JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 32, 495-514 (2016)
Short Paper__________________________________________________
Multi-Radio Multi-Channel (MRMC)
Resource Optimization Method for Wireless Mesh Network*
DEGAN ZHANG1,2,3,†, YANAN ZHU1,2,‡, SI LIU1,2,6,
XIAODAN ZHANG4,5 AND JINJIE SONG1,2,7
1
Key Laboratory of Computer Vision and System
Ministry of Education, Tianjin
2
Tianjin Key Lab of Intelligent Computing and Novel Software Technology
Tianjin University of Technology
Tianjin, 300384 P.R. China
3
School of Electrical and Information Engineering
The University of Sydney
Sydney, NSW 2006, Australia
4
Institute of Scientific and Technical Information of China
Beijing, 100038 P.R. China
E-mail: †[email protected]; {‡724972157; 6406690108; 52310674826; 7172128173}@qq.com
Wireless Mesh network (WMN) is multi-hop heterogeneous network, which breaks
shortcomings of traditional wireless network. WMN comes into sight with more advantages. To the multi-radio multi-channel (MRMC) wireless mesh networks (MRMCWMN), routing distribution, channel assignment and rate allocation can be united to optimize network performance. MRMC resource optimization method based on convex
theory for WMN is presented in this paper. According to convex theory, we use the convex optimization function to get the optimal solution in the limited network supporting
by Ad hoc On-Demand Distance Vector (AODV) routing method. At the same time, we
resolve the optimal solution into three simple sub-problems according to the Lagrange
duality method supporting by multi-radio multi-channel AODV (MAODV). We use
MATLAB simulation tools to simulate the new and improved optimization method. The
experimental results show that our method has better network performance in the applications of WMN.
Keywords: MRMC, WMN, convex, optimization, MAODV, Lagrange duality method
1. INTRODUCTION
With the rapid development of the Internet of Things (IOT) technology and the
explosive demand of connecting network at anytime, the completion of the high-quality
and stable performance communication services become the primary task of wireless
Received September 24, 2014; revised August 11, 2015; accepted September 1, 2015.
Communicated by Jiann-Liang Chen.
*
This work was supported by the National Natural Science Foundation of China (Grant No. 61571328), Tianjin Key Natural Science Foundation (No. 13JCZDJC34600), Training plan of Tianjin University Innovation
Team (No. TD12-5016), Major projects of science and technology in Tianjin (No. 15ZXDSGX00050).
5
Corresponding author.
495
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DEGAN ZHANG, YANAN ZHU, SI LIU, XIAODAN ZHANG AND JINJIE SONG
Mesh network (WMN). WMN is multi-hop heterogeneous network, which breaks shortcomings of traditional wireless network [1-3]. WMN comes into sight with more advantages. To the multi-radio multi-channel (MRMC) wireless mesh network (MRMCWMN), routing distribution, channel assignment and rate allocation can be united to optimize network performance.
Recently Ad hoc On demand Distance Vector (AODV), Destinations Sequenced
Distance Vector (DSDV), Dynamic Source Routing Protocol (DSR) routing protocols
are used in WMN, which generally tend to choose the path of least number of hops in the
network and to maintain the route to provide best-effort service when the network topology changes. But these routing protocols cannot meet the requirements of various
applications of the IOT [4-7].
Many scholars who at home and abroad conduce popular studies to MRMC-WMN
in recent years [8-12]. To improve the utilization of the radio channel at the same time to
reduce the inter-channel interference, we use wireless channel allocation refers to device
different radio channel for wireless node radio frequency [13-17]. The radio channel is
assigned three methods. Firstly, statically allocated channel method refers to the communication prior to the channel assignment and so long constant state. Although the link
communication can be re-access to the allocated channel, it will increase the time complexity. Secondly, the dynamic allocation of channel method allows the wireless node of
the Radio Frequency (RF) switch in different radio channels [18-25]. Although the RF
equipment freely select the channel, switching the channel many times will cause the
delay through the network communication. Thirdly, the combination way which is combination between the static method and dynamic method, using the static method is part
of the RF device allocation of public channels. And then according to the network traffic
needs conduct dynamic channel allocation to another part of the RF, which ensures the
wireless mesh network connection resistance and stability.
Data transmission technology is the basic needs of wireless mesh network [26-30].
Although there is a delay, it can optimize network protocol to increase the network performance using hop-by-hop or end-to-end wireless link transmission according to different network applications [31-33]. In addition, the data transmission rate can be controlled by adjusting the wireless link to balance the network load and re-transmission of
number of times in order to reduce energy consumption and delay of the packet.
In order to meet the load balancing and user quality of service requirements, wireless mesh networks use the cross-layer optimization strategy [3-8] to design the routing
metric and protocol. To the multi-radio multi-channel wireless mesh networks, routing
distribution, channel assignment and rate allocation are united to optimize network performance. It turned the complex communication problems into a simple optimization
problem. We use the convex optimization to get the optimal solution in the limited network. At the same time, according to the Lagrange duality method, we resolve the optimal solution into three simple sub-problems. That is to say, we use the convex optimization to get the optimal solution in the limited network supporting by Ad hoc On-Demand
Distance Vector (AODV) routing method in this paper. At the same time, we resolve the
optimal solution into three simple sub-problems according to the Lagrange duality
method supporting by multi-radio multi-channel AODV (MAODV). The experiment and
analysis of the data show that the designed MAODV is better than that of the original
AODV in data packet delivery ratio, end-to-end delay, normalized routing overhead and
MRMC RESOURCE OPTIMIZATION METHOD FOR WIRELESS MESH NETWORK
497
routing. We use MATLAB simulation tools to simulate the new and improved optimization method, in addition, we also use OMNET++, NS2 simulation tools to simulate. In
this paper, we only show the experimental results by MATLAB simulation tools.
2. RELATED WORKS
In recent years, many scholars are studying the cross-layer fused optimization problem of MRMC-WMN resources [22-24]. Most of the research network is modeled as a
mathematical problem, and they use the Lagrangian decomposition technique to separate
the mathematical problem into several sub-problems. Each layer in the network protocol
stack corresponds to a decomposed sub-problems. Coordination of the various sub-problem of optimization variables as the interface between the layers is needed. Akyildiz
[25, 26] summarized the motivation and the need for cross-layer optimization, and study
the mechanisms and algorithms for cross-layer optimization between different protocol
layers [27]. Ernst summarizes scheduling and resource allocation of cross-layer design
method. Chen reviews cross-layer design in wireless mesh network [28, 29].
The fused optimization mechanisms can be divided into two types of centralized
and distributed. Centralized cross-layer optimization mechanism, the optimization is
performed by the gateway node, and therefore will bring high computational complexity
and signaling overhead. Alireza [12-14] studied centralized fused admission control and
scheduling algorithm of MRMC-WMN data services, but this paper assumes that the
network is not capable of concurrent transmission, so the total throughput of the network
is low. Mohsenian [15-17] studied distributed congestion-aware channel assignment
problem in-depth and also studies the cross-layer fused channel allocation, interface assignment and media access control problems based on the approximation dual decomposition of in the literature. The MRMC-WMN resource optimization involves many problems, including channel assignment, routing allocation, rate control, congestion control,
link scheduling and QoS [18-22]. This requires us to unified consideration to cross-layer
optimization of the various parameters.
Many researchers on cross-layer optimization algorithm only considering the maximum throughput [23-29]. Inflexible routing algorithm design is too complex, at the
same time considering many factors. In order to solve the existing MRMC-WMN resources optimization algorithm insufficient, we make full use of the potential advantages
of MRMC-WMN and design MRMC resource optimization method based on convex
theory for WMN, which is from global point of view to perform parameters and information of each layer. It could help to achieve a more reliable and efficient routing performance.
3. BASIC TOPOLOGY AND THEORY
To meet the load balancing and user quality of service requirements, wireless mesh
networks use the cross-layer optimization strategy to design the routing metric and protocol. We use the convex optimization function to get the optimal solution in the
MRMC-WMN. At the same time, we use the Lagrange duality method to make the optimal solution into three simple sub-problems. We give the relative definition and theo-
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DEGAN ZHANG, YANAN ZHU, SI LIU, XIAODAN ZHANG AND JINJIE SONG
rem to support the later design of method and experiments of simulation as follows.
Definition 1 Convex Real-valued function f(x) defined on an interval is called convex
(or convex downward or concave upward) if the line segment between any two points on
the graph of the function lies above the graph, in a Euclidean space (or more generally a
vector space) of at least two dimensions. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. Wellknown examples of convex functions are the quadratic function f(x) = x2 and the exponential function f(x) = ex for any real number x.
Lemma 1 Convex sets connection lemma If S is a collection of real or complex vector space. All and all, S is called convex set, if all x, y  S and t  [0, 1]. In short; if the
connection of any two points in still belongs to S convex set, Convex set is connected.
Definition 2 Convex function The assumption is that the f(x) is a function which definition on a closed interval, if any x, y  [a, b] and   [0, 1], and, f ( x+(1  )y)   f (y)
+ (1  ) f (y), so f (x) is convex function in [0, 1] .
Convex function plays an important role in many areas of mathematics. They are
especially important in the study of optimization problems where they are distinguished
by a number of convenient properties. For instance, a convex function on an open set has
no more than one minimum. Even in infinite-dimensional spaces, under suitable additional hypotheses, convex function continues to satisfy such properties and, as a result,
they are the most well-understood function in the calculus of variations. In probability
theory, a convex function applied to the expected value of a random variable is always
less or equal to the expected value of the convex function of the random variable.
Theorem 1 Convex optimization theorem A convex set is optimization if and only if
it meets the following minimization relationship:
min f0(x)
fi(x)  0, i = 1, …, m
s.t. hj(x) = 0, j = 1, …, l
f (x) is convex function which meets f (x) < 0 set is convex sets of x. h(x) is a linear
function, so h(x) is both convex function and concave function, at the same time, satisfies the x set is a convex set when h(x) = 0. Optimization problem that is the minimum
point of convex sets and convex function, such problems are collectively referred to as a
convex optimization problem. Similarly if the constraint conditions are convex set, optimization objective is to seek the maximum value of the concave function is also convex
optimization problem. Because convex optimization problem is an important type of
nonlinear optimization; it has great significance for the actual network. If optimization
function of convex optimization problem is a strictly convex function, and there is a
minimum value, then the value is the only minimum value. These years, with the rapid
development of optimization techniques, convex optimization technology has been studied by scholars very thorough. The literature [17-19] indicates that: “to judge an optimi-
MRMC RESOURCE OPTIMIZATION METHOD FOR WIRELESS MESH NETWORK
499
zation problem is simple and feasible, its judgment is no longer based on the linear conditions, but satisfy the convex optimization features. In other words, if an optimization
problem was proved to be a convex optimization problem, this indicates that the problem
must be solved.
Lemma 2 Convex set metric lemma. If functions based on convex sets xEn is convex,
when any two points x1, x2X, and to all [0,1], it should meet
f [x1+(1)x2]  f (x1)+ (1) f (x2).
We present an integrated metric M(i,j) to describe the performance of communication
link between the wireless access point vi and vj.
M(i,j)=NLR+LLR+ETX,
(1)
where α, β, γ are weighting factor and meet α+β+γ=1. The value of the three parameters
depends on the different network applications. When network traffic increases, the node
load correspondingly becomes heavier, the first part influences the formula mostly, so
the value of α increases and the value of β, γ reduces correspondingly. When the node
power increases, the link is busy, the values of β the corresponding increases, the value
of α, γ will reduce. When the network environment becomes bad, link will be busy, the
value of γ corresponding will increase, α, β will reduce. We set α=β=0.3, γ=0.4. NLR is
Node Load Ratio, it can be calculated by NLRi =
Qit
, Q is cashing queue length of node
Qitmax
i at the time point t, and Qmax is the maximum cashing queue length of node. LLR is Link
linking Ratio, it can be calculated by LLR(i , j ) =1 
B(i , j )
AB( i , j )
, available band of link l1, l2, …, ln
is B(i,j) = min{B(i,j)l1, B(i,j)l2, …, B(i,j)ln}, available band of link p1, p2,…, pm is AB(i,j) =
min{B(i,j)P1, B(i,j)P2, …, B(i,j)Pm}. ETX is Expected Transmission Count, the definition is as
follows.
For a given source node i and destination node j, there is a set L made by all possiM l to be the routing from v to v , which is
ble routing, if L, we will choose the min
i
j
lL
the minimum value of the accumulating routing between two nodes. In graph G (V, E)
any of the routing paths l=l0, l1,…,lk, we define the metric of routing is the sum of metric
of all links. The metric of node from source node vi to destination node vj is
k 1
M L   M l (i , j ) .
(2)
l 0
Definition 3 Expected Transmission Count (ETX) Taking into account the link
quality difference will affect the performance of WMN, we introduce the ETX routing
metric. The value of link ETX is the forecast of data traffic using this link to contract.
The calculation of ETX uses the forward and reverse transfer rate of link. The forward
transfer rate pf represents the measure of probability that is the packet reaches the recipient successfully. The reverse transfer rate pr represents the probability of successful arrival of an ACK (Acknowledge Character) packet. The loss packet rate p=1(1pf)(1pr),
s(k) means data packets after the attempt of K times the probability of successful trans-
DEGAN ZHANG, YANAN ZHU, SI LIU, XIAODAN ZHANG AND JINJIE SONG
500
mission times. Expected transmission count

ETX   k  s (k ) 
k 1
1
.
1 p
(3)
Theorem 2 Lagrange dual decomposition theorem The reason that we introduce
Lagrangian is that the dx direction of convex function f(x) change is constrained by inequality, changing direction of dx and gradient perpendicular f(x) could get the extreme.
The objective function f0(x) and constraints fi(x) and hj(x) have the following relationship:
min f0(x)
fi(x)  0, i = 1, …, m
s.t. hj(x) = 0, j = 1, …, l.
The Lagrange formula is as follows,
k
L
i 1
i 1
L( x,  , ） f 0 ( x)    i f i ( x )    i h j ( x).
(4)
Here we define (x) as
 ( x)  max L( x,  ,  ).
 ,  : i  0
(5)
Assumptions fi(x)  0 and hj(x)  0, and  can be adjusted and make (x) to get
maximum positive infinity. However, when fi(x) and hj(x) are satisfying the constraint
condition, (x) is f0(x). Therefore, the original problem min f0(x) can be transformed
min(x) in order to
min  (x)= min max L( x, , ).
x
x
 , : i  0
Then getting the partial derivative of x, ,  and making its partial derivative to 0.
Finally we get x, , .
4. MRMC RESOURCE OPTIMIZATION METHOD BASED
ON CONVEX THEORY
Assume that wireless mesh network has N nodes, the network topology is relatively
stable, for i which could be any node (which may be the source node and the destination
node or relay node), Ni a collection of nodes within the transmission interference range
of i node. The node is equipped with a plurality of radio frequency (RF) devices. It can
be transmitted or received data by different channels simultaneously. Ri is the number of
node i. L(s,d) is the link between the node s and the node d. C={1, 2, 3,…, c} is the set of
all orthogonal channels O in the network. Based on Lemmas 1 and 2 with convex theory, we design MRMC resource optimization algorithm as follows.
MRMC RESOURCE OPTIMIZATION METHOD FOR WIRELESS MESH NETWORK
501
(1) Channel allocation
On any link l and any channel cC allows the establishment of a multi-link communication between the two neighbors. These links work on different channels. At same
time, maximizing network resource utilization and increase the data transfer rate between
nodes of two neighbors.
Any channel allocation must meet the following constraints [21]: radio frequency
(RF) constraints and interference constraints (IC). Radio frequency constraints is that at
any time, a node can use a maximum of Ri channels to send a data packet:
C
y
ct
l
sNi c 1
 Ri , d  N , t  1,..., T .
(6)
Interference constraints is that at any time, two interference links cannot active on
the same channel.
'
 y
s Nu' Nu'
d
'
Nu'
ct
l'
s ,d'
1,(s' , d ' ) L, c 1,...,C,t 1,...T
(7)
The number of link channels which is established by any node i with its neighbors
must be less than the number of RF. That is, there is channel allocation limit as follows:
C
y
c 1
c
i
 Ri , i  N .
(8)
(2) Rate allocation
Let vlc is the data transfer rate of link l on the channel c. In WMN, vlc depends on the
activation time of the link l. If tlc=0, the node S cannot transmit any data to the node on
channel c, that is vlc=0. There is vlc  tlc vp, vp which means that the physical layer link
bandwidth.
The link activation also disturbed restrictions, this section uses the protocols interference model of the communication range and interference range. The set of all nodes
within the interference range of defined node S is IN(S). The link (s, d) set can be obtained mutual interference is
ILsd  ( m , n ) |  m  IN ( s ) or n  IN ( d )}  {( s , d )}.
(9)
We adopt CSMA access method based on the IEEE802.11, the link and its interference link cannot be activated at the same time [22], they need to share the link bandwidth
of the physical layer. Therefore, there is a rate allocation restriction:
vlc l' ILsd vl'

 1, l  L, c  C.
vp
vp
c
(10)
vlc  vp which means the activation time of the link l on the channel c.
(3) Routing
Due to the presence of interference in the system, conflict is inevitable. So once the
DEGAN ZHANG, YANAN ZHU, SI LIU, XIAODAN ZHANG AND JINJIE SONG
502
conflict ensues, re-transmissions are needed to ensure the successful transmission in the
system. Wireless Mesh Networks provide the different type of network access services,
so that F = {1, 2, …, K} which means that the collection of traffic flow. The transmission rate of traffic flow k is fk. Bandwidth and delay of each business price is Bk and Tk
respectively. Link l to provide access services to mobile users.
Whether the service request kF through the network link or not, we define binary
variable as
1, Business k through the network link l
rl k  
.
0, else
r represents the vector which containing all routing variables. In order to maintain
the Packet arrival order of traffic flow and routing simplified, we only consider singlepath routing. Therefore, between any two neighboring nodes, allowing only one data
stream is transmitted with a link,
Namely there is the following relationship
C
r
c 1
k
l
 1, l  L, k  F .
(11)
Any service flow transmission path length k can be expressed as that
C
 r
l L
c 1
k
l ,c
.
(12)
Link transmission time is
C
 r
k
l ,c
lL c 1
/ fk .
(13)
SLkWhich means the shortest transmission time that the traffic flow k in the network,
in order to avoid long transmission time of the traffic flow, the defined path transmission
time is limited as follows:
C
 r
lL c 1
k
l ,c
  ETTl c   , k  F .
(14)
l L
Where  is parameter used to limit the path of transmission time, ETT is Expected
Transmission Time [1-5]. Settings =0 can be such that the routing algorithm to find the
shortest path of transmission time for each business stream.
The total volume through like l is
xl =   bk  rl k .
(15)
k F
The remaining bandwidth of the network link l is
bl = fk  xl.
(16)
MRMC RESOURCE OPTIMIZATION METHOD FOR WIRELESS MESH NETWORK
503
Total throughput of the entire wireless mesh network system is
 =  xl .
(17)
l L
To meet the demand of wireless services and optimization of wireless mesh network
routing problem, maximizing bandwidth utilization and minimizing the cost of wireless
access during the network connection. Unlimited Mesh network cross-layer optimization
target is max, minbl.
Therefore the objective of network optimization in this paper is U min  (-, bl ) .
X ,V , R
The optimization objective is the minimal residual transmission rate Jminre of all
the nodes in the maximize the network based on Lemmas 1 and 2 with convex theory.
It is possible to obtain a link between the maximum-minimum equity of resource allocation. Optimization problem is described as follows
U min =(-,bl ).
X ,V , R
Subject to
C
y
sNi c 1
s
'
ct
sd
 Ri , d  N , t  1,..., T ,
 
Nu'
C
 Nu'
y
c 1
c
i
d
'
N u'
ysct' d '  1, ( s, d )  L, c  1,..., C , t  1,...T ,
 Ri , i  N ,
vlc  l ' ILsd vl '

 1, l  L, c  C ,
vp
vp
(18)
(19)
(20)
c
C
 r
lL c 1
k
l ,c
  ETTl c   , k  F .
(21)
(22)
l L
The restriction variable of the optimization problem assignments variable X for the
channel, the link rate allocates variables V and routing variables R. optimization problem
is a mixed integer linear programming problem. It is a complex optimization problem of
the fused network layer, transport layer and the data link layer, which can be broken
down into the following two sub-problems:
The channel assignment problem: S(X) means that a channel allocation scheme.
When all variables X satisfy link channel allocation restrictions and node channel allocation limit, it can be called works. Here we assume Ω is a set of all feasible channel allo-
DEGAN ZHANG, YANAN ZHU, SI LIU, XIAODAN ZHANG AND JINJIE SONG
504
cation schemes. Feasible channel allocation scheme is S(X), non-empty, closed, and
bounded convex set.
For rate allocation and routing, using resource fairness utility function U min =( (,
X ,V , R
bk) to measure the value of the network performance is a continuous convex function.
5. FUSED RESOURCE OPTIMIZATION METHOD
When the channel allocation scheme S (X) is determined, Based on Lemmas 1 and
2 with Convex theory, using the Lagrangian theory, introducing Lagrange variables
pmk to any node m and business flow k, and relaxing the type of flow balance constraint
to optimize target, we could get Lagrangian function as follows.
U min =(-, bk )
X ,V , R




=U min     bk  rl k ,  f k -  bk  rl k   , plk  .
lL kF


 l L k F

(23)
plk is the Lagrange multiplier which is introduced by us and which is congestion
factor of k traffic on link l. plk reflects the degree of network congestion and also reflects
the relationship between supplying and demanding of resources from various layers.
When reducing node congestion and remaining resources having multiple selections,
there will be congestion at low prices whereas high congestion prices. Based on Theorems 1 and 2 with Convex theory, we design the fused optimization mechanism is as
follows.
In the Transport Layer, each node with TD1 has the time cycle according to the
congestion price factor p, the business flow rate factor F and link rate allocation factor R
and so on, the fused design method updates distributed congestion prices and adjusts
their business flow rate. Then the new price information is passed to the link layer
broadcast to its neighbors. Link layer channel allocates information S(X) and collects
neighbor price factor p, distributed scheduling algorithm for rate allocation, the link rate
allocation information R passed to the transport layer and the network layer.
In the Network Layer, the link rate allocation information R can get the transmission path of the traffic flow. The Gateway Node allocates information R and price information p based on the least interfering cost. If needing to update, the new channel
allocation scheme will be broadcast to other nodes. Herein, TCA(TCATSTD) is referred as
channel allocation period.
Because in the MRMC-WMN, every node has a human readable name, EID (End
identifier), physical locator (PL, such as, geo@ of MR (Mesh Router)). When sending a
packet to the distant location, the sender should resolve the corresponding EID of the
destination by using the naming service, which is one of the core services in the
MRMC-WMN. The sender will resolve the relation between the EID and the PL by
querying the location service. By using the derived locator, the consecutive forwarding
nodes of MRMC-WMN compute the next hop, and send the packet further on. This
method can guarantee every node will be reachable through its EID during mobile application.
MRMC RESOURCE OPTIMIZATION METHOD FOR WIRELESS MESH NETWORK
505
6. SIMULATION AND PERFORMANCE ANALYSIS
Now we do performance testing and network performance analysis for MRMCWMN routing method. We use MATLAB simulation tools to simulate the new and improved optimization method. This network simulation comparison parameter include
Packet Delivery Fraction, Average end to end delay, The normalized cost of the route,
Routing initiated frequency. Now we give the computing formula for these four parameters.
(1) Packet Delivery Fraction: This is the ratio of the number of packets from destination node receives to the source node and it reflects the integrity and reliability of routing
protocols in a certain extent. Submission rate is higher the network reliability is greater.
packet _ delivery _ fraction =
received _ packets
sent _ packets
(24)
(2) Average end to end delay: This includes routing look up latency, packet waiting
delay in the interface queue, the transmission delay and the re-transmission delay of the
MAC layer, reflecting the effectiveness of routing. The serious delay will affect the
communication quality. The indicators is very important to measure and statistics of the
efficiency of routing algorithm. Using the following equation, where N represents the
number of packets transmitted successfully, rt represents the time the packet to the destination node, st indicate that the packet generation time
average _ end _ to _ end _ delay 
1 N
 (rti  sti ).
N i1
(25)
(3) The normalized cost of the route: The route occupy ratio is a route rate during communication process of correctly received data packets, reflecting off the situation data
link. It reflects the degree of congestion and node power efficiency in the network.
routing _ normaliazed _ overhead =
data _ packet
control _ message _ packet
(26)
(4) Routing initiated frequency: This is the total discovery number of route secondly.
To some extent, it reflects the running status of routing protocol in the link. N denotes
the source node sends a routing number of requests, T represents the simulation time.
route _ dis cov ery _ frequency 
N
T
(27)
In our simulation, we use the convex optimization to get the optimal solution in the
limited network supporting by Ad hoc On-Demand Distance Vector (AODV) routing
method based on convex theory. The process is as follows.
Channel allocation of the least interference cost is that when the network for the
first time allocated channel, the channel c is assigned to all the links. In the initial channel allocation scheme S(X), the gateway node collects periodically rate allocation infor-
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DEGAN ZHANG, YANAN ZHU, SI LIU, XIAODAN ZHANG AND JINJIE SONG
mation R and price information p of each link firstly. The information reflects the relationship between the layers of resource supply and demand; so the gateway can use the
information of other nodes from many layers to optimize the allocation of a channel. In
time slot t, each node m to any flow k timing updates cost prices pmk(t+1) and broadcasts
cost price information p to all neighbors. Based on Theorems 1 and 2 with Convex
theory, to any service flow k, the source node adjusts the transmission rate is
f k ( p)  U K'1 ( PK ).
(28)
Any node m collects price information from its neighbor node n, finds kmn (t )  arg max
k
( pmk (t )  pnk (t )) and makes the differential price kmn (t )  arg max( pmk (t )  pnk (t )) to be broadk
caster neighbors. The node m collects the differential price information of its neighbor
nodes each slot. At the beginning of time slot t, using distributed scheduling algorithm
k
kmn
kmn
(t )
(t ) meets the limit. The rate rmn
allocates rate rmnmn (t ) to the link (m, n), such that rmn
is assigned from each link to each traffic flow which could get transmission traffic flow.
The transmission traffic flow is traffic flow which is assigned by the transmission path.
Fig. 1. One scenario of actual network environment.
In the actual network environment as scenario like Fig. 1, we use expansion modules in the base of MATLAB platform, provide a more object entities function interface
so as to support testing for multi-radio multi-channel wireless Mesh network. Simulation
parameter settings for MRMC-WMN is as Table 1.
Figs. 2 to 4 are simulation by MATLAB for stationary node network performance
over time changes in MRMC-WMN. Figs. 5 to 8 are simulation by MATLAB for The
changing of the node network performance with the moving of nodes in MRMC-WMN.
They include routing matrix generation, channel allocation and optimization algorithm.
And the final output is the optimal routing and channel assignments of source node to the
destination node.
(1) Stationary node network performance over time changes
Stationary time of node represents the mobility of the scene, the shorter the time of
MRMC RESOURCE OPTIMIZATION METHOD FOR WIRELESS MESH NETWORK
Table 1. Simulation parameter settings for MRMC-WMN.
Radio channel type
Wireless transmission module type
The network interface type
MAC agreement type
Node mobile model
Signal propagation model
Bandwidth
Packet length
Packet transfer rate
Example of Convex function
Relevant parameters of Lagrange dual decomposition
Wireless Channel
Propagation/TwoRayGround
Wireless Phy
DCF IEEE802.11
Random Waypoint
free space spread
2 Mbit/s
512 byte
10 packet/s
f(x)=ex or f(x)=x2
++=1, α=β=0.3, γ=0.4
Fig. 2. Comparison of packet delivery fraction rate.
Fig. 3. Comparison of average delay of end to end.
Fig. 4. Comparison of normalized routing overhead.
507
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DEGAN ZHANG, YANAN ZHU, SI LIU, XIAODAN ZHANG AND JINJIE SONG
stationary scene the faster mobility of scene is. This is a network which is set up for simulation scenarios including 50 wireless nodes. The simulation time is 50s. The node still
times are 0s, 10s, 20s, 30s, 40s, 50s. When the still times of nodes are changed, the data
packet transmission rate of the node is 10pkt/s, maximum moving speed is 10m/s. Fig. 2
shows comparison of packet delivery fraction rate of AODV(Ad hoc On-Demand Distance Vector) and MAODV (multi-radio multi-channel AODV) routing of MRMCWMN. Fig. 3 shows comparison of average delay of end to end. Fig. 4 shows comparison of normalized routing overhead. Based on the following experimental results, now
we give the following data analysis: with still times of node increase, mobility of the
entire MRMC-WMN scene is reducing, the network topology is becoming stable, the
node is moving out, at the same time of the communication time of other nodes is reduced. The packet submission rate of MRMC-WMN increases, while the system interference is reduced, so making the network latency is reduced. The packet delivery rate,
route allocation and the channel allocation optimization of MAODV of MRMC-WMN is
always higher than the packet delivery rate of network that using AODV protocol network. As the network communication of MRMC-WMN opens, routing overhead is reduced, route launched overhead is reduced.
(2) The changing of the node network performance with the moving of nodes
In this case, we set up a network simulation scenario which includes 10 wireless
nodes, the simulation time is 50s, the node still time is 0s. Line number is 10, the node of
the data packet transmission rate is 10pkt/s, moving speed of the node are 0m/s, 5m/s,
10m/s, 15m/s, 20m/s, 25m/s, 30m/s.
Fig. 5. Comparison of packet delivery fraction rate.
Fig. 5 shows comparison of packet delivery fraction rate of AODV and MAODV
routing of MRMC-WMN. Fig. 6 shows comparison of average delay of end to end. Fig.
7 shows comparison of normalized routing overhead. Fig. 8 shows comparison of sum of
routing rate under different Ppeak / Pavg, Ppeak is data packet amount of peak state, Ppeak is
data packet amount of average state, (a), (b), (c), (d) and (e) of the figure represents the
method of this paper, [6-8, 11] respectively.
Based on the above experimental results, now we give the following data analysis:
under the nodes different rates in the MRMC-WMN, the accuracy of the target node region, which is predicted by the neighbor’s cache recording, reduce, and cause the search
MRMC RESOURCE OPTIMIZATION METHOD FOR WIRELESS MESH NETWORK
509
Fig. 6. Comparison of average delay of end to end.
Fig. 7. Comparison of normalized routing overhead.
8
7
Average Sum-Rate(Mbps)
6
(a)
(b)
(c)
(d)
(e)
5
4
3
2
1
0
2
3
4
5
6
7
P__【 Peak 】 /P__【 avg】
8
9
10
Fig. 8. Comparison of sum of routing rate under different Ppeak / Pavg.
area and routing overhead increase. In this situation, the AODV algorithm’s improvement is limited. The routing protocols under MAODV, packet delivery rate has increased,
the delay is smaller, the normalized routing overhead reduced, the route discovery frequency has reduced, and this is because the new method can effectively reduce the
blindness of route discovery. This optimization strategy plays a good role, its advantage
is obvious, it’s more suitable for mobile network node.
From the above experiments of two cases, network throughput, delay and routing
overhead and other aspects of optimization strategy which is based on channel allocation,
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DEGAN ZHANG, YANAN ZHU, SI LIU, XIAODAN ZHANG AND JINJIE SONG
routing and rate allocation of MAODV are better than these of AODV. The main reasons
include the following: Firstly, the channel allocation, AODV using the bigger frequency
of the same channel. Because the route seeking strategy is launched on the basis of this
channel, which will cause network congestion, it makes low network performance. In
this paper, we use MAODV approach which is based on convex optimization theory. It
avoids using the same common channel. It is based on MRMC and assigns the number of
available channels to each link, at the same time; it makes the channel tend to diversity.
The intra-stream and inter-stream flow interference is also reduced. Secondly, the distribution of the route, AODV uses minimum hop routing mechanism as a criterion, ignoring the factor of network link quality. The routing metric used herein balances the major
factors in the link. The path selected in this manner typically has a smaller and a variety
of optional delay characteristics. Thirdly, the integrated channel allocation, routing allocation and rate allocation and other aspects, MAODV strategy in finding routes will not
randomly selected channel. In the global optimization process, the path of hops, the data
transfer rate using wireless channel, and so the factors will be considered in balanced
mode, even if the limited wireless network resources, the selected path is also to avoid a
link with large costs interference. But the AODV protocol does not consider these network performance parameters of the link, so it can not perceive the channels idle and
busy degree. Especially, with the limited wireless resources it is very difficult to choose
the path of excellent performance for communication. In summary, the MRMC-WMN
has been improved significantly by the proposed solutions of packet delivery ratio, delay,
routing overhead and frequency, etc.
From the above analysis of simulation experimental data, improved routing metric
criterion and network resources optimization strategy has better system performance,
such as reducing network transmission delay, increasing throughput, enabling mobile
users with superior network services.
7. CONCLUSIONS
MRMC resource optimization method based on convex theory for WMN is presented in this paper. According to convex theory, we use the convex optimization function to get the optimal solution in the limited network supporting by Ad hoc On-Demand
Distance Vector routing method. At the same time, we resolve the optimal solution into
three simple sub-problems according to the Lagrange duality method supporting by
MAODV. We use MATLAB simulation tools to simulate the new and improved optimization method. The experimental results show that the method has better network performance in the applications of WMN. In order to make the algorithm better network
performance, follow-up work is focused on further simplify routing algorithm and protocols in MAODV explored on the basis of multi-path method.
REFERENCES
1. D. G. Zhang and G. Li, “An energy-balanced routing method based on forwardaware factor for wireless sensor network,” IEEE Transactions on Industrial Informatics, Vol. 10, 2014, pp. 766-773.
MRMC RESOURCE OPTIMIZATION METHOD FOR WIRELESS MESH NETWORK
511
2. D. G. Zhang, X. Wang, and X. D. Song, “A novel approach to mapped correlation of
ID for RFID anti-collision,” IEEE Transactions on Services Computing, Vol. 7,
2014, pp. 741-748.
3. A. U. Chaudhry, “Fault-tolerant and scalable channel assignment for multi-radio multi-channel IEEE 802.11a-based wireless mesh networks,” in Proceedings of Globecom Workshops, Vol. 11, 2010, pp. 1113-1117.
4. I. Akyildiz and X. D. Wang, “Cross-layer design in wireless mesh networks,” IEEE
Transactions on Vehicular Technology, Vol. 57, 2008, pp. 1061-1076.
5. M. Noori and M. Ardakani, “Lifetime analysis of random event-driven clustered
wireless sensor networks,” IEEE Transactions on Mobile Computing, Vol. 10, 2011,
pp. 1448-1458.
6. F. C. Martins and E. G. Garrano, “A hybrid multiobjective evolutionary approach
for improving the performance of wireless sensor networks,” IEEE Transactions on
Sensors, Vol. 11, 2011, pp. 545-554.
7. I. F. Akyildiz and X. Wang, “A survey on wireless mesh networks,” IEEE Communications Magazine, Vol. 43, 2005, pp. 23-30.
8. L. T. Nguyen and R. Beuran, “An interference and load aware routing metric for
wireless mesh networks,” Ad Hoc and Ubiquitous Computing, Vol. 7, 2011, pp. 2330.
9. D. G. Zhang, K. Zheng, and T. Zhang, “A novel multicast routing method with
minimum transmission for WSN of cloud computing service,” Soft Computing, Vol.
19, 2015, pp. 1817-1827.
10. D. G. Zhang, K. Zheng, and D. X. Zhao, “Novel quick start (QS) method for optimization of TCP,” Wireless Networks, Vol. 22, 2016, pp. 211-222.
11. H. K. Garg and P. C. Gupta, “Minimization of average delay, routing load and
packet loss rate in AODV routing protocol,” International Journal of Computer Applications, Vol. 44, 2012, pp. 14-17.
12. S. Vural and E. Ekici, “On multi-hop distances in wireless sensor networks with random node locations,” IEEE Transactions on Mobile Computing, Vol. 9, 2010, pp.
540-552.
13. J. Lee, W. Su, and M. Gerla, “On-demand multicast routing protocol in multi-hop
wireless mobile networks,” Mobile Networks and Applications, Vol. 7, 2002, pp.
441-453.
14. M. C. Vuran and I. F. Akyildiz, “Spatial correlation-based collaborative medium
access control in wireless sensor networks,” IEEE/ACM Transactions on Networking, Vol. 14, 2006, pp. 316-329.
15. D. G. Zhang, X. Wang, and X. D. Song, “New medical image fusion approach with
coding based on SCD in wireless sensor network,” Journal of Electrical Engineering and Technology, Vol. 6, 2015, pp. 2384-2392.
16. D. G. Zhang, “Design and implementation of embedded un-interruptible power supply system (EUPSS) for web-based mobile application,” Enterprise Information
Systems, Vol. 6, 2012, pp. 473-489.
17. C. Chiang, M. Gerla, and L. Zhang, “Forwarding group multicast protocol (fgmp)
for multi-hop mobile wireless networks,” Cluster Computing, Vol. 1, 1998, pp. 187196.
18. D. G. Zhang and X. J. Kang, “A novel image de-noising method based on spherical
512
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
DEGAN ZHANG, YANAN ZHU, SI LIU, XIAODAN ZHANG AND JINJIE SONG
coordinates system,” EURASIP Journal on Advances in Signal Processing, Vol. 110,
2012, pp. 1-10.
D. G. Zhang and Y. N. Zhu, “A new constructing approach for a weighted topology
of wireless sensor networks based on local-world theory for the internet of things
(IOT),” Computers and Mathematics with Applications, Vol. 64, 2012, pp. 10441055.
J. L. Sobrinho, “Algebra and algorithms for QoS path computation and hop-by-hop
routing in the Internet,” IEEE/ACM Transactions on Networking, Vol. 10, 2002, pp.
541-550.
J. L. Sobrinho, “Network routing with path vector protocols: theory and applications,” in Proceedings of ACM SIGGOMM Conference on Computer Communications, 2003, pp. 49-69.
L. Xu, “Enterprise systems: state-of-the art and future trends,” IEEE Transactions
on Vehicular Informatics, Vol. 7, 2011, pp. 630-640.
D. G. Zhang and C. P. Zhao, “A new medium access control protocol based on perceived data reliability and spatial correlation in wireless sensor network,” Computers and Electrical Engineering, Vol. 38, 2012, pp. 694-702.
K. B. Sung, J. J. Yoo, and D. H. Kim, “Collision warning system on a curved road
using wireless sensor networks,” Vehicular Technology Conference, 2007, pp. 19421946.
D. G. Zhang, X. D. Song, and X. Wang, “New agent-based proactive migration
method and system for big data environment (BDE),” Engineering Computations,
Vol. 32, 2015, pp. 2443-2466.
L. Buttyán, D. Gessner, and A. Hessler, “Application of wireless sensor networks in
critical infrastructure protection challenges and design options,” IEEE Transactions
on Wireless Communications, Vol. 17, 2010, pp. 44-49.
D. G. Zhang and Y. P. Liang, “A kind of novel method of service-aware computing
for uncertain mobile applications,” Mathematical and Computer Modeling, Vol. 57,
2013, pp. 344-356.
Z. Erenel and H. Altincay, “Explicit use of term occurrence probabilities for term
weighting in text categorization,” Journal of Information Science and Engineering,
Vol. 27, 2011, pp. 819-834.
D. G. Zhang, “A new method of non-line wavelet shrinkage denoising based on
spherical coordinates,” Information  An International Interdisciplinary Journal,
Vol. 15, 2012, pp. 141-148.
R. C. Biradar and S. S. Manvi, “Review of multicast routing mechanisms in mobile
ad hoc networks,” Network and Computer Application, Vol. 35, 2012 pp. 221-239.
M. Liu and R. R. Talpade, and A. McAuley, “AMRoute: Ad hoc multicast routing
protocol,” Mobile Networks and Applications, Vol. 7, 2002, pp. 429-439.
D. G. Zhang, “A new approach and system for attentive mobile learning based on
seamless migration,” Applied Intelligence, Vol. 36, 2012, pp. 75-89.
S. J. Douglas, D. Couto, and D. Aguayo, “A high-throughput path metric for multihop wireless mesh network routing,” Wireless Networks, Vol. 11, 2005, pp. 419434.
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Degan Zhang (张德干) is Ph.D., a Member (M) of IEEE in 2001, graduated from
Northeastern University, China. Now he is a Visiting Professor of School of Electronic
and Information Engineering, University of Sydney, Sydney, NSW 2006, Australia;
Professor of Tianjin Key Lab of Intelligent Computing and Novel software Technology,
Key Lab of Computer Vision and System, Ministry of Education, Tianjin University of
Technology, Tianjin, 300384, China. His research interest includes WSN, industrial application, etc. E-mail: [email protected].
Yanan Zhu (朱亚男) is Ph.D. candidate, a Member of IEEE in 2010. Now he is a
Researcher of Tianjin Key Lab of Intelligent Computing and Novel Software Technology, Key Lab of Computer Vision and System, Ministry of Education, Tianjin University
of Technology, Tianjin, 300384, China. His research interest includes WSN, etc. E-mail:
[email protected].
Si Liu (刘思) is Ph.D. candidate, a Member of IEEE in 2010. Now she is a Researcher of Tianjin Key Lab of Intelligent Computing and Novel Software Technology,
Key Lab of Computer Vision and System, Ministry of Education, Tianjin University of
Technology, Tianjin, 300384, China. Her research interest includes WSN, etc. E-mail:
[email protected].
Xiaodan Zhang (张晓丹) is Ph.D, a Member of IEEE in 2001. Now she is a researcher of Institute of Scientific and Technical Information of China, Beijing, 100038,
China. Her research interest includes WSN, mobile computing, etc. She is corresponding
author of this paper. E-mail: [email protected].
Jinjie Song (宋金杰) is Ph.D, a Researcher of Tianjin Key Lab of Intelligent
Computing and Novel Software Technology, Key Lab of Computer Vision and System,
Ministry of Education, Tianjin University of Technology, Tianjin, 300384, China. His
research interest includes WSN, mobile computing, etc. E-mail: [email protected].