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Efficient Deployment of Gateways in Multi-hop Ad-hoc
Wireless Networks
Luis Urquiza-Aguiar, Andrés Vázquez-Rodas, Carolina Tripp-Barba*
Ahmad Mohamad Mezher, Mónica Aguilar Igartua , Luis J. de la Cruz Llopis
Telematic Engineering Dept., Universitat Politècnica de Catalunya (UPC), Barcelona, Spain
*Faculty of Computer Science, University of Sinaloa, Mazatlan, Mexico
{luis.urquiza,andres.vazquez,ahmad.mezher,maguilar,ljcruz}@entel.upc.edu
ctripp@uas.edu.mx
ABSTRACT
This paper proposes a mixed linear and integer optimization
model for multi-hop ad-hoc networks to select the positions
of the gateways over a certain area. This model mimics the
routing behavior of such network and takes into account the
maximum bandwidth capacity of the network gateways. We
also include a suboptimal solution for the cases in which the
complexity or the amount of the data make the optimal so-
lution infeasible. Results in a pedestrian mesh network and
in a VANET scenarios show that the model locates gate-
ways in an efficient way and that the suboptimal solution is
close to the optimal one in terms of the number of required
gateways or the common selected gateways.
Categories and Subject Descriptors
C.2.1 [Computer-Communication Networks]: Network
Architecture and Design—Network Communications, Wire-
less Communication; C.2.2 [Computer-Communication
Networks]: Network Protocols—Routing Protocols; D.4.8
[Operating Systems]: Performances—Simulation
General Terms
Design; Optimization; ad-hoc networks
Keywords
Wireless multi-hop networks; VANET; mesh; discrete net-
work model; integer optimization
1. INTRODUCTION
Multi-hop ad-hoc wireless networks were conceived to pro-
vide communication among their nodes without the need of
any fixed network infrastructure. Nevertheless, under nor-
mal conditions ad-hoc networks need to reach fixed network
infrastructure to access public information services or surf
the Internet. This work proposes a mixed linear and inte-
ger multi-hop network model that can be solved by linear
PE-WASUN’14, September 21–26, 2014, Montreal, QC, Canada.
http://dx.doi.org/10.1145/2653481.2653487.
optimization techniques to get an efficient deployment of
gateways over a specific area.
The proposed model emphasizes in a realistic routing be-
havior and in the control of the bandwidth capacity of the
network gateways. Moreover, the resulting solution consid-
ers a whole set of possible movements of the nodes in the
area. Besides, a suboptimal procedure is included for the
cases in which the model cannot be solved due to the size
of the problem and the solution space, which depend on the
size and complexity of the data. The rest of the paper is or-
ganized as follows: Sec. 2 surveys related work, then Sec. 3
explains the model and the alternative procedure to get a
suboptimal solution. After that, Sec. 4 analyzes the result of
the model for a mesh multi-hop network and for a vehicular
ad-hoc network (VANET). Finally, conclusions and future
work are drawn in Sec. 5.
2. RELATED WORK
Typically, the deployment of gateways is seen as a cover-
age area problem. In wireless sensor networks (WSNs) this
problem is narrowly related to energy saving, connectivity,
network reconfiguration and quality of service. Therefore,
maximizing coverage using resource constrained nodes is a
non-trivial problem. The coverage problem for WSNs has
been studied extensively in recent years. In [3] the authors
present a fully sponsored sensor discovery scheme called the
intersection point method (IPM), which works under irre-
gular sensing range and can efficiently increase the accuracy
of the discovery method through a unit circle test. By ad-
justing the radius of this unit circle test, the scheme can
be made tolerant to holes of a certain size, making the solu-
tion flexible when the degree of accuracy must be controlled.
Hence, this solution is suitable to maintain a high coverage
rate in WSN under an irregular polygon sensing range. The
works [6] [10] are focused in wireless mesh networks (WMN),
where [6] first formulates the Internet gateway placement as
an integer linear programming incorporating QoS consider-
ations. In [10] the authors use the normal logarithm dis-
tribution model of the shadow effect to design a weighted
objective function to guarantee the node’s connectivity and
coverage. They also consider an heuristic tree-set partition
algorithm based on the number of hops to achieve that nodes
with high throughput and better connectivity acts as gate-
ways. On the other hand, it is well-known that the roadside
infrastructure, which serves as gateway, is an important part
of the VANETs assisting in tasks such as connectivity or
routing. This is required in such vehicular communications,
since vehicle networks frequently suffer uncertain connectiv-
ity changes. Currently, there are several studies on vehicular
networks that try to design efficient roadside infrastructure
deployments, most of them focused on maximize coverage
and reduce implementation costs. For instance, in [14] the
authors propose an optimization framework for road side
unit (RSU) deployment and configuration. The objective
in that work is to minimize the total cost to deploy and
maintain the RSUs that participate in the network, playing
with constraint of covering streets and maximum number of
hops. Other studies take into account the maximum trans-
mission delay. The proposal of [24] considers the movement
of the vehicles and the multi-hop forwarding to study the
spatial propagation of information in VANETs to model a
placement strategy of the RSU with bounded delays. The
authors in [7] study the effect of the position of fixed in-
frastructure in vehicular networks obtaining an increase in
coverage of 15% if the RSU is placed in the center of inter-
sections instead of in the corners. In [5] the authors present
a geometry-based coverage strategy to solve the maximum
coverage in vehicle-to-infrastructure communications in ur-
ban environments. They take into account the shape and
area of road segments. Their solution uses a genetic algo-
rithm that provides a global optimal solution for the irregu-
lar regions. In [20] and [19] the authors formulate a model to
deploy Dissemination Points (DP) as a maximum coverage
problem (MCP). The formulation maximizes vehicle-to-DP
contacts. In [4] the problem of maximizing the number of
vehicles covered by the RSUs deployed in the city is mod-
eled using a maximum coverage with time threshold problem
(MCTTP). The same model was used in [21] where greedy
algorithms were used to improve it. The authors conclude
that the vehicular mobility is the main factor in achieving
an optimal deployment of RSUs.
3. A DISCRETE MODEL TO DEPLOY GATE-
WAYS IN A MULTI-HOP NETWORK
The aim of our proposed linear model is to choose the
minimum integer number of gateways that should be de-
ployed in a specific area such that the big amount of nodes
considering the whole set of different movement snapshots
can reach a gateway in a multi-hop scenario. Our proposal
takes into account several distributions of nodes in the area.
It also emphasizes the realistic multi-hop behavior, where
nodes employ greedy approaches to reach the closest gate-
way. Besides, our model considers an approximation of the
effective capacity of the wireless channel due to the multi-
hop transmission. Moreover, our model takes into account
the maximum demand that a gateway can serve. In the
following subsections, the different parts of the model are
explained.
3.1 Data Sets
The following data sets and parameters are required by
the model.
Nis the set of nodes, with cardinality |N|, that are over
the area where the gateways will be deployed.
GW is the set of candidate gateways among which our model
chooses the most valuable ones. The candidate gate-
ways are already located over the map area.
Mis the set of movement observations. A movement
snapshot m∈Mis defined by the different positions
where the set of nodes are located at a given moment.
Hrepresents the set of path lengths allowed by the model
to connect nodes with a gateway. In the model the
maximum route length is denoted by h=|H|.
LNis the set of average traffic load associated with each
node n∈N. This data set is useful, for instance, when
there is an interest to test different traffic loads among
nodes. In this work we will use the same traffic load
for all nodes and in all movements snapshots m∈M.
PHis a set of cost factors associated with the path length H.
Traffic loads sent through longer paths will use more
bandwidth resources than through a one-hop path. In
this work, we use as penalty factor the mean number
of times that a message should be sent to get one suc-
cessful reception as a function of the number of hops.
This penalty factor follows a geometric distribution.
The probabilities of a successful message reception for
different path lengths were obtained from [22].
Pdis the penalty factor for the disconnected nodes. This
factor is very big to capture the effect of a traffic that
will never reach the gateway.
CNM×N×Nis the adjacency matrix among client nodes n∈
Nat each movement snapshot m∈M. The adjacency
matrix is a (0,1) matrix that has a 1 in the position
CNm,j,k when node j∈Nis aware of the presence of
node k∈Nin the movement snapshot m∈M.
CGWM×N×GW is also an adjacency matrix, but between
client nodes n∈Nand gateways g∈GW at each
movement snapshot m∈M.
CGW is the set of traffic load capacities associated with each
candidate gateway g∈GW. In this work we set the
capacity for all the gateways to half of the channel bit
rate to consider the time spent by the backoff process
and ACK transmission.
3.2 Variables of the model
Our model uses the following variables to determinate
which gateways should be selected.
SGW is a boolean variable that indicates if a gateway g∈
GW is chosen in the solution (Sg= 1) of the model or
not (Sg= 0).
DM×NIf a node n∈Ncannot reach a gateway in the move-
ment snapshot m∈M, then Dm,n = 1. Disconnected
nodes in the model are due to different reasons, for
instance: nodes that do not have any node or gate-
way around them, or nodes that cannot be connected
through the maximum established path length.
NNHM×N×H×NThis boolean variable stores the informa-
tion about the next hop in the path of a node. If the
variable NNHm,j,h,k = 1 then the node kwhich is lo-
cated at h∈Hhops from a gateway, is the next hop
of node j∈Nfor the movement snapshot m∈M.
NGWM×N×H×GW This variable associates a node with a
selected gateway. The aim is to know how much traffic
receives each gateway. For instance, N GWm,j,h,g = 1
indicates that in the movement snapshot m∈M, the
node j∈Nis located at h∈Hhops from gateway
g∈GW and that node jis connected with gateway g.
Notice that NGW stores information about the path
length of a node to reach the selected gateway.
NHM×N×His a boolean variable that indicates if in the
solution of the model for a movement snapshot m∈
M, a node n∈Nhas a path length of h∈Hto
reach any selected gateway g∈GW . This means that
Sg= 1. This variable is not strictly necessary, but
using it some constraints can be written and checked
by the optimization solver faster. Nonetheless, this
come at the cost of using more boolean variables.
3.3 Objective function
As we mentioned, the aim of our model is to maximize the
connectivity between nodes and gateways but maintaining
the number of deployed gateways in a wireless ad-hoc net-
work as low as possible. The ob jective function is shown in
Eq. (1).
min X
m∈M,n∈N
Dm,nPdLn+X
m∈M,g∈GW
SgCg!(1)
The first term of the objective function adds all the traffics
of disconnected nodes across all the movements snapshots,
taking into account the penalty factor Pdfor the traffic that
cannot be sent to a gateway. On the other hand, the second
term adds all the capacities of the selected gateways. The
objective function will minimize the disconnected nodes with
larger demands but using the lowest number of candidate
gateways. It is worth to mention that the model will not
disconnect a node to avoid the use of a gateway because the
penalty factor of disconnected nodes is much greater than
the capacity of a gateway. Consequently, the solution will
prefer to activate gateways instead of to disconnect nodes
because the latter increases the value of the objective func-
tion.
3.4 Constraints
Our proposal aims to accurately model the routing behav-
ior of ad-hoc networks. In particular, our model considers
the following aspects:
•Nodes try to connect to the closest gateway with respect
a routing metric. In this proposal, the routing metric
used is the number of hops, which is directly related with
distance and delay.
•We assume that nodes keep a single route to a destination,
i.e. in our case a gateway. This implies that all traffic that
a node receives from other nodes will be forwarded to the
same gateway.
The last is a strong consideration of the model, because
none of the nodes can be used as a smart router that bal-
ances the traffic of its neighbors among different gateways.
The following constraints guarantee a proper solution of the
problem.
A first condition is related to the fact that a node only
has one route to a specific gateway. Eq. (2) establishes that
a node can only have one route of length hto a gateway in
every movement m∈M, or that a node is disconnected.
X
h∈H,
i∈NGW
NGWm,j,h,i +Dm,j = 1,∀m∈M, ∀j∈N(2)
Equation (3) allows to know which is the path length of
a node without using the four index variable NGW . This
constraint binds NH with the value of N GW .
NGWm,j,h,i ≤N Hm,j,h ,∀m∈M, ∀j∈N,
∀h∈H, ∀g∈GW (3)
A second condition is expressed in equations (4) and (5).
They intend to allocate nodes providing a next forwarding
node to each node. Restriction of Eq. (4), where A\B
indicates the set Awithout the elements of set B, states
that if a node jis located at hhops of a gateway, then it
must select only one nexthop among their neighbors ksuch
that it must be at h−1 hops from a gateway. In the case of
a node located at one hop from a gateway (h= 1), it must
be connected to only one gateway iin the solution.
NHm,j,h =X
k∈N:
CNm,j,k =1
NNHm,j,h−1,k,
∀m∈M,
∀j∈N,
∀h∈H\ {1}
(4)
NHm,j,1=X
i∈GW :
CGWm,j,i =1
NGWm,j,1,i,∀m∈M , ∀j∈N(5)
Two additional constraints are needed for a proper fulfill-
ment of the next forwarding node conditions (Eq. (4) and
Eq. (5)). Eq. (6) requires that if a node jis selected as next
forwarding by a node kwhich is located at h+ 1 hops, then
node jmust be at hhops in the movement snapshot m.
NHm,j,h ≥NNHm,k,h,j ,∀m∈M, ∀j, k ∈N,
∀h∈H, ∀g∈GW (6)
Similarly, in Eq. (7) if a node jis located at one hop from a
gateway and it selects the gateway i(NGWm,j,1,i = 1) then
gateway imust be in the set of gateways of the solution
(Si= 1). This constraint guarantees that the selected gate-
ways in the solution are the gateways which fulfill all the
other constraints.
NGWm,j,1,i ≤Si,∀m∈M, ∀j∈N , ∀i∈G(7)
The condition that guarantees that a node does not forward
traffic of their neighbors to other gateways apart from its
own gateway, avoiding a balance of traffic load, is achieved
through Eq. (8).
NNHm,j,h−1,k +NGWm,j,h,i ≤N GWm,k,h−1,i + 1,
∀m∈M, ∀j, k ∈N, ∀h∈H\ {1}(8)
The above constraint binds to a node k, which is the next
hop of node j, to have the same gateway. This is because
when node jis associated with gateway i(NGWm,j,h,i = 1)
if node kwould be attached to another gateway gwhich
means NGWm,k,h−1,g = 1, then the inequality of Eq. (8)
would be violated since Eq. (2) forces a node to be associated
with only one gateway.
Constraints that mimic the behavior of routing protocols
are written in equations (9) and (10). With Eq. (9), our
model guarantees that if a node jhas in its coverage area
at least one selected gateway iin the solution (Si= 1), then
node jmust have a path length equal to one.
NHm,j,1=Am,j,1,∀m∈M, ∀j∈N(9)
where Am,j,1is :
Am,j,1
1 if X
i∈GW :
CGWm,j,1=1
Si≥1
0 otherwise
The previous equation forces that a node never connects to
a gateway in two or more hops when a gateway through a
direct connection is available in the solution.
The solution will not include artificial long paths thanks
to the constraint described in Eq. (10).
NHm,j,h ≤Bm,j,h ∀m∈M, ∀j∈N,
∀h∈H\ {1,2}(10)
where Bm,j,h is a boolean value given by:
Bm,j,h
1 if X
s∈{1,..,h−2},
k∈N:
CNm,j,1=1
NHm,k,s = 0
0 otherwise
Basically, Bm,j,h = 0 when there is at least one neighbor of
node jlocated two or more hops s∈ {1, .., h−2}nearer to a
gateway. Hence node jcannot be located at hhops from a
gateway and it must be placed just after its closest neighbor
to a gateway.
Another important feature of the proposed model is that
it allows us to impose a maximum capacity load to each
candidate gateway i∈GW, so that we can guarantee that
no gateway in the solution will receive an unmanageable
traffic load. Restriction written in Eq. (11) is in charge of
this task.
Ui=X
j∈N,
h∈H
NGWm,j,h,iPhLj≤Ci,∀m∈M ,
∀i∈GW (11)
Finally, Eq. (12) sets the maximum number of gateways
(MaxGw) that the solution can have.
X
i∈GW
Si≤MaxGw (12)
3.5 A fast suboptimal solution
The proposal of this paper provides an optimal solution
considering a whole set of movements snapshots for an area.
However, the solution of this model can become infeasible
to be obtained by an optimization solver depending on the
range of the values of the data and depending on the number
of variables and constraints that it has. In this section, we
propose a procedure to get a suboptimal solution in a fast
way when an optimization solver cannot provide a solution
for our discrete network model.
Instead of getting the solution of the whole set of move-
ments snapshots, we propose to use the optimal solutions of
the independent subsets of movements as follows:
1. To get the subsets of movements X∈M
kobtained from
all k−combinations of the set of movements M.
2. To solve the discrete network model for all subsets X∈
M
k. Each subset Xprovides a solution set of gateways
Swith its corresponding capacity utilization U.
3. Next, we use the optimal solution of each subset X. A
good and fast solution for the whole set of movements
can be found in the join of all set of selected gateways S
in each solution. For the cases where there is a constraint
in the maximum number of gateways to M axGW , the ca-
pacity utilization Uof all subsets is added and the top
MaxGW gateways in decreasing order from joined capac-
ity utilization, are the selected gateways in the solution.
The idea behind this procedure is similar to the idea of a
greedy algorithm, in the sense that we use “local solution”
(independent solutions for each subset X∈M
k) to get a
global solution (for the whole set of movements snapshots
M). This procedure is fast because the addition of the times
required by a solver for each subset will be generally shorter
than the time needed to solve the entire set M, especially for
large cardinality sets, for which this approach was specially
targeted. Nevertheless, the following procedure is subopti-
mal because, as it can be seen in Sec 4, it will use more
gateways than needed or will not employ the same set of
gateways than the optimal solution when a constraint of the
maximum number of gateways is set.
We want to point out that the cardinality kof the subsets
Xshould be as high as possible to be solved in a reasonable
time by an optimization solver. If each subset Xhas a high
number of movements snapshots m∈M, less “local” the
solution will be. This is because each of these ”local” (inde-
pendent) solutions will take into account several movement
snapshots.
4. TEST AND RESULTS OF THE MODEL
This section presents the solutions obtained by our model
and by the proposed fast and suboptimal procedure for two
different scenarios. The first is a pedestrian scenario where
users are moving over an open area while they try to connect
to a gateway directly or through a mesh MANET formed by
other users. The second scenario is a VANET deployed over
a real map layout in which vehicles reach an RSU in one hop
or through other vehicles using some routing protocol.
The model were programmed and solved for the two sce-
narios using the IBM ILOG CPLEX Optimization Studio
software [9]. We ran CPLEX over a workstation with a pro-
cessor Intel core i7 at 2.8GHz with 16GB of RAM memory.
4.1 Pedestrian scenario
We assume that users are located over an open area like
a park, and they can freely move in all the entire area.
Therefore, we assume that nodes move according to a ran-
dom walk 2D mobility model inside the rectangular bounds.
The direction and speed of the nodes are updated every
time they move 100 m. We use the NS-3 simulator [15]
to get a real connectivity matrix for eight different move-
ments snapshots. The simulation scenario consists of 70
mesh stations (user nodes) and 30 candidate gateways uni-
formly distributed over 0.5 km2. These proportion values
guarantee a minimum quality criteria for stringent proto-
col evaluation. Specifically, there are shortest paths longer
than 4 hops among nodes and the average network parti-
tioning is lesser than 5% (to avoid an excessive number of
isolated nodes) [13]. The candidate gateways are located at
fixed points where nodes typically have high centrality met-
ric values in similar simulation scenarios. The advantage of
the use of nodes with high centrality metrics was analyzed
in [23]. The simulations were carried out using a log-normal
shadowing channel propagation model. The mesh stations
are based on the IEEE 802.11s amendment. Mesh nodes
must create and maintain a logical topology using the mesh
peering management protocol. Every mesh station discov-
ers its mesh neighbors (peers) by means of beacon frames
which are periodically sent. When a new neighbor has been
discovered, the mesh station starts a peer link open hand-
shake. The established peer have to be done and agreed by
both nodes. Only if the complete handshake procedure is
successfully executed, a peer link is established between two
mesh stations.
For the solution of the model in this scenario, there is
no constraint in the number of gateways. The maximum
number of hops in a path is set to ten. Figure 1 shows the
difference in the first movement snapshot between what we
call “local optimal” solution and the “global optimal” solu-
tion. By “local optimal” solution, we mean solutions that
only consider a specific movement snapshot. By ”global op-
timal” solution we mean the nodes connectivity considering
the eight movements snapshots used in this scenario. From
here, three important facts can be appreciated:
1. The “local optimal” solution will always require less or
equal number of gateways than the “global optimal” solu-
tion.
2. The selected gateways (green points in Fig. 1(a) and 1(b))
are located near to the least connected users rather than
near to nodes with many neighbors. This means that the
solutions (local and global) locate gateways in areas where
there are isolated nodes (see the two selected gateway in
the top right of the Fig. 1(a)). The solutions also includes
that well-connected nodes can reach any gateway through
a multi-hop routing.
(a) Global optimal solution.
(b) Local optimal solution.
Figure 1: Comparison between global and local op-
timal solutions for the pedestrian mesh network for
a specific movement snapshot. Allowed No. of
hops≤10.
Fig. 2 shows the multi-hop routing effect. It is clear that
most of the nodes are connected to a gateway through other
nodes. Typically, local solutions have more nodes and long
routes than the global solution. This is because the global
solution always uses the four gateways while local solutions
only require in most of the cases three gateways.
Table 1 shows the differences in the selection of gateways
between the “global solution” and the “fast suboptimal” so-
Figure 2: Nodes by hops distance comparison be-
tween global and local solutions in pedestrian mesh
network scenario. Maximum No. of hops =10.
Table 1: Gateways comparison between optimal and
suboptimal solutions for the pedestrian mesh sce-
nario.
Number of gateways in the solution
Max. No. optimal fast sub fast sub Com- Com-
of Hops opt. 1 opt. 2 mom 1 mom 2
10 4 11 6 4 4
5 6 18 8 4 2
Execution Time (hh:mm:ss)
10 00:20:35 00:02:40
5 00:09:15 00:00:42
lution obtained, as explained in Sec. 3.5, with subsets of one
movement. This is the critical case because each subset so-
lution will completely ignore the rest of the movements of
the whole set. This table includes how many gateways are
required by each solution and how many of them appear in
both solutions. Also, it shows the results for the scenario
with a maximum path length equal to five. We include
a suboptimal solution 2, which is obtained by eliminating
outlier selected gateways from the suboptimal solution. We
define a selected gateway as outlier when this only appears
in less than the 10% of the subsets, in our case the gate-
ways that are selected in only one movement. As it can be
noticed, the number of selected gateways in the suboptimal
solution without outliers decreases considerably. This is be-
cause of the high level of connectivity among the nodes. A
good connectivity leads to a wide set of gateways that can
provide a local optimal solution. In Fig. 3(a), it can be seen
that the two additional gateways of the suboptimal solution
are close enough to the common selected gateway of this
area. Therefore, any of them was selected in the different
movement indistinctly because all of them give local optimal
solutions. As expected, the number of gateways suitable to
provide optimal solutions increases when the maximum path
length decreases, because the solution will need more gate-
ways to cover smaller areas. This is clear looking at Fig. 3(b)
where there are selected gateways only in the suboptimal so-
lution (light-blue points) near to selected gateways only in
the optimal solution (green points).
4.2 Vehicular scenario
We employed Estinet Network Simulator and Emulator [8]
to obtain the connectivity matrix for 10 different moments
(a) Maximum No. of hops = 10.
(b) Maximum No. of hops = 5.
Figure 3: Selected gateways (GWs) comparison
between optimal and suboptimal solutions for the
VANET scenario. No constraint for the maximum
No. of gateways.
Figure 4: VANET 2 km2scenario. Eixample district
of Barcelona. Positions of candidate gateways.
in the vehicular scenario. We used a real area of around
2 km2taken from the Eixample district of Barcelona (see
Fig. 4) to model an urban scenario formed by streets and
crossroads. The mobility of vehicles was obtained with the
SUMO engine [11] according to the Krauss model [12]. Fur-
thermore, the scenarios have buildings information (orange
lines in Fig. 4) extracted from the OpenStreetMap and im-
ported to Estinet using the SUMO tools and our own code to
generate Estinet-Buildings. The buildings’ walls attenuate
the signal of vehicles during the simulation process.
We considered 150 vehicles, which correspond to a den-
sity of 75 vehicles per km2. There were 95 RSUs (i.e. GW)
placed in the intersections of the streets (see Fig. 4). Sim-
ulations were carried out using the IEEE 802.11p standard
on physical and MAC layers and our geographical routing
Figure 5: Global optimal solution for the VANET
scenario for the eighth movement snapshot. Max.
No. of GWs = 30. Max. No. of hops = 5.
proposal GBSR [18]. In GBSR, adjacency between nodes is
only determined through the reception of 1-hop broadcast
messages (hello messages, HMs). HMs include information
about position and the node ID. When a node receives a HM,
it adds the node ID to its neighbor list. We used an empiri-
cal model of radio shadowing [17] in IEEE 802.11p networks
as path loss model. Also, as fading model we used Rician
when vehicles are in line of sight (LOS) and Rayleigh when
vehicles are not in LOS [16]. We set a receiving sensing of -68
dbm according to the receiver performance requirement for
an allowed rate of 27 Mbps as specified in the IEEE 802.11
standard [1]. Moreover, we used the realistic packet error
model proposed in [2].
The aforementioned characteristics lead with the biggest
number of RSUs required to cover an specific area because
the effective transmission range of a node decreases con-
siderately (in this case between 100 to 200m depending on
the interference) compared to the low rates modulations.
Hence, the adjacency matrix of the VANET scenario is very
spare, in contrary to the pedestrian scenario, where there
were many possible routes. In this case there are many ve-
hicles (around of 20%) that do not have connectivity with
any other vehicle or RSU. Notice that we constrained the
maximum number of gateways to be used in the solution to
thirty, and the maximum number of hops in a route to five.
Taking into account the low connectivity and the restricted
number of RSUs to be deployed, the solutions provided by
the “global” and“local” approaches share the following char-
acteristics:
1. Both solutions locate the RSU in positions with high de-
gree of connectivity to reach as many vehicles as possible
through direct connection with a gateway or multi-hop
forwarding. Notice that these positions (Active RSU in
Fig. 5) match with the streets of more vehicular traffic
flow like avenues (wide streets in Fig. 4).
2. A big amount of vehicles are connected through direct
link to a gateway and maintain similar number of vehicles
connecting by the different path lengths. This is depicted
in Fig. 7 and is consequence of the low connectivity of the
network. Also, it can be seen that both solutions have
roughly the same number of disconnected nodes.
It is expected that “optimal” and “suboptimal” solutions
will provide close results, given the close arrangement of
vehicles among the path lengths, depicted in Fig. 7. Table 2
shows the results of this comparison. In fact, both solutions
use the maximum number of RSU and they have in common
26 out of 30 RSUs. We also include the results for an even
more reduced number of allowed RSUs, when only eight out
of fifteen RSUs are the same in both solutions.
A close look to Fig. 6(a) allows us to realize that the sub-
optimal solution puts its “non-common” RSUs (light-blue
color) in positions with more connectivity and near to other
selected RSUs, while the optimal solution locates its non-
shared RSUs in areas that are no covered by the suboptimal
solution. The fact that the suboptimal solution covers first
the crowed areas, which is more evident in Fig. 6(b), is be-
cause the local optimal solution picks one RSU among all
the set that can cover an area, and the chosen RSU is not
the same in all the independent solutions. Nevertheless, this
effect should be less important when the size of the subsets
of movements increases.
Finally, we want to notice that the execution time needed
to solve the model, shown in Tables 1 and 2 depends on
the scenario characteristics. For instance, the pedestrian
scenario spends twice the time required by the VANET sce-
nario in spite of the higher number of nodes of the latter.
The reason is the higher number of routing alternatives of
the pedestrian case. In conclusion, there is not a fixed subset
size that guarantees its solution by the model and such size
depends on the trade-off between connectivity complexity
and number of total nodes.
Table 2: RSUs comparison between optimal and
suboptimal solutions for the VANET scenario.
Number of gateways in the solution
Allowed Gateways optimal fast suboptimal Common
30 30 30 26
15 15 15 8
Execution Time (hh:mm:ss)
30 00:03:15 00:01:48
15 00:03:24 00:01:41
5. CONCLUSIONS
In this work we propose a mixed linear optimization model
for multi-hop ad-hoc networks for an efficient deployment of
gateways. The goal of the model is to minimize the integer
number of gateways but providing connectivity to as many
users as possible based on some constraints. The proposed
model takes benefit of the specific routing criteria employed
in this kind of networks to provide a realistic solution. On
the other hand, these efforts come at the price of more com-
plexity to get the solution of the model. This solution could
become infeasible to obtain depending on the size of data
and adjacency matrix of the nodes. To tackle this issue, we
proposed a suboptimal procedure based on combinations of
solutions of subsets of the original data. Results over two
types of ad-hoc networks (mesh and VANET) show that the
model prioritizes to locate gateways in low connected ar-
eas whereas the other well connected ones can reach these
gateways thanks to the multi-hop forwarding. In opposite
way, the model prefers to cover first the crowded areas when
(a) Max. No. of RSUs = 30.
(b) Max. No. of RSUs = 15.
Figure 6: Selected RSU comparison between opti-
mal and suboptimal solutions for the VANET sce-
nario. Max. No. of hops = 5.
Figure 7: Comparison between global and local op-
timal solutions for the VANET scenario. Max. No.
of GWs = 30. Max. No. of hops = 5.
there is a low connectivity among nodes. Regarding to the
optimal and suboptimal solution, the results show that the
suboptimal solution uses more gateways than the optimal
to cover an area or that the suboptimal solution does not
cover the sparest areas when there is a limit in the number
of gateways to be used.
Future work include to test the outputs of the models in
network simulators. Also, we are planning to use a matrix
of quality of links instead of and (0,1) adjacency matrix,
which will improve the realism of the solution in terms of the
multi-hop routing. A final work includes to find the minimal
cardinality kof the subsets in the suboptimal solution to get
the closest result to the optimal solution.
6. ACKNOWLEDGMENTS
This work was partly supported by the Spanish Govern-
ment through projects TEC2010-20572-C02-02 “CONSE -
QUENCE” and TEC2011-26491 “COPPI”. Luis Urquiza-
Aguiar and Andr´es V´azquez-Rodas are recipients of full schol-
arships from “Secretaria Nacional de Educaci´on Superior,
Ciencia y Tecnolog´ıa (SENESCYT)”and the“Escuela Polit´ec-
nica Nacional” and “Universidad Polit´ecnica Salesiana” re-
spectively (Ecuador). Carolina Tripp-Barba would like to
thank the support of the “Universidad Aut´onoma de Sinaloa
(Mexico)”. Ahmad Mezher is the recipient of a FI-AGAUR
grant, from the Government of Catalonia.
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