ORE Open Research Exeter
TITLE
Green communication in energy renewable wireless mesh networks: routing, rate control, and power
allocation
AUTHORS
Luo, Chunbo; Guo, Shengyong; Guo, Song; et al.
JOURNAL
IEEE Transactions on Parallel and Distributed Systems
DEPOSITED IN ORE
22 March 2016
This version available at
http://hdl.handle.net/10871/20802
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For Peer Review Only
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 1
Green Communication in Energy Renewable
Wireless Mesh Networks: Routing, Rate Control,
and Power Allocation
Changqing Luo, Shengyong Guo, Song Guo, Laurence T. Yang, and Geyong Min
Abstract—The increasing demand for wireless services has led to a severe energy consumption problem with the rising of greenhouse
gas emission. While the renewable energy can somehow alleviate this problem, the routing, flow rate, and power still have to be well
investigated with the objective of minimizing energy consumption in multi-hop wireless mesh networks (WMNs). This paper formulates
the problem of network-wide energy consumption minimization under the network throughput constraint as a mixed-integer nonlinear
program by jointly optimizing routing, rate control, and power allocation. Moreover, the min-max fairness model is applied to address
the fairness problem because the uneven routing problem may incur the sharp reduction of network performance in multi-hop WMNs
with renewable energy. Due to the high computational complexity of the formulated mathematical programming problem, an energy-
aware multi-path routing algorithm (EARA) is also proposed to deal with the joint control of routing, flow rate, and power allocation in
practical multi-hop WMNs. To search the optimal routing , it applies a weighted Dijkstra’s shortest path algorithm, where the weight is
defined as a function of the power consumption and residual energy of a node. Extensive simulation results are presented to show the
performance of the proposed schemes and the effects of energy replennishment rate and network throughput on the network lifetime.
Index Terms—Multi-hop wireless mesh networks, renewable energy, fairness, energy consumption minimization, routing.
F
1 INTRODUCTION
The increasing demand for ubiquitous network access
leads to the rapid development of wireless access net-
works. The multi-hop wireless mesh network (WMN),
as a promising solution for low-cost broadband Internet
access, is being used on the last mile for enhancing In-
ternet connectivity for mobile users. A multi-hop WMN
is usually constructed by wireless mesh nodes that are
wireless mesh routers or gateways. The nodes are rarely
mobile, and do not have power constraints. A high
volume of traffic can be effectively delivered on wireless
channels via multi-hop wireless paths.
In the past years, researchers largely concentrate on
the channel assignment, routing, and rate allocation
problems in multi-hop WMNs [1], [2], [3]. Subramanian
et al. [4] investigated the channel assignment problems
in multi-radio WMNs, and designed centralized and
distributed algorithms for the channel allocation with the
objective of minimizing the overall network interference.
Capone et al. [5] addressed the radio resource assignment
optimization problem in WMNs where routing, schedul-
ing and channel assignment were jointly considered. Pas-
sos and Albuquerque [6] considered the routing and rate
adaptation problem in WMNs, and proposed a joint au-
C. Luo, S. Guo, L. T. Yang, and G. Min are with the School of Com-
puter Science and Technology, Huazhong University of Science and Tech-
nology, Wuhan, China (email: chqluo2013@gmail.com, gshyong@gmail.com,
ltyang@gmail.com, and g.min@brad.ac.uk); L. T. Yang is also with the
Department of Computer Science, St. Francis Xavier University, Antigonish,
Canada, and G. Min is with the Department of Computing, School of
Informatics University of Bradford, Bradford, UK
S. Guo is with the School of Computer Science and Engineering, The
University of Aizu, Tsuruga, Ikki-machi, Japan (email: sguo@u-aizu.ac.jp)
tomatic rate selection and routing scheme to provide best
routing and rate. Besides, since energy consumption is
becoming a very important problem in the world for the
rising of greenhouse gas emission, energy efficiency has
been attracting much attention [7], [8]. Vijayalayan et al.
[9] considered the energy efficient scheduling scheme in
WMNs and an enhanced pseudo random access scheme
was proposed to improve the energy efficiency. The
power control problem in WMNs was also investigated
to reduce the interference and energy consumption [10],
[11], [12]. However, although some work have been done
to reduce energy consumption, the effect is essentially
marginal.
On the other hand, the power grid infrastucture,
which provides electricity to multi-hop WMNs, has been
experiencing a dramatic change from the tranditional
electricity grid to the smart grid where renewable energy
is integrated [13], [14]. Renewable energy is usually
extracted from renewable resources (e.g., solar and wind)
so that no fossil fuel is burn and thus no greenhouse gas
is produced. Therefore, the use of renewable energy, to
some extent, can alleviate the greenhouse gas emission
problem.
However, the routing, flow rate, and power allocation
problem still has to be well investigated in multi-hop
WMNs with renewable energy because renewable en-
ergy replenishment of each node in multi-hop WMNs
is highly dependent on the environment. The energy
replenishment rate dynamically changes over time, and
is affected by the weather and surrounding environment.
Hence, new problems are posed in multi-hop WMNs
with renewable energy. In recent years, a few research
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efforts have been made to investigate the problems
in multi-hop WMNs with renewable energy. Badawy,
Sayegh, and Todd [15] investigated the resource as-
signment problem so as to minimize the network de-
ployment cost. Cai et al. [16] investigated the resource
management problem in sustainable energy powered
WMNs and an adaptive resource management scheme
is proposed to distribute traffic under the energy sus-
tainability constraint. In particular, a G/G/1 queue is
applied to model the energy buffer of a mesh node and
a diffusion approximation is then used to analyze the
transient evolution of the queue length. Zheng et al.
[17] proposed an energy-aware AP placement scheme
in WLAN mesh networks with renewable energy where
the optimal placement of APs is determined and the
power constrol and rate adaptation at APs are jointly
considered. Lin, Shroff, and Srikant [18] investigated the
routing problem for multi-hop WMNs with renewable
energy, and proposed an asymptotically optimal energy-
aware routing scheme in which energy replenishment,
mobility, and erroneous routing information were jointly
considered.
However, the work on joint control of routing, rate,
and power to minimize network-wide energy consump-
tion under network throughput constraint in multi-hop
WMNs with renewable energy is still missing in the cur-
rent literature. In fact, routing, rate control, and power
allocation are highly interdependent, and have signif-
icant influence on the energy consumption in multi-
hop WMNs. Therefore, they should be simultaneously
considered to minimize the network-wide energy con-
sumption.
To this end, this paper proposes a scheme jointly
considers the routing, rate control, and power alloca-
tion tominize network-wide energy consumption with
network throughput constraint in multi-hop WMNs.
The key contributions of this paper are summarized as
follows.
1) The network-wide energy consumption minimiza-
tion under the network throughput constraint in
multi-hop WMNs with renewable energy is investi-
gated and a scheme that jointly considers the rout-
ing, flow rate, and power allocation is proposed
to deal with this problem. Moreover, the network-
wide energy consumption minimization problem is
formulated as a mixed-integer nonlinear program
(MINLP) that is in general NP-hard.
2) Fairness is also taken into account in the proposed
scheme to address the uneven routing problem
which may lead to some severe performance issues
(e.g., some nodes frequently enter the sleep mode
for the residual energy of these nodes is below
a threshold.) in multi-hop WMNs with renewable
energy compared to traditional multi-hop WMNs.
The min-max fairness model is applied to address
the fairness problem, which can achieve the trade-
off between the power consumption and residual
energy of a node in multi-hop WMNs with renew-
able energy.
3) An energy-aware multi-path routing algorithm
(EARA) is proposed to deal with the joint control
of routing, rate control, and power allocation in
practical multi-hop WMNs where the solution to
MINLP problem has high computation complexity.
This algorithm uses a weighted Dijkstra shortest
path algorithm to search an optimal routing and
the weight is defined as a function of the power
consumption and residual energy of a node. More-
over, the concept of unit flow that consists of a
session flow is proposed to address the issue that
the weighted Dijkstra shortest path algorithm can
not support multi-path routing.
The remainder of this paper is organized as follows.
Section 2 describes the network model, including the
considered network scenario, session flow model, and
power and energy consumption model. The network-
wide energy consumption under network throughput
constraint is formulated as a MINLP problem and the
fairness is also consider to address the uneven routing
problem in Section 3. Section 4 proposes an energy-
aware routing algorithm that can be used in practi-
cal multi-hop WMNs. Extensive simulation results are
presented and analysed for performance evalution in
Section 5. Finally, Section 6 concludes this paper.
2 NETWORK MODEL
This paper considers a multi-hop WMN with renewable
energy, represented by a directed graph G = {N , L},
where N and L are the sets of nodes and directional
links, respectively. A link between two nodes exists if
and only if the two are within the a certain commu-
nication range. The communication between two node
without a direct link needs to resort to multi-hop com-
munication with the help of intermediate nodes’ relay-
ing. Orthogonal channels are used by all links so that
the interference can be avoided. It is noteworthy that
the number of channels is as many as the number of
active links because a channel can be reused spatially.
The multi-hop WMN is considered to work as a time-
division system in which the time is divided into slots
with equal length T and t refers to the t-th discrete time
period. We assume that no new session occurs during
a time slot; thus, the existing session flow will not be
changed.
In particular, each node is considered to be powered
only by renewable energy for aiming to investigate ef-
fects of renewable energy on the joint control of routing,
rate, and power allocation with the objective of mini-
mizing the network-wide energy consumption in multi-
hop WMNs. The solar is the renewable energy source
and a large-size solar panel is deployed for a node.
The structure of a node is shown in Fig. 1 where solar
energy is transformed into electrical energy through a
solar panel. The electrical energy will be stored into
the battery via a charging controller, and then used to
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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 3
Fig. 1. The node structure supplied with renewable
energy.
power the access point (AP). Once the energy contained
in the battery is lower than a threshold, the charging
controller will immediately shut down the power supply
so that the node enters the sleep mode. Due to the
low energy production rate, the energy replenishment
rate of a node is assumed to be less than the energy
consumption rate when a session is delivered through
the node. When a node works, its residual energy will
gradually reduce till it reaches the predefined threshold
B
outage
. As long as the residual energy of a node is
greater than B
outage
after replenishing energy, the node
will be activated. Moreover, when the residual energy
reaches the maximum capacity of a battery B
max
, the
energy replenishment will stop. In other words, the
residual energy of a node varies between B
outage
and
B
max
.
2.1 Session Flow Model
There is a set of F active session flows in the network.
It is noteworthy that the unicast communication session
is considered. Let s(f ) and d(f) denote the source and
destination nodes of a session flow f ∈ F, respectively.
Moreover, r(f ) represents the data rate of session flow f.
Therefore, for the network with |F| active session flows,
network throughput U is the sum of data rate of all
session flows, i.e.,
U =
X
f∈F
r(f). (1)
To achieve data transmission between a source node
and its corresponding destination node, the multi-path
flow routing scheme is applied in this study. Hence,
each session flow can be splitted, and delivered through
multiple paths. Let r
l
(f) denote the amount of flow
rate on link l that is attributed to session flow f ∈ F.
L
In
i
and L
Out
i
represent the set of potential incoming
links and the set of potential outgoing links at node
i, respectively. Since session flow needs to satisfy rate
balance, the following equations can then be obtained.
If node i is the source node of session f, i.e., i = s(f),
then
X
l∈L
Out
i
r
l
(f) = r(f). (2)
If node i is the destination node of session f, i.e., i =
d(f), then
X
l∈L
In
i
r
l
(f) = r(f). (3)
If node i is an intermediate node of session f, i.e., i 6=
s(f) and i 6= d(f), then
l6=(i,s(f ))
X
l∈L
Out
i
r
l
(f) =
l
0
6=(d(f),i)
X
l
0
∈L
In
i
r
l
0
(f). (4)
Since the quality of service (QoS) for each users needs
to be guaranteed in multi-hop WMNs, the data rate of
each session flow should be met when the joint control
scheme of routing, rate, and power is designed.
2.2 Power and Energy Consumption Model
In general, when a session is delivered on a link in multi-
hop WMNs with renewable energy, the energy is mainly
consumed due to data transmission and reception. The
receiving power is denoted by P
rec
, which is assumed to
be a constant. The transmission power is represented by
P
l
when link l is active. It is obvious that transmission
power is a variable parameter that is related to the
quality of the link and the rate allocation.
X
l
is denoted as a binary variable indicating whether
or not link l is active, i.e.,
X
l
=
1, if link l is active, l ∈ L,
0, otherwise.
(5)
Hence, the energy consumption for link l is (P
l
+X
l
·P
rec
).
The maximum transmission power for each node is
defined as P
max
. Since transmission power can not ex-
ceed the maximum transmission power, the following
relationship can be obtained
0 ≤ P
l
≤ X
l
· P
max
, l ∈ L. (6)
Since there may be a number of outgoing links at node
i, the transmission power constraint can be expressed as
follows
0 ≤
X
l∈L
Out
i
P
l
≤ P
max
, l ∈ L, i ∈ N . (7)
Let E
i
denote the total energy consumption at node i
during a time slot, which can be expressed as
E
i
= (
X
l∈L
Out
i
P
l
+
X
l∈L
In
i
X
l
· P
rec
) · T, l ∈ L, i ∈ N . (8)
In multi-hop WMNs with renewable energy, renew-
able energy will be supplied to each node except that
its battery is full. Denote B
i
(t) as the residual energy of
node i at the beginning of time slot t and R
i
(t) represents
as the replenished energy of node i during time slot
t. It is a common sense that R
i
(t) is highly related to
geographical location, environment, climate and other
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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 4
natural factors. After a time slot, the residual energy of
node i is
B
i
(t+1) = min{B
max
, max[B
outage
, B
i
(t)+R
i
(t)−E
i
(t)]},
(9)
where R
i
(t) = r
i
(t) · T , and r
i
(t) is the energy replenish-
ment rate. The energy for each node in multi-hop WMNs
with renewable energy is updated through (9).
For link l, the link capacity can be obtained through
Shannon formula
c
l
= W
l
log
2
(1 +
P
l
G
l
σ
2
), l ∈ L, (10)
where c
l
, W
l
, and G
l
are the achievable capacity, band-
width, and channel gain of link l, respectively; σ
2
is the
ambient Gaussian noise power. Accordingly, when max-
imum transmission power is used, the corresponding
maximum capacity c
max
l
is
c
max
l
= W
l
log
2
(1 +
P
max
G
l
σ
2
), l ∈ L. (11)
Since session flow rate on any link cannot exceed the
link’s capacity, we have
X
f∈F
r
l
(f) ≤ c
l
, l ∈ L, . (12)
Through combining (10) and (12), the following relation-
ship can be obtained
X
f∈F
r
l
(f) ≤ W
l
log
2
(1 +
P
l
G
l
σ
2
), l ∈ L, . (13)
3 PROBLEM FORMULATION
The section studies how to jointly control the rout-
ing, rate, and power so as to achieve the network-
wide energy consumption minimization under the net-
work throughput constraint in multi-hop WMNs with
renewable energy. This problem is motivated by the
scenario where users have strict network throughput
limit. Hence, given the network throughput constraint,
the optimization problem is to minimize network-wide
energy consumption by jointly controlling the multi-path
routing, rate for each session flow, and power on each
link.
Mathematically, this problem can be formulated as
follows:
OPT: min Σ
i∈N
E
i
s.t. (1) − (4), (6) − (8), and (13)
x
l
∈ {0, 1}, P
l
, r
l
(f) ≥ 0.
OPT is a mixed-integer nonlinear program (MINLP),
which is in general NP-hard [19]. It seeks a feasible
routing vector for a session flow in f ∈ F along with the
corresponding rate vector on each link l ∈ L and power
vector for each node i ∈ N such that the network-wide
energy consumption of the triples vector (i.e., routing,
rate, and power) is minimum among all feasible vectors.
Based on the results of solving this formulation, the
optimal routing, rate control, and power allocation can
be obtained.
However, simply minimizing the network-wide en-
ergy consumption can lead to a severe bias that some
wireless mesh nodes are starved and some other nodes
are satiated. That is, some nodes may be always se-
lected to deliver session flows due to its high-quality
outgoing or incoming links while some other nodes
may have no opportunity to deliver session flows. It is
well known that this phenomenon will result in some
severe performance problems in multi-hop WMNs, such
as unbalanced traffic load and network acess collision
[20], [21]. This problem may be more severe in multi-
hop WMNs with renewable energy compared with tra-
ditional multi-hop WMNs since the energy at each node
is limited and supplied through energy replenishing
from solar. Because some nodes may frequently enter
the sleep mode for their residual energy is less than
the threshold. Therefore, fairness should be considered
when the scheme of jointly controlling routing, rate, and
power is designed in multi-hop WMNs with renewable
energy.
This paper addresses the fairness issue based on a
simple min-max fairness model, which leads to mini-
mum network-wide energy consumption with guaran-
teed minimum maximum power allocation of each node
according to its residual energy. The goal of achieving
fairness is that the lower energy is consumed by a node
with lower residual energy while the higher energy is
consumed by a node with higher residual energy. There-
fore, min-max fairness is used to limit the transmission
power of each node as a value. By letting
α = max
i∈N
{α
i
}, and
α
i
=
P
i
/
P
i∈N
P
i
B
i
/
P
i∈N
B
i
denote the fairness constraint factor, we then have
P
i
≤
B
i
P
i∈N
B
i
·
X
i∈N
P
i
· α, i ∈ N , l ∈ L, (14)
where P
i
=
P
l∈L
Out
i
P
l
is the transmission power of
node i.
Through (14), the transmission power of each node is
constrained so that the network-wide residual energy is
balanced. It can be shown that the maximum allowed
transmission power is proportional to the residual en-
ergy of the node. Fair constraint factor α can be derived
through solving MIN-MAX, and then is used for solving
OPT-F to obtain routing and power allocation.
MIN-MAX min α
s.t. (1) − (4), (6) − (8), (13), and (14)
x
l
∈ {0, 1}, P
l
, r
l
(f) ≥ 0.
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