論文-A Novel Cross-layer Mesh Router Placement Scheme for Wireless Mesh Networks

IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. -, NO. -, —- 20– 1
A Novel Cross-layer Mesh Router Placement
Scheme for Wireless Mesh Networks
Tein-Yaw Chung, Member, IEEE, Hao-Chieh Chang, and Hsiao-Chih George Lee, Member, IEEE
Abstract—Wireless mesh networks (WMNs) are promised to support ubiquitous multimedia Internet access for mobile or fixed mesh
clients (MCs) in the near future. In WMNs, Internet traffic is aggregated from MCs and forwarded hop-by-hop through mesh routers
(MRs) to an Internet Gateway (IGW) or vice versa. While deploying MRs and IGWs, an intricate relationship among antenna types,
wireless links with adaptive modulation and coding (AMC), MAC scheduling, routing and equipment cost, renders the WMN network
planning problem extremely complex. This paper presents a novel Cross-layer MR Placement (CMRP) scheme to cope with this
problem. CMRP encapsulates the cross-layer factors into three novel attributes: Local Coverage (LC), Backbone Residual Capacity
(BRC) and Deployment Cost (DC), which are used to minimize the network deployment cost. Coupled with our proposed novel tree-
based minimal cost routing (TMCR) scheme and weight-based link assignment (WLA) for user coverage, CMRP is able to efficiently
plan WMN networks. Extensive simulations have been performed to examine the performance and feasibility of CMRP and compared
with existing design schemes based on coverage, connectivity, and combination of both. The result demonstrates that our approach
outperforms existing schemes both in cost performance ratio (CPR) and potential feasibility.
Index Terms—Capacity improvement, gateway placement, multi-hop relay networks, relay node placement, wireless mesh networks,
wireless multi-hop networks.
3
1 INTRODUCTION
IN recent years, broadband wireless mesh networks
(WMNs) [1-2] are expected to be widely deployed for
providing Internet connectivity to users in residential
areas and offices and supplementing wired infrastruc-
ture. WMNs are characterized by self-organizing and
self-configuring capability, and hence are easy to be
deployed. In 3G and Wi-Fi networks, each access point
(AP) is connected through extensive wired infrastructure
to access the backhaul network, which is often expensive
and time consuming to build. On the other hand, WMNs
only use a subset of APs, called Internet Gateways
(IGWs), to have access to the wired network, while the
rest of the APs, called mesh routers (MRs), are connected
to the IGWs in multihop fashion, and are easy to build
and provide an economical alternative to broadband
wireless Internet connectivity.
Although WMN products are available in the market
[3-6], their deployment has faced tremendous challenges
[1-2] due to some inherent problems, such as interference
and high bit error rate (BER). A good location of MRs
can provide high performance and enhance the network
throughput. Furthermore, proper choices of MRs’ loca-
• T. Y. Chung is with Yuan-Ze University, Chung-Li, Tao-Yuan, Taiwan,
R.O.C..
E-mail: csdchung@saturn.yzu.edu.tw
• H. C. Chang was with Yuan-Ze University, Chung-Li, Tao-Yuan, Taiwan,
R.O.C.. He is now enrolled in military service.
E-mail: harvey@netlab.cse.yzu.edu.tw
• H.C.G Lee is with the Oriental Institute of Technology, Pan-Chiao, Taipei,
Taiwan, R.O.C..
E-mail: georgelee@mail.oit.edu.tw
tion can lead to minimum number of MRs for meeting
user demand in the WMN design.
Many different schemes in various layers have been
used in placing MRs and IGWs so as to enhance the
performance. An intricate relationship among antenna
type used, wireless links with adaptive modulation and
coding (AMC) scheme, MAC scheduling, routing, and
equipment cost renders the problem of optimal WMN
planning extremely complex to address. In the past,
researchers [22-28] have introduced various schemes for
this issue. Similar to the IEEE 802.16j scheme, some
researchers [22-23] develop schemes to place relay nodes
so as to improve the WMN throughput, while others
discuss the problem of MR placement scheme either
without considering the wireless backbone network sup-
port for users’ demand [24] or just focusing on the
user coverage while ignoring users’ demand [25, 27-
28], not to mention the wireless backbone network
support. The authors in [26] present a MR placement
algorithm without considering cost for various antenna
types. Overall, to simplify the problem, these works only
consider part of the design parameters associated with
the MR placement. Therefore, a more sophisticated MR
placement scheme is required to design a cost effective
WMN that can meet user demands both at the local level
as well as the backbone, with various technical options
such as antenna types, MAC scheduling and routing.
This paper proposes a cross-layer MR placement
(CMRP) scheme for a comprehensive MR placement
problem. Many researchers have proved the cross-layer
approach [7-10] to be an effective scheme in improving
the network performance. Our new CMRP iteratively
adjusts the user coverage of each MR while new MRs are

being added. As the residual backbone capacity is being
evaluated with respect to the incurred interference, ad-
ditional demands can be satisfied by each newly added
MR. Based on a minimal interference routing scheme and
a concept of bottleneck collision domain (BCD), the back-
bone capacity is also evaluated to see if it can really meet
the user demand. To design a WMN with minimal cost,
CMRP deploys a pair of directional antennas whenever it
is observed to be more cost effective. Therefore, CMRP
offers a powerful MR deployment scheme in planning
WMN.
In CMRP, the cross-layer factors are encapsulated
into three novel attributes: Local Coverage (LC), Backbone
Residual Capacity (BRC) and Deployment Cost (DC), which
are evaluated throughout the MR addition process. LC
specifies the contribution of a MR in offering access
capacity to the users, BRC indicates the contribution of
MRs to the backhaul capacity, and DC represents the
ratio of the cost of using directional antennas to the
cost of deploying a MR. DC enables selection of antenna
types, such as omni-directional or directional antenna,
based on the cost performance ratio (CPR) while a WMN
is being planned. To maximize the objective function
(LC ×BRC/DC), CMRP selects MRs one by one among
all MR candidate locations. This objective function se-
lects MR candidate locations that largely contributed to
the backbone capacity, more user demand coverage, and
lower deployment cost.
Extensive simulations have been performed to exam-
ine the performance and feasibility of our approach.
We also compare CMRP with existing WMN planning
schemes that consider only coverage, connectivity, or
combination of both. The result illustrates that CMRP
outperforms existing schemes both in terms of CPR and
the feasibility. In addition, CMRP can help determine the
user demands and the size of a WMN that can achieve
the best CPR. This information can help in deciding how
many IGWs are needed when a large WMN is being
planned.
The remainder of this paper is organized as follows.
Section 2 describes the related work. Section 3 presents
the network model, and problem formulation. Section 4
describes our heuristic algorithm. Section 5 summarizes
the simulation results. Finally, Section 6 concludes the
paper and discusses our future work.
2 RELATED WORK
The inherent drawbacks of WMNs, such as interfer-
ence, power limit, and high bit error rate (BER), sig-
nificantly limit the performance of WMNs. In the past,
researches [7-12] have presented algorithms to improve
the throughput of WMNs in channel utilization, radio
power setting, and time slots allocation. However, these
researches do not consider the service point placement
problem, which has been shown in the experiments
by Bicket et al. [13] to have a greater impact on the
performance.
The service point placement can be divided into two
types of placement: IGW and MRs. The IGW placement
[14-21] focuses on the wide area WMN planning, in
which many service points are clustered and an IGW
is assigned to each cluster. The MR placement [22-28]
deploys MRs to cover all users’ demand. MRs may
interfere with one another. Thus, if one of the MR
wants to improve its throughput or service range by
using power control, the nearby MRs may suffer serious
interference. So how to optimize the MR placement is an
important problem that dictates the overall performance
in a WMN system. In this paper, we only consider the
MR placement, while the IGW placement will be left for
our future work.
So and Liang [22] place a fixed number of tether-
less relay points (TRPs) to improve the throughput of
a wireless LAN. They present some rate adaptation
scheme to estimate the link rate and analyze how various
parameters, such as path loss exponent, power ratio
of AP and TRP over the power of mobile host (MH),
and the number of TRPs, affect the performance and
TRP placement. Lin et al. [23] analyze the placement of
a single relay node (RN) in the IEEE 802.16j Point-to-
Multi-Point (PMP) networks so as to extend the coverage
and improve the throughput/capacity of the network.
They use a cooperative relay strategy to improve spatial
diversity. Wang et al. [24] use a distributed clustering
scheme to place a minimum number of MRs on can-
didate locations. Although they ensure the connectivity,
user demand and user coverage are met, they do not
consider the link scheduling at the WMN backbone and
thus cannot guarantee users’ demand to be supported
by the wireless backbone. San and Raman [25] define a
complex objective function to minimize the total cost of
MR deployment. Their design considers the number of
antennas, the type of antenna, and the height of the IGW
which affects line-of-sight transmission. Although they
have considered the user coverage and the interference
problem, they do not consider the users’ demand. More-
over, they limit their design to only two-hop networks.
To cover user needs, So and Liang [26] solve the MR
placement problem by constructing a fixed power of
local and backbone links. However, they do not consider
the costs of different types of antenna. Robinson and
Kinghtly [27] analyze the throughput of WMNs with
various types of topology, such as triangle, rectangle,
hexagon, and random, and then compare the coverage
performance. But they only consider user coverage, but
not user demand. Franklin and Murphy [28] consider
both the network backbone connectivity and the local
coverage problem and use signal strength to represent
the connectivity. But, they do not consider users’ de-
mand, which limits the usefulness of their approach.
Deploying network service points with minimum cost
is challenging. Although the above researches have
worked on this issue, they did not consider comprehen-
sive factors such as users’ demand, signal interference,
MR deployment cost, and antenna type. This paper

presents a cross-layer MR placement scheme to minimize
the cost of MR deployment by taking users’ demand,
MAC scheduling, routing, and cost of each MR and
antenna into consideration.
3 MESH ROUTER PLACEMENT MODEL-
ING AND SOLUTION
This paper focuses on IEEE 802.16 based WMNs, in
which a set of MRs are connected with multihop wire-
less links to form a wireless backbone, which is then
connected to the Internet through an IGW.
3.1 Network Model
Given n randomly generated user demands V =
[v1, . . . , vn] and m MR candidate locations V ′
=
[v′
1, . . . , v′
m], according to the IEEE 802.16s mesh network-
ing standard, assume all user nodes are fixed and only
one IGW is selected from these candidate locations. Each
MR uses omni-directional antenna for serving its local
network, and uses either omni-directional or directional
antenna as the backbone of the WMN. A directional
antenna (also called a sectored antenna) is different from
an omni-directional antenna in that it only transmits the
signal in the range of a sector. Because it can concentrate
transmitting power, it can cover a longer range while
the interference is limited to a smaller area than that of
an omni-directional antenna. Let PL be the maximum
power of all antennas used in the local network, and
PB and PD, respectively, be the maximum power of an
omni-directional and a directional antenna used in the
backbone network. In general, the local service antenna
has a smaller service range, and the backbone service
antenna has a larger range, i.e., PD > PB > PL.
Let CH = {c1, . . . , ck} denote a set of k non-interfering
channels in the wireless system, and different channels
are used to access MRs from mesh clients (MCs) and the
backbone network so that they do not interfere with each
other. In the PHY-layer, a TDMA scheme as specified by
the 802.16 mesh mode is used and the link rate is set
by the adaptive modulation and coding (AMC) scheme.
In the TDMA scheme, time is structured into frames,
which are composed of several equal duration time slots.
Links are scheduled to maximize spatial reuse of the link
bandwidth while avoiding collision.
In a WMN, every MR aggregates traffic load from local
MCs. Unlike ad hoc networks where traffic is randomly
distributed between peer nodes, the traffic in a WMN is
predominantly directed in a multi-hop fashion from MRs
towards IGW or from IGW to MRs, i.e., so called inter-
flow traffic. Assume every MC i has inter-flow demand
qi and a symmetric scheme is used in the transmission
system, i.e., both downlink and uplink flows interfere the
same area. Thus, we only consider uplink flow demands,
as it is easy to extend the system to the downlink flow
demands.
3.1.1 MRP Problem
In this subsection, we define the MR placement (MRP)
problem as a cost minimization problem. Given inter-
flow demand qi, ∀i ∈ V , MR candidate locations V ′
,
and the price of a MR and the price of a pair of
directional antennas, the goal of MRP is to deploy MRs
and directional antennas to meet user traffic demands
with minimum cost. Assume the default cost of an MR
includes two omni-directional antennas: one for local
traffic and another for backbone traffic. The MRP prob-
lem can be defined as a mixed integer linear program-
ming (MILP) as follows when a routing tree rooted on
IGW is employed.
min α
m
j=1
xj + β
m
j=1
xjyj, (1)
s.t. m
j=1
xij = 1 ∀i ∈ V, (2)
qi ≤ lR
ij ≤ LR
∀i ∈ V, j ∈ V ′
, (3)
n
i=1
qixij = CL
j ≤ CL
∀j ∈ V ′
, (4)
Qr + Ir ≤ LB
r ≤ LB
∀r ∈ V ′
, (5)
where
α: cost of a MR
β: cost of a pair of directional antennas
xj =
1, if position j is installed an MR
0, otherwise
yj =
1, if a directional antennas is used by MR j
0, otherwise
xij =
1, if user i is served by MR j
0, otherwise
lR
ij: transmission rate between user i and MR j
LR
: maximum link capacity of a local access antenna
CL
j : local capacity coverage of MR j
CL
: maximum local capacity coverage of an MR
Qr =
m
j=1
Qjhjr + CL
r : aggregate inter-traffic of MR j
(6)
where
hjr =
1, if the traffic of MR j goes through MR r
0, otherwise
Ir: wasted capacity due to interference from other
MRs to MR r
LB
r : backbone uplink capacity of MR r
LB
: maximum backbone link capacity of
a backbone access antenna with AMC.
Eq. (1) minimizes the total cost of MRs and directional
antennas deployed. Eqs. (2) and (3) guarantee that each
user i can be served by one MR and its demand can
be supported by the transmission rate lR
ij smaller than

the maximum link capacity LR
with AMC between user
i and MR j. Eq. (4) guarantees that all user demands
could be fully covered by the MRs deployed. Eq. (5)
guarantees that every MR j can relay inter-traffic and
support local access traffic through its uplink backbone
capacity LB
j under interference from other nearby MRs.
This constraint of Eq. (5) is highly related to the locations
of MRs, how a routing path is selected for relaying traffic
between MRs and IGW, and the MAC layer scheduling
with spatial reuse constraint. The capacity LB
j is deter-
mined by the distance between MR j and its adjacent
upstream node based on AMC. Qj, the aggregate inter-
traffic of the uplink of MR j as expressed in Eq. (6),
depends on the routing algorithm, which gives the value
of hjr. Finally, Ir is determined by the MAC layer
scheduling scheme based on the spatial reuse according
to the routing tree constructed by the routing algorithm.
The MRP problem as defined in Eq. (1) is a cross-layer
design problem, which involves equipment cost, antenna
type used, wireless AMC, network routing and MAC
scheduling. Such an interrelated MILP problem is NP
hard. This motivates us to find an effective approach to
handle this problem.
In order to solve the MRP problem, we use three novel
performance factors to capture the multi-layer design
consideration for the local network and the backbone
network: Local Coverage (LC), Backbone Residual Capac-
ity (BRC), and Deployment Cost (DC). LC denotes the
user demands that can be covered by an MR with an
AMC wireless link, which can be used to evaluate the
contribution of an MR to fulfill Eq. (4). BRC calculates
the residual backbone capacity that can support more
user demand originated from a newly deployed MR.
Since the inter-flow traffic must be routed hop-by-hop to
IGW, it consumes bandwidth of many links and cause
interference among links. BRC captures the effect of Eq.
(5) as it considers the synergy effect of AMC, MAC
scheduling, and routing because the chosen location for
placing an MR determines the link rate with AMC, while
the routing path between the MR and IGW consumes the
capacities of the path links, which further interferes with
those links in its neighborhood and thus the MAC layer
must schedule the links to prevent transmission collision.
DC can help us evaluate the tradeoff between using
directional antennas to increase the backbone capacity or
just deploying a plain MR to save cost while deploying
MR. It provides us a vehicle to optimize the cost of the
MRP problem given in Eq. (1).
With these three factors, we develop a heuristic algo-
rithm to resolve the MRP. First, given a user demand
vector, we can use some existing IGW selection scheme,
such as the one given in [24], to place an IGW at one
of MR candidate locations. Second, with or without
directional antennas, we deploy an MR at a selected
location with a maximal utility value. Then, check if all
user demands have been met. If not, deploy another MR
that can meet the residual users’ demand. The process
is repeated until either all users’ demand is met or the
algorithm fails.
3.1.2 Network Model
Our cross-layer design contains two major parts: local
network design and backbone network design. In the
local network, we try to satisfy all local users’ demand
with a minimal number of MRs. In the backbone net-
work design, we must ensure all MRs have sufficient
bandwidth to forward their traffic hop-by-hop to IGW
through a MAC scheduling algorithm and a good rout-
ing tree. This subsection first discusses the AMC model
in the physical layer and a tree-based minimum cost
routing (TMCR) in the network layer. Then, we do the
MAC layer scheduling based on the AMC and TMCR.
• Physical Layer
In the PHY-layer, what we care about is the trans-
mission quality and the link rate. In the measurement
based deployment, the received signal strength (RSS)
is measured for each candidate MR by using the path
loss model [28] as given in Eq. (7). The path loss model
describes the attenuation experienced by a wireless sig-
nal as a function of distance. The signal power decays
exponentially with the distance. Given a reference signal
strength PdBm(d0) at distance d0, the RSS at distance d
is given as
PdBm(d) = PdBm(d0) − 10γlog10(
d
d0
) + ǫ. (7)
where γ is the path loss exponent and ǫ is the shadowing
term.
A higher rate modulation requires a higher RSS or a
shorter transmission distance between two nodes with
a given transmission power. In order to increase the
link capacity while maintaining transmission quality, the
AMC technology is used at the Physical layer that im-
proves data transmission rate. Given RSS, an appropriate
modulation scheme is selected. Thus, according to Eq. (7)
and AMC [29], we can estimate the link rates of the local
and the backbone network with an omni-directional or
a directional antenna.
• Network Layer
A multi-hop wireless network must have a routing
scheme that selects a path to relay packets between
IGW and MRs. The shortest path routing and the
minimum hop routing (e.g. AODV) are two popular
routing schemes. However, different routing schemes
are suitable for different WMNs, such as ad hoc net-
works, sensor networks and stationary networks, such
as WMNs. Routing has been primarily designed to
maintain connectivity for ad hoc networks or sensor
networks, whereas it is more important to maximize
network throughput for WMNs.
In this study, we use a routing scheme, called tree-
based minimum cost routing (TMCR), for backbone
traffic relay. We define the cost of a link lij as the ratio
of the interference degree Iij and the link rate lR
ij:

Algorithm 1 TMCR
Input: backbone topology G = (V ′, E) and link rate LR.
Output: a scheduling routing tree T.
// MP: the set of MRs that have been included
// in a routing tree.
// MC: the set of MRs that have not yet been included
// in a routing tree.
1: MP = {IGW}; CostIGW = 0;
2: if lR
IGW,k = 0
3: CostIGW,k = lIGW,k/lR
IGW,k;
4: else
5: CostIGW,k = ∞;
6: while MC = φ
7: j = arg mink∈MC Costk;
8: MC − {j};
9: MP ∪ {j};
10: Costk = mink∈MC Costk, Costj + Costjk ;
// relabel cost of MR nodes in MC
11: endwhile
Costij = Iij/lR
ij, (8)
where Iij is the degree of interference that can interfere
link lij. Thus, Costij represents the interference cost of
transmitting a unit of data on the link lij. The goal of
TMCR is to minimize the aggregate cost along a routing
path. The larger lR
ij is, the shorter will be the transmission
time for a data packet, and hence, the shorter the block-
ing time will be for other links in its collision domain.
Also, the smaller Iij is, the fewer number of links to
be interfered by link lij, and thus the smaller aggregate
blocking time of interfered links.
TMCR is a variant of the Prim’s algorithm. It finds
a minimum spanning tree by using a greedy strategy.
TMCR works similar to that in [31], but considers both
the total interference links on a path and the degree of
interference. Thus TMCR selects a path with minimum
interference capacity.
Algorithm 1 shows the TMCR algorithm. After TMCR
terminates, each MR k will be labeled a routing cost:
Costk =
ij∈Pk
(Iij/lR
ij), (9)
where Pk represents the path from IGW to MR k based
on the routing tree built by TMRC.
• MAC Layer
It is important to handle all users’ demand evenly by
nearby MRs. However, the MRs closer to IGW consume
less network resource than that of MRs farer away
from IGW. Thus, we shall give a higher priority to
MRs closer to IGW when we assign user demands to
MRs. To achieve this goal, we define a weight-based
link assignment (WLA) at the MAC-layer. In WLA, we
first sort MRs in an increasing order based on their
routing cost, as defined in Eq. (9). Then, we assign user
demands to MRs according to their order by the nearest
neighborhood scheme, i.e., we assign user demand qi to
MR j whose lR
ij is the largest while guaranteeing such an
allocation is supported by the backbone. If the backbone
Algorithm 2 WLA
Input: a routing tree T, a set of MR cost C = {Costk}.
Output: the user demand allocation.
1: initialize S = MP;
2: flag = 1;
3: while S = φ && flag == 1
4: j = arg mink∈S {Costk};
5: sort CS = {qi ∈ Q} in a descending order of lR
ij;
6: CL
j = CL;
7: while CS = φ and CL
j is not exhaused
8: assign the first qi in CS to MR j;
9: Q = Q − {qi}; CS = CS − {qi}; CL
j = CL
j − qi;
10: allocate backbone resource to qi;
11: if backbone resource is exhausted
12: flag = 0; break;
13: endif
14: endwhile
15: S = S − {j};
16: endwhile
cannot support such a user demand, WLA terminates,
which implies the scheduling fails. Algorithm 2 shows
the procedure for WLA.
As MR is deployed incrementally, the routing tree also
changes accordingly. Thus, WLA must be repeated for
every MR added. With such a dynamic allocation, we
are able to achieve close-to-optimal assignment while
ensuring the feasibility of the MR placement.
3.1.3 Performance Factors
On the MRP problem, it is hard to solve Eq. (1) while
satisfying Eq. (4) and (5) because of interference. In this
subsection, based on the concept of collision domain,
we first consider the upper bound for the capacity of
a WMN. Then we introduce two performance factors:
local demand coverage and backbone residual capacity.
Using these two factors, we can evaluate the degree of
contribution when deploying an MR both in the user
demand coverage as well as in the backbone. Then, we
present a heuristic algorithm based on the novel factor
for MR placement.
• WMN Capacity Upper Bound
Evaluation of the capacity upper bound Cwmn of a
WMN is important for the network planning. It tells
us how much user demand that can be satisfied with a
WMN. To estimate Cwmn of a WMN, this study utilizes
heuristic of [30]. In [30], the concept of collision domain
(CD) is first defined and then the most congested CD
in a WMN, called Bottleneck collision domain (BCD), is
identified and used to compute Cwmn.
A CD covers a set of nodes which should not transmit
or receive any data at the same time so as to avoid
mutual interference. To demonstrate how Cwmn of a
WMN is computed, a chain topology of Fig. 1, taken
from [30], is used as an example. In the example, every
node has a demand of 1G to gateway. The CD centered
at link 2-3 contains link 1-2, 2-3, 3-4, and 4-5. When link
2-3 is activated, the links in the 2-3 CD cannot be active
at the same time. With similar analysis, we can readily
find out CDs of all links, out of which the CD of link 2-3

G
8
G
7
G
6
G
5
G
4
G
3
G
2
G
1 GW
G 2G 3G 4G 5G 6G 7G 8G
Fig. 1. A case of BCD in chain topology
contains the most link flows (4+5+6+7+8)G and hence
is the BCD of the WMN. If each link in the collision
domain of 2-3 cannot forward more than the nominal
MAC layer capacity B, the maximal throughput cannot
exceed Cwmn = B/(4 + 5 + 6 + 7 + 8)G.
Because all traffic data must be forwarded to-
ward/from IGW, the CD of IGW is the most heavily
loaded CD in the network and often becomes the BCD
of a WMN [32]. Thus, by analyzing the capacity of BCD,
we can compute Cwmn of a WMN, by which we can
decide if the backbone capacity is sufficient to support
all users’ demand.
• Local Demand Coverage
The location of an MR is very important for serving
MCs. A user demand is satisfied when both the local
network and the backbone network have sufficient ca-
pacities to handle it. As per PHY-layer property, if the
distance between two nodes is short, the transmission
rate becomes large with AMC. Thus, if we want to
enhance the backbone link quality, we must reduce the
transmission distance between MRs. On the other hand,
if we want to serve more MCs, we should place an
MR close to many uncovered MCs. Hence, it is more
beneficial to prolong the distance between MRs. By the
local demand coverage factor, we only care about how
many MCs we can serve to meet their demand.
The users’ demand allocation not only must meet the
link and local network constraints respectively in Eq. (3)
and (4) but also ought to be supported by the backbone
network as follows:
Thr = CL
IGW +
j∈BCD
Qj ≤ Cwmn, (10)
where CL
IGW the local demands of IGW. Eq. (10) com-
putes the total throughput of the mesh network Thr,
which must be smaller than or equal to the total network
capacity, Cwmn.
When the backbone capacity is large enough to sup-
port more users’ demand, every newly added MR can
cover more user demands and hence contributes more
throughput. To evaluate the value of a candidate MR,
the Local Coverage (LC) factor is used to represent the
contribution of a MR in enhencing the network through-
put. We define LCn as an increment to the network
throughput when the nth
MR is deployed:
LCn = Thrn − Thrn−1, (11)
Algorithm 3 Backbone Residual Capacity (BRC) computation
Input: the scheduled links L.
Output: the residual capacity of the backbone.
// L: the universal set of the backbone links
// Lr and Lr
ij: the residual capacity of the backbone
// and the residual capacity of link ij
1: U = L;
2: Lr = 0;
3: while U = φ
4: select a link Lij from U;
5: U = U − {Lij};
6: if Lij is in the BCD
7: Lr
ij = Tr
ij × lR
ij;
8: Lr = Lr + Lr
ij;
9: endif
10: endwhile
where Thrn denotes the throughput of the WMN after
the nth
MR is deployed. Apparently, the larger the LC of
a MR is, more beneficial will be in deploying it.
• Backbone Residual Capacity
Transmitting data in a wireless multi-hop network
consumes substantial resources due to interference
among links. Thus, we must try to cover more users’
demand while reducing resource consumption. Because
we place MR one by one, it is necessary to compute how
much residual resource is available for other unserved
users. We define the Backbone Residual Capacity (BRC)
factor that estimates the amount of backbone capac-
ity available to serve un-assigned users’ demand after
placing an MR. BRC computes the residual capacity of
all links in the BCD. Because all data flows must be
transmitted through BCD, the resource in BCD will be
exhausted first. Thus, if BRC is larger, more users far
away from the IGW can be served.
Algorithm 3 presents the BRC computation algorithm.
The BRC, denoted as Lr
, is the sum of the residual
timeslots (Tr
ij) of each link in the BCD multiplied by
the link transmission rate (lR
ij), where Tr
ij is defined as
follows:
Tr
ij = 1 −
kl∈BCD
Qk
lR
kl
, (12)
where lR
kj is the uplink of MR k. When Lr
is zero while
some user demands are still un-assigned, the WMN
design either fails or omni-directional antennas of some
MRs must be replaced by directional antennas to reduce
the interference and increase the link rate for more
capacity.
4 CROSS-LAYER MESH ROUTER
PLACEMENT
By using two performance factors and the cross-layer
design described above, we introduce a first heuristic
algorithm, named cross-layer MR placement, CMRP-1,
to efficiently place MRs in the WMN. In CMRP-1, we
choose a candidate MR i to maximize the objective
function OF1 as follows:

Algorithm 4 CMRP-1
Input: user location N, demand Nq, MR candidate locations
M C, and IGW location.
Output: the number of selected MRs and their respective loca-
tions.
1: initialize the scheduling routing tree T by TMCR;
2: M P = {IGW};
3: set up IGW location;
4: M C = M C − {IGW};
5: while Thr =
n
i=1
qi
6: j = arg maxM C {OF1 > 0};
7: if j = −1 //current backbone capacity
// is large enough
8: M C − {j};
9: M P ∪ {j};
10: update the routing tree T by TMCR;
11: reallocate users’ demand by WLA;
12: else //j = −1
13: find a location k ∈ M C
with Max R = maxk∈MP {BRCk/ |MP|};
14: if(Max R > ω) //ω is a threshold
15: M C − {k};
16: M P ∪ {k};
19: else //no MR can be selected from M C
//with Max R > ω
20: find a link lij ∈ BCD
with maximal Qi
lR
ij
× Iij;
21: if no such a link is found
22: break;
23: endif
24: replace Lij by a pair of directional antennas;
27: endif
28: endif
29: endwhile
MRi = arg max
i
{OF1 (MRi) = BRCi × LCi} . (13)
Instead of selecting MR with a maximal BRC or a
maximal LC, we select MR with the maximum product
of BRC and LC first. The reason we select BRC × LC is
to maximize the backbone capacity while covering more
users’ demand. If only LC is used, the MR deployment
will always select an MR with maximal user demand
coverage, which can cover substantial users’ demand
initially, but exhaust the backbone resource soon, result-
ing in a non-optimal placement. Thus, the product of
BRC and LC can allow us to balance the effectiveness
in covering the user demand and improvement in the
backbone capacity
Based on OF1, Algorithm 4 contains three main parts.
The first part is to select an IGW location, the second
part is to deploy an MR, and the last part is to deploy
directional antennas for backbone links.
Step1 initializes the routing tree T using TMRC as
given in the Algorithm 1. Step 3 determines the IGW
location. The IGW deployment problem is beyond the
scope of this paper, so we use an existing approach given
in [24] to select the IGW location. In Step 6, we calculate
all candidate MR locations to find a location with the
maximum OF1, and deploy it. In Steps 10 and 11, we
reconstruct the scheduling routing tree and re-allocate
user demands with TMRC and WLA respectively. If we
cannot find an MR location with OF1 > 0, it implies that
the backbone capacity is exhausted and cannot satisfy
any more demand. However, there may be some links
that could be split by another MR to enhance their link
rates and hence increase the backbone throughput. Thus,
we temporarily ignore LC and select an MR with a
maximal average BRC, Max R, larger than a threshold
and deploy it. If no such an MR exists, Step 20 finds a
link that interferes with other links for the longest time
period and replaces it with a pair of directional antennas.
This algorithm will be terminated either when all user
demands are satisfied or when we cannot deploy a MR
at any location to increase the backbone throughput any
further
In CMRP-1, directional antennas are used only when
the WMN topology cannot meet all users’ demand and
the MR locations are not changed when directional
antennas are added. Because using directional antennas
not only reduces the interference, but also enhances the
transmission range, such a deployment scheme may not
be optimal. Furthermore, CMRP-1 does not consider the
deployment cost of an MR and an antenna and cannot
optimize the cost of the WMN deployment.
To cope with the weakness of CMRP-1, we define
a Deployment Cost (DC) factor as an index to estimate
the cost of using directional antennas on a link. DC is
defined as follows:
DC = 1 +
β
α
, (14)
where β is the cost of using a pair of directional antennas
and α is the cost of deploying an MR. Then, the original
objective function OF1 is modified as:
OF2 = BRC × LC/DC. (15)
The CMRP-1 is also revised to be CMRP-2 that always
chooses a candidate MR as follows:
MRi = arg max
i
{OF1 (i) , OF2 (i)} . (16)
If MR i is selected and its OF2 is larger than its OF1,
MR i will use a pair of directional antennas on the link
between itself and its parent node in the routing tree.
5 THE ALGORITHM SIMULATION AND
ANALYSIS
By using the proposed heuristic algorithm, we evaluate
the cost of deploying an IEEE 802.16 WMN with only
one IGW. Users are randomly distributed in a consid-
ered area. In the network, we use IEEE 802.16 TDMA
technology. TABLE 1 indicates the parameters used in
the simulation. The interference range is set to be twice
the transmission range.

TABLE 1
The setting of parameters in PHY-layer
Local power 0.01w
Backbone omni-directional antenna power 0.5w
Backbone directional antenna power 0.8w
Backbone directional antenna angle 30o
Local path loss 3.8
Backbone path loss 3.6
Local transmission range 1050m
Backbone transmission range 2100m
Backbone transmission range with directional antenna 2500m
Local Link Bandwidth 10Mbps
Backbone Link Bandwidth 10Mbps
5.1 Comparing with the Other Algorithm
We compare our algorithms, CMRP-1 and CMRP-2, with
another Probability algorithm proposed in [28] which
is also a heuristic algorithm that places a mesh node
one by one while considering the local coverage and the
backbone connectivity probability. In our simulation, 180
users and 180 candidate MR locations are configured in
a square of 6 kilometers. Each user has 1.0Mbps uplink
flow demand.
The simulation result shown in Fig. 2 illustrates that
the Probability cannot produce the maximum network
throughput, i.e. 180Mpbs, until the 107th MR is de-
ployed. This is because the algorithm is not designed to
maximize the network throughput, and thus it cannot let
a network adapt well to large users’ demand. However,
CMRP-1 and CMRP-2 can reach the maximum network
throughput with only 33 MRs and 2 pairs of directional
antennas, and 20 MRs and 10 pairs of directional an-
tennas, respectively. CMRP-2 can provide the maximum
network throughput with the minimum deployment cost
and with less computation time. Assume the normalized
cost ratio (CR) for a pair of directional antennas to a
mesh router equipped with omni-directional antenna is
0.3. Then, Fig. 3 shows the CPR vs. network through-
put. When the network throughput is low (e.g., below
65Mbps), all three algorithms perform equally well. But,
when a larger network throughput (e.g., over 65Mbps) is
needed, the CPR for Probability rapidly worsens. When
the network throughput is increased further (e.g., over
140Mbps), the CPR for CMRP-1 becomes worse than
CMRP-2. Thus, we conclude that CMRP-2 has the best
CPR for all the ranges of network throughput.
5.2 Comparing CMRP with Fair Scheduling, Short-
est Path Routing, and Greedy MR Selection Method
In order to show the merit of CMRP-1 and CMRP-2,
we first compare the simulation results of the CMRP
framework with various existing schemes such as the fair
user demand allocation, the shortest path routing, and a
greedy MR selection scheme, denoted as CMRP-1/Fair,
CMRP-1/SP, and CMRP/Greedy, respectively. The fair
user demand allocation scheme assigns user demands to
MRs solely based on the nearest neighborhood scheme,
without considering the locations of MRs relative to the
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120
Networkthroughput(Mbps)
Number of MRs
CMRP-2
CMRP-1
Probability
Fig. 2. Network throughput vs. number of MRs for the MR
deployment by CMRP-2, CMRP-1 and Probability
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
20 40 60 80 100 120 140 160 180 200
CostPerformanceRatio(NormalizedCost/Mbps)
Network throughput (Mbps)
CMRP-2
CMRP-1
Probability
Fig. 3. Cost performance ratio vs. network throughput for
the MR deployment by CMRP-2, CMRP-1 and Probability
IGW. The shortest path routing scheme constructs the
smallest hop count routing paths between IGW and MRs
without considering the link rate and the interference.
The greedy MR selection scheme always chooses a MR
with the best throughput based on LC only.
The testing environment is the same as discussed
earlier in Subsection 5.1, except that the user demand is
varied from 0.6Mbps to 1.5Mbps. We run each scheme
on 100 randomly generated scenarios and retain only
successful results that satisfy all users’ demand. TABLE
2 shows the percentage of simulation failure for each
scheme. The result shows that CMRP-1/SP collapses at
larger users’ demands and performs the worst among all
the schemes. CMRP-1 outperforms CMRP-1/Fair when
user demands are large, which substantiates that WLA
performs better than that of the fair user allocation
scheme. The success rate of CMRP-2 is smaller than
that of CMRP-1 and CMRP/Greedy because CMRP-2
deploys directional antennas along with MRs, which

0
20
40
60
80
100
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
NumberofMRs
User demand (Mbps)
CMRP-2
CMRP-1
CMRP-1/Fair
CMRP-1/SP
CMRP/Greedy
Fig. 4. Number of mesh routers by various schemes
0
5
10
15
20
25
30
35
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Numberofpairsofdirectionalantennas
User demand (Mbps)
CMRP-2
CMRP-1
CMRP-1/Fair
CMRP-1/SP
CMRP/Greedy
Fig. 5. Number of pairs of directional antennas by various
schemes
makes the addition of directional antennas less useful
in augmenting BRC.
Fig. 4 and Fig. 5 show the number of MRs and
the number of pairs of directional antennas deployed
by each scheme. Fig. 4 shows that CMRP-2 deploys
the fewest MRs and the number of MRs deployed by
CMRP-2 is relatively independent of the users’ demand.
Fig. 5 shows that the number of pairs of directional
antennas increases as users’ demand increases for all the
schemes. However, the number of pairs of directional
antennas deployed by CMRP-2 is linearly dependent on
the demand. This shows that taking the antenna type
into account while deploying MRs is an efﬁcient way to
minimize deployment cost.
5.3 Analyzing the Cost of Constructing a WMN
As the cost is an important index to determine how good
a MR deployment algorithm is for service providers,
we discuss the cost of constructing a WMN. Fig. 6
shows the normalized cost of all schemes relative to
0
0.5
1
1.5
2
2.5
3
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Totalcost(RelatedtoCMRP/Greedy)
User demand (Mbps)
CMRP-2
CMRP-1
CMRP-1/Fair
CMRP-1/SP
CMRP/Greedy
Fig. 6. Normalized total cost by various schemes
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
User demand (Mbps)
CMRP-2
CMRP-1
CMRP-1/Fair
CMRP-1/SP
CMRP/Greedy
Fig. 7. Cost performance ratio by various schemes
CMRP/Greedy. It is shown that CMRP-2 achieves the
lowest deployment cost among all schemes and the
CPR is the lowest as users’ demand increase up to
1.0Mbps. The result also shows that the deployment
schemes without considering cost converges as the user
demand increases. Fig. 7 shows that CMRP-2 provides
the least CPR and is nearly constant for all ranges of user
demand, while the CPR of other schemes increases as
user demand increases. This shows that CMRP-2 is much
more cost-effective and efﬁcient in the MR deployment.
Fig. 8 shows CPR vs. user demand for various cost
ratios (CRs) of a pair of directional antennas to a MR. It
is shown that CPR slightly increases as users’ demand
increase. Also, CPR increases as CR increases, and the
deployment cost is relatively stable when CR is small
in various user demands. Fig. 9 shows CPR vs. total
deployment cost (MRs plus directional antennas) for
various CRs in Fig. 8. As shown in Fig. 9, although a
zigzag curve may appear due to statistical deviation in
simulation results, there is a sharp increase in CPR for
each CR, which indicates that the network planning is

TABLE 2
Percentage of simulation failure by different schemes
Demand CMRP-2 CMRP-1 CMRP-1/Fair CMRP-1/SP CMRP/Greedy
0.6 0% 0% 0% 0% 0%
0.7 1% 0% 0% 0% 0%
0.8 1% 0% 0% 0% 0%
0.9 0% 0% 0% 0% 0%
1.0 0% 0% 0% 34% 0%
1.1 1% 0% 0% 94% 0%
1.2 2% 0% 1% 95% 0%
1.3 1% 0% 0% 97% 1%
1.4 3% 1% 5% 99% 2%
1.5 13% 0% 15% 100% 1%
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
User demand (Mbps)
Cost Ratio = 0.1
Cost Ratio = 0.2
Cost Ratio = 0.3
Cost Ratio = 0.4
Cost Ratio = 0.5
Fig. 8. Cost performance ratio vs. user demands for
CMRP-2
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0.32
18 20 22 24 26 28
CostPerformaceRatio(NormalizedCost/Mbps)
Total normalized cost (MR + Dir)
Cost ratio = 0.1
Cost ratio = 0.2
Cost ratio = 0.3
Cost ratio = 0.4
Cost ratio = 0.5
Fig. 9. Cost performance ratio vs. total normalized cost
for CMRP-2
optimal for a certain network throughput. This informa-
tion is useful when we plan a large scale WMN with
more than one IGW in optimizing deployment cost.
6 CONCLUSION AND FUTURE WORK
In this paper, we present a Cross-layer MR Planning
(CMRP) scheme for IEEE 802.16 WMNs. CMRP inte-
grates the AMC technology and the antenna type at the
PHY-layer, Tree-based Minimum Cost Routing (TMCR)
at the network-layer, MAC scheduling and Weight-based
Link Assignment (WLA) at the data link layer to derive
a cost effective WMN design. CMRP encapsulates the
complex design factors into three design attributes: local
coverage, backbone residual capacity and deployment
cost. Numeric results show that CMRP works well, and
provides a good cost performance ratio (CPR) in the
WMN network planning. The simulation results also
conﬁrm that our novel TMCR and WLA schemes can
effectively improve the performance of CMRP. Moreover,
by incorporating the cost ratio directional antenna to MR
in the network planning, a WMN with a low CPR can
be obtained.
From the simulation results, we also see that the CPR
increases substantially as a WMN covers larger users’
demand. Based on this observation, we plan to develop
an IGW placement algorithm based on CMRP to achieve
low CPR in the large-scale WMN planning.
ACKNOWLEDGMENTS
The authors would like to thank the National Science
Council, Taiwan, R.O.C. for ﬁnancially supporting this
research under Contract No. NSC96-2221-E-155-033 and
NSC97-2218-E-155-006.
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Tein-Yaw Chung received the A.S degree in
Electronic Engineering from the National Taipei
Institute of Technology, Taipei, Taiwan, R.O.C.,
in 1980, and the M.S. and Ph.D. degrees in
Electrical and Computer Engineering from North
Carolina State University, Raleigh, NC, USA,
in 1986 and 1990, respectively. His current re-
search interests include active networking, peer-
to-peer networking, multimedia communication
and mobile computing.
From Feb. 1990 to Feb. 1992, he was with
the Network Service Division, IBM, RTP, NC, USA, and involved in the
research and development of heterogeneous network interconnection.
He holds several patterns while he worked in IBM. Since May 1992,
he has been with Yuan-Ze University, Chung-Li, Taiwan, where he is
now an associate professor in the Department of Computer Science and
Engineering.
Dr. Chung is a member of IEEE Communication Society.
Hao-Chieh Chang received the B.S. and the
M.S degrees in Computer Science and Engi-
neering from Yuan Ze University, Chung-Li, Tai-
wan, in 2006 and in 2008, respectively. His
research interests include network optimization,
wireless mesh networks, and peer-to-peer net-
works.
Hsiao-Chih George Lee received the B.S. de-
gree in Electronic Engineering from Chung Yuan
Christian University, Chung-Li, Taiwan, R.O.C.,
in 1979, and the M.S. degree in Electrical En-
gineering from the University of Louisville, KY,
USA, in 1986. He is currently working toward
the Ph.D. degree in the Department of Computer
Science and Engineering of Yuan Ze University,
Chung-Li, Taiwan. His areas of research include
wireless mobile networking and network opti-
mization.
He has been an instructor in the Department of Electronic Engineer-
ing, the Oriental Institute of Technology, Pan-Chiao, Taiwan, since 1986.
Mr. Lee is a member of IEEE Communication Society.

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