deployed.
Theorem 2
: For multisource linear network, there must be a
d_{hop}
which minimizes
E_{tot}
in (0,
D
] , while
Proof
: The total energy consumption is the minimum when nodes are equidistantly deployed, that is:
Obviously, when
d_{hop}
→ 0, since
nd_{hop}
=
D
,so
n
→ + ∞,
n
(
n
+ 1) / 2 → +∞. While when
when
d_{hop}
=
D
,
n
= 1, since
so
E_{tot}
is bounded and
E_{tot}
is continuously derivative in (0,
D
] , so there must be a
d_{hop}
∈ (0,
D
] which minimizes
E_{tot}
.
Theorem 1 proves that the network total energy consumption is optimal when
n
nodes are equidistantly deployed. Theorem 2 shows that there must be an optimal nodal distance (
d_{hop}
)which can minimize network total energy consumption. According to the definition in Section 2 we can see the second goal is to maximize
ξ
, which is to minimize unit nodal energy consumption. While the energy consumption for unit node is:
ξ
=
E_{tot}
/
n
Theorem 3
: For multisource linear network in Rayleigh block fading channels, there is a
d_{hop}
which can minimize
ξ
in (0,
D
]
Proof
: Put
n
=
D/d_{hop}
into (25) and reorganize it, we can get:
Obviously, when
d_{hop}
→0, we have
ξ
→+∞, when
d_{hop}
=
D
, since
ξ
is bounded, and
ξ
is continuously derivative in (0,
D
] ,then there must be a
d_{hop}
∈(0,
D
) D which minimizes
ξ
(The certification process is similar to theorem 2).
When
n
is determined, the network lifetime is determined by the node which has the maximum energy consumption, while in multisource network, it is the node which is nearest to the sink. Therefore, the network utilization optimization is to minimize the energy consumption of this node, that is, min max (
E_{i}
)
i
∈{1..
n
}.
Theorem 4
: For multisource linear network, to solve
d
_{1}
,
d
_{2}
, ...
d_{n}
which achieves min max (
E_{i}
)
i
∈{1..
n
}, s.t.
d
_{1}
+
d
_{2}
+...+
d_{n}
=
D, d
_{0}
≤
d
_{1}
≤
d
_{2}
≤ ... ≤
d_{n}
is to solve the following:
Proof
: The network lifetime is the maximum when all nodal energy consumption equals, the following formula can be obtained:
Then:
Set
Put the above formula into the equation set (28), that is (27).
For instance, in the network when D=240, C=0.9, n=6, then the following data can be got:
d
_{1}
= 24.6450, 24.6450,
d
_{2}
= 27.8566,
d
_{3}
= 32.0767,
d
_{4}
= 38.0849,
d
_{5}
= 47.8909,
d
_{6}
= 69.4462. Compare these two schemes, the proportion of declined energy is:
Theorem 4 has proved that
η
can be improved by decreasing
d_{hop}
for nodes near the sink and increasing
d_{hop}
for nodes far from the sink. Similarly, the energy consumption for node
i
near the sink can be decreased by decreasing nodal reliability
c_{i}
, and increase energy consumption for nodes far from the sink by using remaining energy, to ensure the reliability C of the entire routing meet the requirement of applications. Then, Theorem 5 can be derived.
Theorem 5
: For multisource linear network in Rayleigh block fading channels, there must be
c
_{1}
≤
c
_{2}
... ≤
c
_{n}
which achieves min max(
E_{i}
)
i
∈ {1..
n
} s.t
Proof
: If there are
n
nodes and the energy consumption is balanced, thus we can derive the following :
And
Set
Put the formula into (29) ,then put result into the equations which above (29) ,arrange it we can get:
Set
Obviously,when
, so
H
_{1}
(
C
_{1}
) < 0 : when
C
_{1}
= 1, ln
C
_{1}
= ln 1 = 0,so
H
_{1}
C
_{1}
) = 1 ・ exp(0) 
C
= 1=
C
, hus
H
_{1}
(
C
_{1}
) > 0, since
H
_{1}
C
_{1}
) is a continuous function, then there must be a solution in
C
_{1}
∈ [0,1] hich achieves
H
_{1}
(
C
_{1}
) = 0.
 3.2 Grid Network
Grid network
In this section, it is extended to twodimensional network. In this kind of network, nodes are regularly deployed in intersections of rows and columns. The sink is located in the intersection of bottom left row and column, as shown in
Fig. 3
. In a grid network, each node generates one data and then it is sent to the sink in a cycle, and the transmission direction is restricted in downward or leftward direction with the same probability. To address the problem, this section first calculates the energy consumption for each node in the network and then discusses how to process cross layer optimization for grid network.
Theorem 6
: In grid network, the nodal data load is:
Proof
: Since
we obtain
, then
n^{th}
row is determined. The following is
n
1
^{th}
row, through analysis, we get:
While
Thus,
n
1
^{th}
row is determined. And so on, the summarized formula is (30).
Theorem 7
: In grid network, each node in the first row (column) has bigger data load than other nodes in the same row.
Proof
: According to Theorem 6, we get:
Since
B_{n,n1}
<
B_{n,n2}
,
B_{n,n1}
<
B_{n1,n1},
so
B_{n1,n2}
>
B_{n1,n1}
. Similary,
B_{n1,1}
>
B_{n1,2}
. Then, it follows that
B_{i,1}
>
B_{i,2}
(1 ≤
i
≤
n
). Therefore, each node in the first row (column) has bigger data load than other nodes in the same row.
This section discusses optimization in Rayleigh block fading channels for grid networks. In such networks, the number of nodes is fixed
n^{*}n
, and thus the deployment cost is determined, the optimization goal is how to maximize the network lifetime. Factors that can be optimized are the placement of nodes (
d^{*}
) and nodal transmission structure (
P^{*}
). In this paper, two optimization methods are proposed, one is to optimize
d^{*}
, the other is to optimize
P^{*}
. The network lifetime can be maximized through these two approaches. In Theorem 8, we propose an optimal solution of nodal placement.
Theorem 8
: In Rayleigh block fading channels grid network, the energy consumption of nodes in maximum consumption row (column) can be balanced if
d_{i}
meets:
Proof
: According to (30), the data amount of each node can be calculated. Therefore, the optimal
d_{i}
(1 ≤
i
≤
n
) can be obtained if the first column is optimized. First, we need to solve optimal
d_{i}
(1 ≤
i
≤
n
). It is optimal when the energy consumption is balanced, then: As can be seen from previous analysis, we get:
Set
Put the above formula into (34) yields :
Put the above formula into (35), we get (33). Then, compute the front
n
 1 equations of (35), there is:
Represent all
d_{i}
with
d_{1}
(
D
≥
d_{1}
> 0), and then put them into the n
^{th}
equation, thus:
Set
Through analysis, it is obvious that
H
_{2}
(
d
_{1}
) is a monotone increasing function in
d
_{1}
∈ (0,
D
]. Obviously, when
d
_{1}
=
D
,
when
Therefore, if and only if the above is not more than 0, then the original equation has solutions and the solution is obtained.
Theorem 10
: In Rayleigh block fading channels grid network, the energy consumption of nodes in maximum consumption row(column) can be balanced if reliability
c_{i}
.
Proof
: As can be seen from previous analysis, if
d_{i}
(1 ≤
i
≤
n
) is obtained, then the problem is converted to solve optimal
c_{i}
(1 ≤
i
≤
n
). It is optimal when the energy consumption is balanced, then:
Then, that is:
Set
Put the above formula into (38) we yield:
Put the above formula into (37), we have (36). Then, compute the front
n
1 equations of (38), we get:
Represent all
C_{i}
with
C_{i}
, and then substitute them into the
n^{th}
equation and yield:
Set
Obviously, when
and
thus
H
_{3}
(
C
_{1}
) > 0, since
H
_{3}
(
C
_{1}
) is a continuous function, there must be
C
_{1}
∈ [0,1] which achieves
H
_{3}
(
C
_{1}
) = 0.
4. Performance Analysis and Experimental Results
 4.1 Multisource Linear Network
The energy consumption of MTC VS MPNC
In this section, we provide some simulation examples to verify the cross layer optimal design proposed in this paper. We define
M
inimum
T
otal energy
C
onsumption for transmitting unit bit data to the sink as MTC, and
M
inimum
P
er
N
ode
C
onsumption for transmitting unit bit data to the sink as MPNC.
Fig. 4
shows the energy consumption of MTC VS MPNC in Rayleigh block fading channels. As can be seen from
Fig. 4
and
Fig. 5
, the energy consumption of MPNC is only 10% to 67% of the energy consumption of MTC. Obviously, utilization based on design can improve network lifetime (decrease energy consumption).
Ratio of energy consumption by MPNC VS MTC
In this paper, balancing energy consumption is obtained by reducing transmission distance near the sink and increasing transmission distance far from the sink, which is called Unequal Distance of Nods Policy (UDNP). While nodes have equal distance in previous research is called Equal Distance of Nods Policy (EDNP).
Fig. 6
shows the energy consumption under UDNP and EDNP in Rayleigh block fading channels. Combined with
Fig. 7
, the energy consumption of UDNP is decrease by 2.36 to 2.46 times compared with EDNP, that is, the network lifetime is improved by more than 2 times.
Table 2
shows the nodal deployment distance with UDNP in Rayleigh block fading channels.
The energy consumption under UDNP and EDNP
The ratio of energy consumption by UDNP and EDNP
The unequal distance of nodes
The unequal distance of nodes
In addition, the network lifetime can be improved by decreasing nodal reliability near the sink and increasing nodal reliability far from the sink, under the premise of total reliability meets the requirement of applications, which is called URNP (Unequal reliability of nods policy) in this paper. The policy each node adopts equal reliability is denoted as ERNP (equal reliability of nods policy).
Fig. 8
gives the energy consumption under these two schemes (URNP vs ERNP) and
Fig. 9
gives the ratio of energy consumption. As can be seen, URNP has better performance, which can improve network lifetime by more than 20%.
Table 3
shows nodal reliability with URNP. If the total reliability requirement is 0.579, then the nodal reliability for each node in ERNP is 0.933, however, in URNP scheme, nearly Sink node reliability is 0.8 when it can meet the requirements of 0.579. Thus in URNP policy, energy consumption of the maximum energy consumption node is less than that in ERNP strategy. So the network lifetime can be improved in URNP scheme.
The energy consumption under URNP and ERNP
The ratio of energy consumption of ERNP VS URNP
The reliability of node (Rayleigh block fading channels)
The reliability of node (Rayleigh block fading channels)
 4.2 Grid Network
In this section, we present the verification for grid network optimization design in this paper, which is in a 5*5 grid network.
Table 4
shows the nodal deployment distance with UDNP under Rayleigh block fading channels for grid network.
Fig. 10
shows the energy consumption under UDNOP and EDNP in Rayleigh block fading channels, combined with
Fig. 11
, it can be known easily that when compared with EDNP the energy consumption is decreased by more than 3.7 times with UDNP.
The unequal distance of nodes (Rayleigh block fading channels)
The unequal distance of nodes (Rayleigh block fading channels)
The energy consumption under UDNOP and EDNP (Rayleigh block fading channels)
Ratio of energy by EDNP over UDNOP (Rayleigh block fading channels)
The reliability of node (Rayleigh block fading channels)
The reliability of node (Rayleigh block fading channels)
The energy consumption under URNP and ERNP
Table 5
shows the nodal reliability with URNP in Rayleigh block fading channels. When the required total reliability is 0.764, the nodal reliability for each node with ERNP is 0.948. In URNP, the reliability of maximum energy consumption node is only 0.8, and thus the energy consumption is less than that in ERNP.
Fig. 12
shows the energy consumption under URNP and ERNP, as can be seen, URNP can improve network lifetime by more than 30%.
5. Conclude and Discussion
In this paper, the optimization for multisource linear network and grid network under Rayleigh blockfading channels have been proposed. The main conclusion can be drawn as follows: (1) The optimal nodal number
N^{*}
, nodal placement
d^{*}
and nodal transmission structure
p^{*}
are given which can meet minimum total energy consumption and minimum unit data transmitting energy by the strict mathematics method. When the network total energy consumption for unit data is minimum, the unit data energy consumption
ξ
is not necessarily the minimum; (2) The minimum
ξ
does not necessarily maximize utilization efficiency
η
. A cross layer optimal design is proposed which adopts lower nodal reliability and shorter transmission distance for nodes near the sink. Through those, the network energy consumption can be balanced, and the network utilization is improved. Besides, we find that the network lifetime can be improved by several times (25 times) with UDNP, compared with EDNP. Meanwhile, the network lifetime can be improved by more than 30% with URNP, compared with ERNP; (3) Different from previous research, this paper gives the optimization equations and their solvable conditions by the strict mathematics, which have good theoretical significance.
BIO
Xue Chen received B.Sc on 2012. Currently she is a master in School of Software of Central South University, China. Her research interest is wireless sensor network.
Yanling Hu received B.Sc on 2013. Currently she is a master in School of Information Science and Engineering of Central South University, China. Her research interest is wireless sensor network.
Anfeng Liu is a Professor of School of Information Science and Engineering of Central South University, China. He is also a Member (E200012141M) of China Computer Federation (CCF). He received the M.Sc. and Ph.D degrees from Central South University, China, 2002 and 2005, both in computer science. His major research interest is wireless sensor network.
Zhigang Chen received B.Sc. the M.Sc. and Ph.D degrees from Central South University, China, 1984, 1987 and 1998, He is a Ph.D. Supervisor and his research interests are in network computing and distributed processing.
Miorandi D.
,
Sicari S.
,
Francesco D. P.
,
Chlamtac I.
2012
“Internet of things: Vision, applications and research challenges”
Ad Hoc Networks
Article (CrossRef Link)
10
(7)
1497 
1516
DOI : 10.1016/j.adhoc.2012.02.016
Oh Hoon
,
Han TrungDinh
2012
“A demandbased slot assignment algorithm for energyaware reliable data transmission in wireless sensor networks”
Wireless Networks
Article (CrossRef Link)
18
(5)
523 
534
DOI : 10.1007/s1127601204165
Kim SeongJoong
,
Park DongJoo
2013
“A selfcalibrated localization system using chirp spread spectrum in a wireless sensor network”
KSII Transactions on Internet and Information Systems
Article (CrossRef Link)
7
(2)
253 
270
Mario Di Francesco
,
Giuseppe Anastasi
,
Marco Conti
,
K Das Sajal
,
Vincenzo Neri
2011
“Reliability and energyefficiency in IEEE 802.15.4/ZigBee sensor networks: An adaptive and crosslayer approach”
IEEE Journal on Selected Areas in Communications
Article (CrossRef Link)
29
(8)
1508 
1524
DOI : 10.1109/JSAC.2011.110902
Benazir Fateh
2013
“Govindarasu Manimaran. Energy minimization by exploiting data redundancy in realtime wireless sensor networks”
Ad Hoc Networks
Article (CrossRef Link)
11
(6)
1715 
1731
DOI : 10.1016/j.adhoc.2013.03.009
Zhang Ruifeng
,
Berder Olivier
,
Gorce JeanMarie
,
Sentieys Olivier
2012
“Energy–delay tradeoff in wireless multihop networks with unreliable links”
Ad Hoc Networks
Article (CrossRef Link)
10
(1)
1306 
1321
DOI : 10.1016/j.adhoc.2012.03.012
Chen P.
,
O'Dea B.
,
Callaway E.
2002
“Energy efficient system design with optimum transmission range for wireless ad hoc networks”
in Proc. of IEEE International Conference on Communications (ICC’02),
vol. 2, Article (CrossRef Link)
945 
952
Gao J.L.
2002
“Analysis of Energy Consumption for Ad Hoc Wireless Sensor Networks Using a Bitmeterperjoule Metric”
Jet Propulsion Laboratory, California Institute of Technology
Tech. Rep. 42150
Article (CrossRef Link)
Chen Yunxia
,
Chuah ChenNee
,
Zhao Qing
2008
“Network configuration for optimal utilization efficiency of wireless sensor networks”
Ad Hoc Networks
Article (CrossRef Link)
6
(3)
92 
107
DOI : 10.1016/j.adhoc.2006.09.001
Tahir M.
,
Farrell R.
2013
“A crosslayer framework for optimal delaymargin, network lifetime and utility tradeoff in wireless visual sensor networks”
Ad Hoc Networks
Article (CrossRef Link)
11
701 
711
DOI : 10.1016/j.adhoc.2011.09.011
Sastry Srikanth
,
Radeva Tsvetomira
,
Chen Jianer
,
Welch Jennifer L.
2013
“Reliable networks with unreliable sensors”
Pervasive and Mobile Computing
Article (CrossRef Link)
9
(2)
311 
323
DOI : 10.1016/j.pmcj.2012.02.004
Villas Leandro Aparecido
,
Boukerche Azzedine
,
Heitor Soares
,
De Oliveira Horacio A.B.
,
De Araujo Regina Borges
,
Loureiro Antonio Alfredo Ferreira
2013
“DRINA: A lightweight and reliable routing approach for innetwork aggregation in wireless sensor networks”
IEEE Transactions on Computers
Article (CrossRef Link)
62
(4)
676 
689
DOI : 10.1109/TC.2012.31
Liu Anfeng
,
Zheng Zhongming
,
Zhang Chao
,
Chen Zhigang
,
Shen Xuemin (Sherman)
2012
“Secure and EnergyEfficient Disjoint MultiPath Routing for WSNs”
IEEE Transactions on Vehicular Technology
Article (CrossRef Link)
61
(7)
3255 
3265
DOI : 10.1109/TVT.2012.2205284
Liu Anfeng
,
Jin Xin
,
Cui Guohua
,
Chen Zhigang
2013
“Deployment Guidelines for Achieving Maximal Lifetime and Avoiding Energy Holes in Sensor Network”
Information Sciences
Article (CrossRef Link)
230
197 
226
DOI : 10.1016/j.ins.2012.12.037
Octav Chipara
,
Chenyang Lu
,
GruiaCatalin Roman
2013
“Realtime query scheduling for wireless sensor networks”
IEEE Transactions on Computers
Article (CrossRef Link)
62
(9)
1850 
1865
DOI : 10.1109/TC.2012.172