Towards combining admission control and link scheduling in wireless mesh networks

Abstract

Wireless mesh networks (WMNs) have emerged recently as a key solution for next-generation wireless networks; they are low cost and easily deployed technology. However, WMNs have to deal with a low bandwidth which prevents them from guaranteeing the requirements of applications with strict constraints. To overcome this limitation, we propose in this paper a new admission control model which integrates a dynamic link scheduling scheme, named ACLS, in order to optimize the network bandwidth use. We formulate the admission control problem as a binary linear programming problem (BL2P). The proposed admission control integrates an algorithm, based on the Dakin’s branch and bound (B&B) method, which respects the bandwidth and delay required by the flows. The proposed ACLS solution has been validated on ns2, and the simulation results showed that ACLS model has better performance than the reference solution BRAWN; it accepts more flows while guaranteeing their delay and bandwidth.

Full text

Telecommun Syst (2017) 66:39–54
DOI 10.1007/s11235-016-0273-0
Towards combining admission control and link scheduling in
wireless mesh networks
J. Dromard1·L. Khoukhi1·R. Khatoun2·Y. Begriche2
Published online: 9 January 2017
© Springer Science+Business Media New York 2017
Abstract Wireless mesh networks (WMNs) have emerged
recently as a key solution for next-generation wireless net-
works; they are low cost and easily deployed technology.
However, WMNs have to deal with a low bandwidth which
prevents them from guaranteeing the requirements of appli-
cations with strict constraints. To overcome this limitation,
we propose in this paper a new admission control model
which integrates a dynamic link scheduling scheme, named
ACLS, in order to optimize the network bandwidth use. We
formulate the admission control problem as a binary lin-
ear programming problem (BL2P). The proposed admission
control integrates an algorithm, based on the Dakin’s branch
and bound (B&B) method, which respects the bandwidth and
delay required by the flows. The proposed ACLS solution has
been validated on ns2, and the simulation results showed that
ACLS model has better performance than the reference solu-
tion BRAWN; it accepts more flows while guaranteeing their
delay and bandwidth.
Keywords Admission control ·Quality of service ·Wireless
mesh networks ·Link scheduling
BR. Khatoun
rida.khatoun@telecom-paristech.fr
J. Dromard
dromardj@utt.fr
L. Khoukhi
lyes.khoukhi@utt.fr
Y. Begriche
youcef.begriche@ieee.org
1University of Technology of Troyes, 12 Rue Marie Curie, BP
2060, 10010 Troyes, France
2Telecom Paristech, 46 Rue Barrault, 75013 Paris, France
1 Introduction
Wireless mesh networks (WMNs) introduce new opportu-
nities for wireless networks especially in smart cities [1]
where infrastructures utilizing thousands of sensors. Indeed,
they can, for a low cost, rapidly extend Internet access in
areas where cables’ installation is impossible or economi-
cally not sustainable such as hostile areas, battlefields, old
buildings, rural areas, etc. [2]. A WMN is made up of fixed
mesh routers (MRs) which relay the information of mesh
clients (MCs) from MR till reaching a gateway. Most WMNs’
studies assume that every node has a single antenna 802.11-
based [3–7]. Furthermore, IEEE has recently developed a set
of standards for WMNs (e.g., the IEEE 802.11s) [8], where
every node possesses a WiFi antenna [9]. In our study and
hereinafter, we only consider single antenna 802.11-based
WMNS, as it seems to be the most widely spread technol-
ogy. However, the lack of resources in these networks in
terms of bandwidth, limits their deployment. Indeed, the lack
of bandwidth, due mainly to the contention access to the
channel, may lead to unfairness between nodes and conges-
tion [7,10,11]. For example, in [12], the authors show that,
when the number nof nodes increases, the nodes’ through-
put of WMN decreases in O(1/n). Thus, WMNs may often
not respect the requirements of flows which have strict con-
straints. To solve this issue, many admission control (AC)
schemes have been proposed for WMNs [13–17].
An AC scheme aims at accepting a new flow in the network
only if its requirements and the requirements of still-active
previously admitted flows can be met [18–20]. However,
these solutions are limited in the number of flows they can
accept due to the WMNs’ lack of bandwidth. In order to
increase WMN’s capacity, multiple-antenna systems have
been proposed [21–24]. However, there are several reasons
for not using multi-antenna nodes; like the cost and size of
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40 J. Dromard et al.
nodes which must be often kept small and the minimum
required distance between the antennas of a multi-antenna
system [25]. Indeed, to have effective antennas on the same
node, they must be separated by a distance of more than half
a wavelength [25,26].
Thus, to improve WMNs throughput, we focus on link
scheduling (LS) schemes rather than multi-antenna systems.
In [27], the authors show, via simulations, that using an LS
scheme rather than IEEE 802.11 scheme can increase up to
three times a WMN’s throughput. LS scheme aims at assign-
ing, to each link, the slots during which a node can send
data without any risk of collision while maximizing the net-
work throughput. However, the scheduling often does not
evolve in time and with the network load. Indeed, a fixed
link scheduling may lead to a loss in the WMN throughput
use. Slots, which are not used by the links to which they are
assigned, are lost while they could be used by some other
links.
In order to take advantage of both AC and LS schemes, we
propose in this paper a new AC which integrates LS scheme.
Our idea is to make the network’s LS evolves each time a new
flow is admitted or leaves the network. The aim of our solu-
tion is to respect the delay and bandwidth of every admitted
flow while increasing the number of accepted flows compared
to existing admission controls. We note that the MAC proto-
col is changed to a synchronous time-based link scheduling
mechanism; only the physical layer of IEEE 802.11 standard
can be used. The contributions of this paper can be summa-
rized as follows:
•A modeling of the AC with LS problem as a binary linear
programming problem (BL2P).
•A new algorithm which solves the admission control with
LS problem and which is based on the Dakin’s branch
and bound (B&B) method [28]. This algorithm is, in the
following, denoted ACL2S for Admission Control with
Link Scheduling Solver.
•A complete solution of admission control with link
scheduling in a WMN, named ACLS.
To the best of our knowledge, our proposed ACLS is
one of the first works integrating two separate concepts:
admission control and link scheduling. The remainder of
the paper is organized as follows. In the following section,
we present a brief state of the art in the admission control
and link scheduling fields. In Sect. 3, we propose a mod-
eling of the WMN. Then, the admission control problem
with link scheduling is modeled as a binary linear program-
ming problem. In Sect. 5, we introduce a new method to
compute flows’ delay, knowing their scheduling. Then, we
present ACL2S, an iterative algorithm based on Dakin’s
B&B method which solves our admission control problem.
In Sect. 7, we describe the implementation of our admission
control with link scheduling. Finally, we display the results
obtained via simulations on ns2 and then we conclude the
paper.
2 Related work
In this section, we present related work in both link schedul-
ing and admission control fields. We also introduce some
existing works joining both admission control and link
scheduling concepts. Link scheduling schemes allows to
guarantee collision-free transmissions and increase the band-
width use [27]. They select, for each link in the network, the
slots in a frame during which the link is periodically activated.
The selection process aims at ensuring interference-free
transmission and at maximizing the network throughput [29].
To avoid collisions, LS schemes employ an interference
model in order to identify the links that could be activated
simultaneously without causing any interference issue. The
problem of maximizing the throughput in WMNs using the
link scheduling is known as a NP-hard, even with a sim-
ple interference model [30]. LS schemes can be classified,
according to the interference model they are based on. It
is usually either (1) a hop-based (e.g., [30,31]), or (2) a
distance-based (e.g., [32,33]), or (3) a SINR-based interfer-
ence model (e.g., [27,34–36]).
With the hop interference model, a node can transmit suc-
cessfully, if no node, situated at k-hops or more from it, is
activated at the same time. The authors in [27,31,37] propose
LS scheme based on the hop interference model. In [27], the
authors formulate the k-hop interference model as a k-valid
matching problem using graph theory. The authors develop
LS scheme based on a greedy algorithm which computes sets
of independents maximum k-valid matching in the network
graph. A maximum k-valid matching is the maximum set of
edges which are at least k-hops from each other. According
to the k-hop interference model, the nodes of such a set can
be activated simultaneously without any risk of interference.
Nonetheless, this model can only be deployed to a limited
number of topology.
In a distance-based model, a transmission succeeds if the
distance between the transmitter and the receiver is smaller
than or equal to the communication range Rcand if no
other node is transmitting in the interference range Riof
the receiver [32,35] (see Fig. 1).
In [33], the authors develop new models for calculating
upper and lower bounds on the optimal throughput for any
given network and propose an algorithm to schedule links.
Nevertheless, they assume that packet transmissions at the
individual nodes can be controlled and scheduled by an omni-
scient central entity, which is hard to achieve.
With the SINR-based interference model, a node can suc-
cessfully receive data if its SINR is greater than or equal to
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Towards combining admission control and link scheduling in wireless mesh networks 41
Fig. 1 It shows the communication range Rcand the interference range
Riof a link A–Busing the distance based interference model
a threshold which value depends principally on the physical
layer properties of the network card [29].
In [27], the authors propose a link scheduling model based
on a centralized polynomial time algorithm using the SINR-
based model interference. This algorithm schedules link by
link; each link is scheduled at slots such that the resulting
sets of scheduled transmission is feasible. To maximize the
network throughput, this algorithm aims at minimizing the
schedule length (i.e., at finding the shortest frame which
allows to schedule every link). However, the authors assume
that flows’ requirements are known a priori by the scheduling
module, which is an unrealistic assumption.
Some studies show that hop-based and distance-based
interference models allow low computation; nevertheless,
they can both accept flows that lead to interference and may
reject other flows that are interference-free [35,38]. Many
studies show that the SINR-based interference model is the
most accurate interference model; however, it is also the more
complex one [35,38]. In the works presented above, as in
most of existing works on link scheduling, the scheduling is
done in a static way. This means that the number of slots,
dedicated to each link, does not evolve in time and with the
network load. Thus, whether the network is loaded or not, a
link has always the same number of reserved slots which can
lead to congestion issues and a non-optimal bandwidth use.
An admission control scheme aims at accepting a new
flow in the network only when it can guarantee its require-
ments (often delay and bandwidth) and the requirements of
previously admitted flows. To decide whether a flow can be
accepted, an AC scheme evaluates whether each node, along
the path, can meet the new flows’ requirements. If it is the
case, it accepts the new flow; otherwise, it rejects it. One
of the distinctive features of an AC scheme is its method to
compute the available bandwidth of nodes [39]. In the AC
models developed in [6,39–41], the authors reported that a
node’s available bandwidth depends mainly on its channel
idle time ratio (CITR). A node’s CITR is equal to the frac-
tion of idle time of its carrier sensing range multiplied by
the capacity of its channel. However, considering only the
CITR may lead to an inaccurate estimation of the available
bandwidth. Indeed, sending a packet when a node’s channel
is idle does not guarantee an interference free transmission
due mainly to hidden nodes.
To overcome this issue, the authors in [41] propose a
probabilistic approach to estimate the available bandwidth
of a node which does not trigger any overhead and which
considers the node’s CITR and hidden terminals. Upon this
available bandwidth estimation, an Admission Control Algo-
rithm (ACA) is developed to differentiate QoS levels for
various traffic types.
In [42], the authors design a fuzzy decision-based multi-
cast routing resource admission control mechanism (FAST).
In FAST, once every node on a flow path has accepted the
flow in terms of bandwidth, the source node takes the final
decision to accept or not the flow according to the result of a
fuzzy-decision scheme. The fuzzy-decision scheme consid-
ers delay, jitter, packet loss, and bandwidth. The validation
of this solution shows good performance; nevertheless, the
authors do not explain how they obtain the values of the QoS
parameters used in their fuzzy decision scheme.
In [43], the authors propose IAC, an Interference-aware
Admission Control for WMNs. The originality of IAC lies
in a dual threshold based method to share the bandwidth
between neighboring nodes. However, this method cannot
deal with multi-rate nodes and does not consider the option of
parallel transmissions which may lead to an under-estimation
of the nodes available bandwidth.
It is worth noting that most of the proposed AC schemes
are based on CSMA/CA standard. The latter is well known
to lead to poor throughput [27]. Indeed, CSMA/CA triggers
interference and dedicates a huge amount of time to avoid
collision (via the backoff algorithm and the RTS/CTS mech-
anism). To overcome these issues, few solutions integrate
both AC and LS schemes [8,18,44,45].
For example, the IEEE 802.11s standard [8] proposes
the protocol mesh coordinated channel access (MCCA). In
MCCA, nodes can reserve future slots in advance for their
flows. To reserve a slot for a transmission, a node must first
check if no node situated at two hops from it or from its
receiver has already reserved the slot. However, MCCA may
suffer from collisions due to the hidden nodes problem [4]
and does not specify any link scheduling algorithm [3].
In a previous work [44], we proposed to integrate link
scheduling in an admission control scheme. The link schedul-
ing scheme we proposed, is totally distributed among the
WMN’s nodes and is based on the distance-based interfer-
ence model. A flow is admitted, if there exists a path ensuring
that every node is able to compute a link scheduling for this
flow while guaranteeing its demands in terms of bandwidth.
However, this solution generates an important overhead due
to the broadcast of advertisement packets. In [18], we pro-
posed a solution which integrates both an AC and LS scheme
based on SINR-based interference model. In this solution, the
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42 J. Dromard et al.
Fig. 2 Power graph
AC is performed at the gateway. When a flow is accepted, the
gateway informs nodes on the flow path of their new schedul-
ing. However, this solution lacks of a theoretical background;
furthermore, it has not been evaluated and compared to exist-
ing AC solutions.
3 Network model
We represent the WMN by a power graph (see Fig. 2). The
power graph is denoted G(V,E,f), where Vrepresents the
set of nodes in the WMN, Eis the set of directed links in the
network and fis a function. Each node uhas a directed link
to every node v∈V−{u}in the network denoted (u,v),
where uis said to be the sender and node vthe receiver. Every
node u∈Vhas also a loop denoted (u,u). The function
f:E→Rassociates to each link e=(u,v),avalue
which represents, when u= v, the power Puvat which v
receives a signal from u, and when u=v, the noise power
Nuat the node u. This graph can be represented by a matrix
Pofsize|V|∗|V|where each element:
pij =Pij if i= j
Niif i=j
We introduce also two other matrices, which are both of
size |E|·|V|; the senders’ matrix Lsand the receivers’ matrix
Lr. Each element ls
ij of the senders’ matrix is equal to:
ls
ij =1 if node jis the sender of the link ei
0 if node jis not the sender of the link ei
Each element lr
ij of the receivers’ matrix is equal to:
lr
ij =1 if node jis the receiver of the link ei
0 if node jis not the receiver of the link ei
With the previous introduced matrices, we can compute
the power Pvuat which a node ureceives a signal from a node
v, knowing that vsends its data over the link ei=(v, z)and
node uis link ej’s receiver:
Puv=ls
i.·P·t(lr
j.)(1)
lr
j.represents the jth row of the matrix Lr, and ls
i.,theith row
of the matrix Ls. Furthermore, t(lr
j.)is the transpose of the
vector lr
j..Thereafter, we denote t(A) the transpose of a matrix
or a vector A. We assume that time is divided in frames made
up of Nslots. There are Ncslots of competition and Nsslots
of scheduling with N=Nc+Ns. The first Ncslots of a frame
are used to send control packets. The access mode used for
packets of control is based on competition. The Nsfollowing
slots are used to send data packets, and the access mode is
based on scheduling. We assume that all data packets have the
same length and are sent at the same frequency. Thus, every
packet of data and their acknowledgment (ACK) have the
same transmission time. A length of a slot is equal to the time
of transmission of a packet of data plus its acknowledgment
(ACK).
Each flow frequires a certain delay and bandwidth. A
flow is admitted along a path pfif a scheduling, respect-
ing the flow’s delay and bandwidth, is found. Thus, a flow’s
requirements is associated to a triplet af=(Nf,df,pf),
where Nfrepresents the number of slots per frame which
are required by the flow to respect its bandwidth, and dfis
the delay the flow requires. The path pfof a flow fis an
ordered list of links, where the ith element of the list is the
ith link on the flow path. When a flow is admitted along a
path pf, it is then associated to a scheduling matrix, denoted
Sfof size |E|·|Ns|. This matrix indicates for every link on
the flow fpath the slot(s) during which it can send the flow.
An element sf
ij of a matrix Sfis equal to:
sf
ij =⎧
⎪
⎪
⎨
⎪
⎪
⎩
1ifthe(Nc+j)th slot is reserved by
link eito send a packet of flow f
0ifthe(Nc+j)th slot is not reserved by
link eito send a packet of flow f
The network scheduling is represented by the matrix Sof
size |E|·|Ns|. This matrix is the sum of the scheduling matrix
of every flow fadmitted and still active in the WMN, thus:
S=
∀f∈F
Sf(2)
with Fthe set of admitted and still active flows in the network.
In the following, each element of matrix Sis denoted sij.
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Towards combining admission control and link scheduling in wireless mesh networks 43
4 Modeling of the admission control with link
scheduling problem as a BL2P
Aflow fis admitted along a path pfif a matrix Sf
can be found which respects a set of constraints among
which the flow requirements described by the triplet af=
(Nf,df,pf). In the following, we present the six different
constraints the matrix Sfmust respect. First, the matrix Sf
must respect the flow constraint in terms of number of slots
per frame required by the flow, and therefore the following
constraint:
∀i,ei∈pf,Nf=
j=Ns

j=1
sf
ij (3)
Furthermore, a slot can only be scheduled once by a link.
Therefore a link eican be, for a slot j, either scheduled (then
sij =1) or not (then sij =0). The second constraint can be
expressed by the following formula:
∀i,ei∈Eand∀j∈[1,Ns],sij +sf
ij ≤1(4)
Furthermore, every link, not belonging to the path of the
flow, does not need to reserve any slot for the flow; thus, the
matrix Sfmust also respect the third following constraint:
∀i,ei/∈pfand ∀j∈[1,Ns],sf
ij =0(5)
During each slot reserved by a link (u,v), a packet of data
is sent from uto vand an acknowledgment is then sent from
vto u. As many research works (e.g., [38,46]) have shown
that the SINR model is the most realistic interference model,
we have decided to apply this model in our work. A node u
can transmit with success, according to the SINR model, a
packet to a node v, while there is a set of simultaneously
activated links in the network, if:
Puv
Nv+∀(w,z)∈−{(u,v)}Pwv
≥β(6)
βrepresents the SINR threshold, its value depends mainly
on the physical layer technique and the decoding strategy
used [47]. The links must be scheduled so that no link inter-
feres with another according to the SINR model. To reach this
goal, at every slot j, the power at which the receptor of a link
ei, scheduled at slot jreceives the signal from the link ei’s
sender, divided by the sum of the noise and the interference
at the receptor, must be superior to the SINR threshold. The
power, at which the receptor uof a link eireceives the signal
from its sender v, is equal to puv(the element of index uvof
the power matrix P). According to Eq. 1, this power equals
to ls
i.·P·t(lr
i.). Furthermore, the noise at the node uequals
to puu, and therefore to the element of index uu of the power
matrix P. The noise can consequently be obtained by the fol-
lowing formula: lr
i.·P·t(lr
i.). Furthermore, a link sends data
at a slot jif it is scheduled at that slot, i.e., if sij +sf
ij =1.
The interference at link ei’s receptor equals to the sum of
the powers at which its receptor receives the signal from all
the senders of the links which have reserved the same slot j,
i.e., the set of links ez∈Esuch as szj +sf
zj =1 minus the
link ei. The interference at the receptor of link eican be thus
expressed as follows: ∀z,ez∈E−{ei}(szj+sf
zj)·ls
z.·P·lr
i.. Thus,
the matrix Sfmust respect a fourth constraint expressed by
Eq. 7so that every packet of data is received successfully:
∀i,ei∈Eand j∈[1,Ns]
(sij +sf
ij)·ls
i.·P·t(lr
i.)+·(1−(sij +sf
ij))
lr
i.·P·t(lr
i.)+∀z,ez∈E−{ei}(szj +sf
zj)·ls
z.·P·lr
i.
≥β
(7)
is a large positive integer which magnitude will be dis-
cussed later in this paper. It is introduced so that, when a
slot jis not reserved by a link ei,the formula remains true.
Furthermore, the receptor of every link eimust also send
an acknowledgement to the sender after having successfully
received a packet of data. To insure that acknowledgement
arrives successfully at the sender of link ei, the matrix Sf
must also respect a fifth constraint expressed by the follow-
ing inequality 8.
∀i,ei∈Eand j∈[1,Ns]
(sij +sf
ij)·lr
i.·P·t(ls
i.)+·(1−(sij +sf
ij))
ls
i.·P·t(ls
i.)+∀z,ez∈E−{ei}(szj +sf
zj)·lr
z.·P·ls
i.
≥β
(8)
In Inequalities 7and 8,βis the SINR threshold of both
nodes iand j. We assume here, for simplicity, that their SINR
threshold is equivalent. However, our solution stays true even
with nodes with different SINR threshold. Furthermore, as
explained previously, is introduced so that, when a slot j
is not reserved by a link eithe formulas stay true. is a large
positive number which magnitude is estimated as follows.
It must be larger than the product of βand the sum of the
noise and the interference noise at the link ei’s receiver for
the Inequality 8and the link ei’s receptor for the Inequal-
ity 7. The magnitude of depends mostly on the value of
the nodes’ physical layer. If we assume that the power at
which each node sends a packet is about 100 mW, that the
SINR is about 10 dbm and that there is, at most, 100 nodes
active simultaneously and if we don’t consider the attenua-
tion due to the distance and the thermal noise, which is often
small compared to the nodes’ transmit power, can be set to
105(100 ∗100 ∗10). However, to insure that both equations
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44 J. Dromard et al.
stay always true, we advise a margin of magnitude 10 and so
aof at least 106.
A node v∈Vcannot be the sender and the receiver of
a link. Furthermore, a node v∈Vcan be the sender or the
receiver of many links; however, these links cannot be sched-
uled simultaneously, i.e., at the same slot j. For reminder,
a link eiis scheduled at slot jif sij +sf
ij =1 otherwise
sij +sf
ij =0 and vis the receiver or the sender of a link eiif
ls
iv+lr
iv=1. As every node vcannot be simultaneously the
receiver and the sender of a link and as no link scheduled at
the same slot jcannot possess a node in common, the matrix
Sfmust respect a sixth constraint expressed by the following
formula:
∀v∈Vand∀j∈[1,Ns],
i=|E|

i=1
(sij+sf
ij)·(ls
iv+lr
iv)≤1(9)
Finally, finding a scheduling for a new flow fwhich
respects its required bandwidth along a path pf, when the
delay constraint is not taken in account, can be formulated as
a BL2P which objective is to find the elements of the matrix
of scheduling Sfwhich minimizes the number of reserved
slots. The BL2P can be expressed as follows:
Minimize
i=|E|

i=1
j=Nf

j=1
sf
ij with s f
ij abinaryvari able (10)
while respecting the constraints represented by Eqs. 3,4,5,
7,8and 9. Equation 10 is the objective function of the BL2P,
and the value obtained with this function, for a given matrix
Sf, is the objective value.
5 Delay of a flow
This section is divided in four parts. In the first one, we
propose an algorithm to compute the queue length of each
intermediate node on the flow path at the beginning of every
frame. In the second part, we introduce a second algorithm
to compute the queue length of every intermediate node at
any slot of any frame m>1. In a third part, we propose a
method to compute the delay of a packet at a node. Finally,
in a fourth part, we introduce a method to compute a flow’s
delay.
The path pf=(l1...,ln)of a flow fis made up of
an ordered set of links which belong to E. They are ordered
such that every packet is first sent over l1then over l2,etc.We
denote ui, link li’s transmitter. We assume that each interme-
diate node on the flow path has a FIFO queue for the flow.
Each link li∈pfis associated to a Nf-uplet denoted f,i,
where each element f,i
j(j∈[1,Nf])represents the slot’s
Fig. 3 Node uihas reserved the slots number 1, 5 and 7 for the flow f
number of the jth reserved slot of node ui; these slots are
listed in an increasing order. For example, in Fig. 3, node ui
has reserved the slots number 1, 5 and 7 to send packets of
flow f; thus, f,i=(1,5,7),f,i
1=1, f,i
2=5, f,i
3=7
and Nf=3.
As we want to maximize the flows delay, we assume that
the rate is maximum. The rate is maximum when the source
node sends continuously a packet each time it can, i.e., at
each slot it is authorized to send a packet. Thus, to com-
pute the maximum flows delay, we make the two following
assumptions:
•Every node receives a packet at each slot reserved by its
previous node on the flow path.
•Every node, at the beginning of the first frame, does not
possess any pending packets of flow f.
Furthermore, we introduce the following two definitions:
•A packet’s delay is the sum of its delay at each node on
the flow’s path.
•The delay of a flow is the largest delay reached by one of
its packets.
5.1 Node’s queue length at the beginning of a frame
In the following, we denote by qf,i
m,z, the number of packets
of flow fthat node uihas in its queue at the beginning of
the slot z(or zth slot) of the mth frame. For example, we
note qf,i
2,1the queue’s length of an intermediate node uiat the
beginning of the first slot of the second frame.
Each node on the path of a flow f, except the destination,
possesses Nfslots scheduled for f. Thus, every interme-
diate node can forward all the Nfpackets it receives from
a neighbor during a frame before the end of the next one.
It can be concluded that no node possesses more than Nf
pending packets of fin its queue, and that every node can
forward a packet during either the current or the next frame.
For example, in Fig. 4, we can notice that node uireceives
two packets during the first frame. At the end of the first slot
of the second frame, it has forwarded both.
If node ui’s queue length is equal to qf,i
2,1at the beginning
of the second frame, it implies that among the Nfpackets
that uireceives during the first frame, it forwards Nf−qf,i
2,1
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Towards combining admission control and link scheduling in wireless mesh networks 45
Fig. 4 Node uiand ui−1reserved slots for flow fand Nf=2
of them. It also implies that the Nf−qf,i
2,1last reserved slots
of uiare each situated after a different reserved slot of ui−1.
That is why the Nf−qf,i
2,1first packets received by uiduring
the first frame can be all forwarded before the end of the
current frame. During the second frame, every intermediate
node uion the flow path receives Nfnew packets and sends,
during its first qf,i
2,1reserved slots, the qf,i
2,1pending packets it
had at the beginning of the frame. It has then still Nf−qf,i
2,1
last reserved slots available in the current frame. As we have
already proved, that the Nf−qf,i
2,1last reserved slots of ui
are each situated after a different reserved slot of ui−1;this
implies that uican send Nf−qf,i
2,1packets among the Nfit
has received during the second frame. This means that node
uihas, at the beginning of the third frame, again qf,i
2,1pending
packets. We can thus deduce that, from the second frame:
•Every intermediate node ui’s queue length, is the same
at the beginning of each frame.
•Every intermediate node uisends a packet at each
reserved slot.
We propose the Algorithm 1to compute, for any intermediate
node uion the path flow, the number of packets it has at the
beginning of the first slot of the second frame and so of every
following frame. This algorithm relies on the fact that (1) the
preceding node of ui−1sends a packet at each of its reserved
slot, (2) uiforwards a packet at each of its reserved slot only
if it has any pending packet in its queue, and (3) it has no
pending packet at the beginning of the first frame.
5.2 Node’s queue length at any slot
At the ( f,i−1
j)th slot of the mth frame (m>1), a node
ui’s queue length equals to the number of pending packets it
had at the beginning of the frame (i.e., qf,i
2,1) plus the number
of packets it has received since the beginning of the frame
from ui−1(i.e., j−1) minus the number (denoted w( j))of
packets it has already sent since the beginning of the interval.
Algorithm 1 Node ui’s queue length at the beginning of
every frame m>1
Require: f,iand f,i−1
1: initialize y=1andz=1
2: while z≤Nfdo
3: if f,i
z>f,i−1
yand z ≤Nfthen
4: y++and z++ uiforwards the packet received at the slot
number f,i−1
yat the slot f,i
z
5: elseuidoes not send any packet during the slot number f,i
z
because it has no pending packets
6: z++
7: end if
8: end while
9: qf,i
2,1=Nf−y+1number of received packets minus the
number of sent packets
10: return qf,i
2,1
It implies that an intermediate node uiqueue length, at the
( f,i−1
j)th slot of the mth frame (m>1), is equal to j−
1+qf,i
2,1−w( j). Thus, at every frame (after the first one), a
node’s queue length at slot jis always the same:
∀j∈[1;N]and ∀m>1,qf,i
m,j=qf,i
m+1,j(11)
The Algorithm 2returns the queue length of an interme-
diate node uiat the beginning of each reserved slot of its
previous node ui−1in the flow path. This algorithm relies on
the fact that (1) node uisends a packet at each of its reserved
slot, (2) uialso sends a packet at each of its reserved slot,
and (3) uihas qf,i
m,1pending packet at the beginning of the
frame.
Algorithm 2 Node ui’s queue length at the zth slot of any
mth frame (with m>1 and z=f,i−1
m,j)
Require: qf,i
m,1,j,f,iand f,i−1
1: initialize y=1
2: qf,i
m,z=qf,i
m,1+j−1uihas received j−1 packets since the
beginning of the frame and had qf,i
m,1pending packets since its begin-
ning
3: while y≤Nfand f,i
m,y<zdo
4: qf,i
m,z−− uisends a packet at the slot number f,i
m,y
5: y++
6: end while
7: return qf,i
m,z
5.3 Packet’s delay at a node
From the second frame, we have shown that every interme-
diate node sends a packet, at each of its reserved slot, and
forwards a packet received at slot j, always at the same slot.
If an intermediate node uion the flow path receives a packet,
at the ( f,i−1
j)th slot of the mth frame (with f,i−1
j=z)
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46 J. Dromard et al.
Fig. 5 Node uiand ui−1’s scheduling
while it has in its queue qf,i
m,zpending packets of f,itforwards
it at the slot f,i
x, such as:
x=⎧
⎪
⎨
⎪
⎩
φf
i(j)+qf,i
m,zif φf
i(j)+qf,i
m,z
is inferior or equal to Nf
(φ f
i(j)+qf,i
m,z)%Nfelse
(12)
The function φf
i:[1,Nf]→[1,Nf]returns, for an
index j≤Nf, the index of the first reserved slot of link ui
situated after the slot f,i−1
j. To illustrate this formula, we
propose the following example (see Fig. 5). The figure shows
the scheduling of two intermediate nodes on the flow path f:
nodes ui−1and ui. We can also observe that Nf=3. From
Algorithm 1, we can compute the queue length of uiat the
beginning of the second frame and at the beginning of every
frame except the first one; we get qf,i
m,1=2 when m>1.
At the beginning of the first reserved slot of node ui−1(the
slot number 2), ui−1starts sending a packet to node ui,ui
has then in its queue one pending packet (qf,i
m,2=1) as it has
sent a packet at its first reserved slot which is the first slot of
the frame.
From Fig. 5, we can observe that the index of the first
reserved slot of link ui, which is situated after the first
reserved slot of node ui−1, is 2 (i.e., φf
i(1)=(2)). Thus,
according to Formula 12,asφf
i(1)+qf,i
m,2=3 and 3 ≤Nf,
we can assert that uiforwards the packet it has received, at
the slot number 2, from node ui−1at its third reserved slot,
i.e., at the slot number f,i
3=7.
In the following, we denote by ϕf
i:[1,Nf]→[1,Nf],
the function which returns for a given value j,thevalueof
the index x, such as when ei−1sends a packet at the f,i−1
j
of the mth frame (m≥2), uiforwards it at the slot f,i
xof
the current or the next frame.
Thus, from the second frame, the delay of a packet at an
intermediate node can take Nfdifferent values according to
the slot at which its arrives at that node. The delay (in slots) at
an intermediate node ui, for a packet arrived at the ( f,i−1
j)th
slot of the mth frame (m≥2), is:
df
i(j)=f,i
x−f,i−1
jif the result is positive
N−f,i−1
j+f,i
xelse
(13)
the value xis computed with Eq. 12.
5.4 Flow’s delay
In the previous section, we have proposed a formula which
computes the delay of any packet at any intermediate node
uiof any frame (except the first one). We denote df
i(j),the
delay of a packet at a node uiwhen it receives the packet at
the jth reserved slot of its preceding node on the flow path,
this delay is computed with Formula 13. Thus, the packet at
a node can take only Nfdifferent values. Furthermore, as
each node, from the second frame, always forwards a packet
it receives at the jth slot at the same xth slot, then the delay of
a packet along the path can also only take Nfdifferent values.
From the second frame, the delay of a packet depends on the
slot at which the source (node u1) sends it. If it sends it at the
( f,1
j)th slots, the packet’s delay (in slots) is:
df(j)=df
2(j)+df
3(ϕ f
2(j)) +··· +df
n(ϕ f
n−1(...ϕ f
2(j))
(14)
As a reminder, we denote ϕf
i:[1,Nf]→[1,Nf],the
function which returns for a given value j, the value of the
subscript x, such as when ui−1sends a packet at the f,i−1
j
of the mth frame (m>1), uiforwards it at the slot number
f,i
xof the current or the next frame. In Eq. 14, as the delay
of a packet at the source (node u1) and the destination (node
un+1) is assumed to be null, there is no delay computed at
these nodes. Finally, the maximum delay of a flow is the
maximum delay that a packet can reach:
df=max
i∈[1,Nf](df(i)) (15)
6 A modified branch and bound algorithm
In this section, we propose an algorithm, named ACL2S,
which solves the admission control with link scheduling
problem. ACL2S is an iterative algorithm which inte-
grates a modified version of the Dakin’s branch and bound
(B&B) method [48] (MB&BA). In this section, we first
describe ACL2S’s iterative algorithm. Then, we introduce
the MB&BA (i.e., our modified version of the Dakin’s B&B
method).
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Towards combining admission control and link scheduling in wireless mesh networks 47
6.1 ACL2S’s iterative algorithm
ACL2S is an iterative algorithm. At each iteration, in a first
step, it solves the BL2P problem thanks to our MB&BA. Our
MB&BA returns a scheduling for the flow with a low delay.
In a second step, our algorithm verifies whether the delay
of the returned scheduling guarantees that the flow’s delay
is inferior or equal to the required maximum delay. If it is
the case, the scheduling is accepted and the algorithm stops;
otherwise, the algorithm returns to the first step after having
modified the BL2P so that the previous obtained scheduling
are no longer solutions of the problem. To modify the BL2P,
new linear constraints are added to the problem; in other
words, a binary cut is performed on the initial problem. The
algorithm returns then to the first step. The algorithm stops
when (1) one scheduling respects the required delay, or (2)
the number of iterations is superior to a certain threshold β,
or (3) when the MB&BA does not find any longer a solution
to the BL2P. The ACL2S is summarized in Fig. 6.
6.2 MB&BA: a modified version of the B&B algorithm
The Dakin’s B&B algorithm enables to solve linear program-
ming problems and, among others, BL2P. This algorithm
systematically enumerates all feasible solutions of the prob-
lem where large subset of candidates are discarded by using
lower and upper estimation bounds of the quantity being opti-
mized which is, in our case, the quantity obtained with Eq. 10.
The B&B method integrates an algorithm which solves the
linear programming problem. In the following, we have cho-
sen the Simplex method as the underlying method to solve
the linear programming problem as it is a simple and yet effi-
cient solution [49]. To solve a BL2P, which for example has
to return a matrix Sfof size |V|∗|Ns|of binary elements, the
Dakin’s B&B method first initializes z∗the lower bound of
the objective function. z∗is equal to the first integer superior
or equal to the objective value of the solution obtained for
the relaxed BL2P with the Simplex method. A relaxed BL2P
does not consider the binary constraint of the solution. The
Dakin’s method also initializes the upper bound of the solu-
tion zat +∞. Then, it creates a first node which is the root
of a tree. This node is activated and associated with (1) the
original BL2P, (2) the solution Sfobtained with the simplex
method over the relaxed BL2P, and (3) the objective value z
of the solution Sf. Then, the algorithm performs iteratively
the following steps.
1. It chooses an activated node and creates two child nodes.
2. Each child is activated and is associated with the BL2P
of its parent node at which a constrain is added. The
added constraint is chosen as follows. An element sf
ij
of its parent solution Sf, which does not have a binary
Algorithm 3 MB&BA: Modified Branch and Bound Algo-
rithm
Require: BL2P
1: z=+∞
2: Set the first active node u0of the tree, assign it the BL2P, its solution
matrix Sf
0and its objective value z0
3: z∗= first integer superior or equal to z0
4: while there are still active nodes and no node has a binary matrix
which objective value is z∗do
5: Select an active node uxin the tree, its associated matrix is Sf
x
6: Create two child nodes to ux
7: Select a variable sij such as eiis the first link of the flow path
which number nof reserved slots is inferior to Nfand which every
preceding link of the flow path has more reserved slots.
8: If ei= l1, find the slot situated after the n+1th reserved slots of
links lz−1which is not binary for link eiand initialize jto this slot
number.
9: If ei=l1, then choose randomly jsuch as sij is not a binary
element in Sf
x. If it is not possible to find such an element, return
to line 4 and deactivate the two child nodes.
10: Associate, to each child node, the BL2P of uxwith an added
constraint; sf
ij =1 for the first node and sf
ij =0 for the second
11: for each child uyof uxdo
12: Solve its relaxed BL2P
13: if its relaxed BL2P has a solution then
14: Assign it its objective value zyand its solution matrix Sf
y
15: if zy=z∗and Sf
ybinary then
return Sf=Sf
y
16: else if zy>zthen
17: Deactivate node uy
18: else if zy<zand Sf
ya binary matrix then
19: z=zy
20: end if
21: end if
22: end for
23: end while
24: if z== +∞ then return Sf=null
25: else return binary matrix Sf
26: end if
value, is arbitrarily chosen. The first child node’s added
constraint is sf
ij =0, whereas the second child node’s
added constraint is sf
ij =1.
3. The Simplex algorithm is performed for each relaxed
BL2P of the two child nodes. If the Simplex returns no
solution for one child node, this latter is deactivated.
4. The solution returned by the Simplex and its associated
objective value zis assigned to each child node.
5. If every element of the solution of one child node is binary
and if z<z, then ztakes the value z. If a node has a
binary solution then it is deactivated. Finally, the algo-
rithm returns to step 1.
B&B stops either when one node has a binary solution whose
objective value is equal to z∗(which is a solution of the
BL2P), or when there is no more activated node. If there is
no more activated node and if z=+∞, there is no solution
to the problem. If there is no more activated node and if
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48 J. Dromard et al.
Fig. 6 ACL2S
z=+∞, then the BL2P’s solution is the binary solution
which objective value is equal to z.
We enhanced the algorithm so that the constraint added to
each child node guarantees that the solution, returned by the
algorithm, offers a low delay for the flow. To reach this goal,
the proposed algorithm selects, for each intermediate node
on the flow path, slots which are as close as possible from
the scheduled slots of the previous node on the flow path and
situated after these latter. Thus, a packet does not wait long
at a node. As a reminder, the path of a flow fis denoted
pf=(l1,l2...,ln). The MB&BA chooses the element sf
ij
at the step 2 such as:
•it is not a binary element of the parent matrix Sf,
•the index iof sf
ij refers to a link ei∈pf(ei=lz) and ei
must be the first link over the flow path which has the less
reserved slots and its number nof reserved slots must be
inferior to Nf,
•if eiis l1, then the value jof the index sf
ij is randomly
chosen; otherwise, jis equal to the first slot situated after
the n+1th reserved slot of link lz−1for which sf
ij is not
binary at the parent matrix Sf.
If no element sf
ij can be found, the algorithm deactivates the
two current child nodes and returns to step 2. The matrix
Sfreturned by the algorithm represents a scheduling for the
flow. This scheduling guarantees a low delay while respect-
ing the bandwidth required. The Algorithm 3summarizes
our MB&BA. However, even if this scheduling guarantees a
low delay, it does not guarantee that this delay is inferior or
equal to the maximum delay that the flow requires, so that
the MB&BA must be integrated in the ACL2S. Finally, the
ACL2S algorithm admits a flow if it can return a scheduling
which respects the flow constraints in terms of bandwidth
and delay; otherwise, the flow is rejected.
7 Admission control with link scheduling
In our solution, the gateway decides the scheduling of every
flow accepted in the WMN. It stores active flows scheduling
using the scheduling matrix denoted S and described in Eq. 2
of Sect. 3. Therefore it has a global state information on the
network and can decide whether it accepts or rejects a new
flow. Every node in the network stores only a local state
information on the network describing the scheduling of its
links. Therefore, it only knows the slots during which it can
activate a link to send packets for a specific flow.
Our solution relies on a reactive routing protocol like the
Ad hoc On-Demand Distance Vector (AODV) Routing [50]
and takes advantage of the two main messages of any reac-
tive routing protocol; the route request (RREQ) and the route
response (RREP) packets. As in the famous Resource Reser-
vation Protocol-Traffic Engineering (RSVP-TE) [51], our
solution reserves resources across a network for a flow by
sending two packets; a modified RREQ and RREP. We have
modified the RREQ sent by the source to the destination,
in order that it contains the flow’s requirements, like in the
123

Towards combining admission control and link scheduling in wireless mesh networks 49
RSVP-TEs Path message. Furthermore, we have modified
the RREP, sent by the destination to the source, so that it
reserves enough resources for the flow along the path taken
by the RREQ, like in the Resv message of the RSVP-TE.
The admission control process takes place in three steps; (1)
the admission control request, (2) the admission control, and
(3) the admission control reply.
7.1 Admission control request
The node, which receives a request to admit a flow, broadcasts
a modified RREQ where it indicates, the minimum band-
width and the maximum delay required by the flow. Every
node, which receives the packet, checks whether it has not
already received it and if its time to live has not expired. If
this fails, then the node drops the packet; otherwise, it adds
to it its ID before re-broadcasting it. This scheme goes on till
the RREQ reaches a gateway.
7.2 Admission control
Every gateway knows the matrix scheduling of the network S,
the receivers matrix Lr, the senders’ matrix Ls, the power of
the network’s matrix Pand every matrix of flow scheduling.
All gateways of the network exchange their matrices so that
they all have up-to-date matrices. When a gateway does not
receive any packet of a flow, since a time t, it deletes its
scheduling matrix and its entry in the network scheduling
matrix and then informs the other gateways of the network.
When a gateway receives a RREQ, it extracts from this packet
the bandwidth and the maximum delay required by the flow.
It then launches the ACL2S in order to find a schedule for the
flow along the path followed by the RREQ. If a schedule is
obtained, then it ignores the following RREQs it receives for
the flow. It then unicasts a packet, a modified RREP, along
the selected path where it indicates the scheduling of the new
accepted flow.
7.3 Admission control reply
Upon receiving a RREP, a node extracts from the packet its
scheduling for the flow. When the source node receives the
RREP, it starts sending the packets of the flow. If the source,
after a certain time, does not receive any RREP, then the
source rejects the flow which is then not sent on the network.
If a node does not receive, for a time t, any packet of the flow,
then it deletes the scheduling of the flow. t’s value is propor-
tional to the rate required by the flow and to the packets’
payload. For example, if a flow requires a rate of 96 kbit/s
and if the packets payload is 1000 bytes, then a node on the
flow path should receive in average one packet every 84ms.
For safety reason, the value of tis fixed as ten times the aver-
age time between each packet, so that, the flow’s schedule is
still active after a short and temporary failure. Thus, in the
example presented below, the value of tis 840 ms.
To summarize, when the WMN gateway receives a request
RREQ to admit a new flow, it performs the ACLS algorithm.
The RREQ packet specifies the flow requirements in the form
of a triplet. This triplet defines respectively the number of
slots per frame, the path and the minimum delay required for
the flow. The gateway uses the ACLS algorithm to decide
whether it can fulfill the flow requirements and outputs a
scheduling for the flow. It sends a RREP message along the
reverse path of the RREQ packet specifying whether the flow
is accepted or not. If the flow is accepted, the RREQ packet
specifies the flow scheduling. Every node along the path
receiving RREP learns its scheduling for the flow. When the
flow starts every node along the path sends the flows packets
at the slots reserved for that flow.
8 Performance evaluation
To validate our model, we have implemented it on the event-
driven simulator ns2 [52]. We have performed important
changes on MAC modules of ns2 and more precisely on
the Mac802.11Ext DropTail, and network classes. In order
to solve the ACLS algorithm, the network module uses the
GNU Linear Programming Kit [53], which is a package for
solving large-scale linear programming. We have performed
a cross layer between the queue and network modules so that
the queue module is aware of the scheduling of a node. Thus,
the queue module sends a packet of data to the MAC module
at the beginning of the slot scheduled for the packet’s send-
ing. Furthermore, the backoff procedure of the MAC module
has been modified for every packet of data, so that it sends a
packet of data directly after having received it from the queue
module. We have chosen to compare our solution ACL2S
with BRAWN admission control model [54]. BRAWN is
based on the computation of the available bandwidth by each
node in the network. BRAWN’s implementation on ns2 sim-
ulator is freely available on the Internet [55]. We choose to
compare our solution to BRAWN for two reasons:
•as BRAWN is a simple and yet mature and effective
admission control solution.
•in order to show the performance difference between
our admission control which relies on a link scheduling
scheme and an efficient admission control which relies
on CSMA/CA.
We compared these solutions in terms of delay, through-
put and aggregated throughput according to two network
topologies: linear and cross (see Figs. 7,8), where nodes
are separated from each other by 90 meters.
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50 J. Dromard et al.
Fig. 7 A linear topology made up of 11 nodes; one of which (i.e., node
5) is a gateway
Fig. 8 A cross topology made up of 13 nodes; one of which (i.e., node
0) is a gateway
Tabl e 1 Simulation parameters
Layer Parameters Values
Physical layer One antenna per node
Carrier sensing layer 6.31e−9mW
Frequency 2.4 GHz
Transmission power 100 mW
Rate 54 Mbit/s
MAC layer Tslot 250 µs
RTS/CTS mechanism Off
Nfor the linear topology 164
Nfor the cross topology 172
Transport layer UDP size packet 1000 bytes
The parameters used for the simulations are quite usual
and are presented in Table 1. However, we introduced two
new parameters: Nrepresents the number of slots per frame
and Tslot is the length of a slot. Tslot is equal to the time
needed for a node to send a packet of data. Nhas been chosen
in order to maximize the performance of our solution; its
value is different according to the network topology.
For both topologies, each node sends a flow of 300 kbit/s
and requires a delay of maximum 150 ms. The nodes send
a request for their flows admission at one second of interval
from each other. Every node isends a request for its flow
at the end of the i+1th second unless it is a gateway. Fig-
ures 9and 10 show the throughput reached by each node of
the network (except the gateway) in a WMN with the linear
and the cross topology. We can observe that our solution,
with the linear topology, admits 9 flows out of 10 requests of
admission, whereas BRAWN admits 7 flows. ACLS, with the
cross topology, admits 10 flows out of 12, whereas BRAWN
Fig. 9 Nodes’ throughput in a WMN in a linear topology
Fig. 10 Nodes’ throughput in a WMN in a cross topology
admits 7 flows. Indeed, BRAWN admits less flow (it rejects
flows 4, 9, 10, 11, 12 for the cross topology and 1 and 10
for the linear topology) than our solution (it rejects flows 11
and 12 for the cross topology and flow 10 for the linear) as
it has less available bandwidth due to the use of the backoff
procedure which can be quite long and the retransmission
of many data packets due to collisions. Thus, for the cross
topology, we can assume that flows 9, 10, 11 and 12 were
rejected because there was no more available bandwidth on
the network when the requests to admit these flows were sent.
Indeed, the bandwidth has then been reserved for the flows
1, 2, 3, 5, 6, 7 and 8. We can also assume that flow 4 has not
been admitted due to the loss of its admission request.
Furthermore, we can notice that our solution, ACLS,
respects every flow’s expected throughput while it is not
always the case for BRAWN. For example, with the lin-
ear topology, the flow sent by node 9 does not reach its
expected 300 kbit/s. We can also observe that, with the cross
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Towards combining admission control and link scheduling in wireless mesh networks 51
Fig. 11 Flows’ delay in a WMN with a linear topology
topology, the flows sent by the nodes 5 and 6 do not reach
their expected throughput .We can assume that they do not
reach their required throughput due to collisions (BRAWN
is not collision free) and because the nodes, with BRAWN,
may overestimate their available bandwidth before accepting
these flows. Furthermore, we can notice on the cross topology
than flows 3, 8 and 9 have not totally reached their bandwidth,
it may be due to collisions or because some of their packets
are still in pending at intermediate nodes at the end of the sim-
ulation. Our solution reaches better performance in terms of
both throughput and number of admitted flows. Indeed, our
link scheduling scheme offers efficient use of bandwidth for
each node, thus the network can admit more flows. Further-
more, the proposed link scheduling scheme enables to avoid
collisions and unfairness compared to CSMA/CA and can
better guarantee the throughput of each admitted flow. The
problem of unfairness induced by CSMA/CA in WMNs has
already been observed in existing papers [7,10,56,57].
Figures 11 and 12 show the mean delay of each flow with
the linear and cross topologies. We can observe that ACLS,
in both topologies, always guarantees that the flows’ delay is
inferior or equal to the maximum delay required by the flow.
The maximum delay is represented by the red horizontal line.
In contrary, BRAWN does not respect the delay required by
each flow; when the source of the flow is far away from
the gateway, its delay is important. We can observe in both
topologies that, when the source of the flow is at three hops or
more from the gateway, the maximum delay of the flow is no
longer respected except for the node 2 in the linear topology.
However, the node 2’s delay in the linear topology is quite
high. The good performance in terms of delay of ACLS can
be explained by the fact that our model admits a flow if it can
respect both its delay and bandwidth, whereas BRAWN only
aims at respecting flows’ throughput. Furthermore, BRAWN
suffers from the unfairness of CSMA/CA.
Fig. 12 Flows’ delay in a WMN with a cross topology
Fig. 13 Aggregated throughput in a WMN with a linear topology
Figures 13 and 14 show the aggregated throughput with,
respectively, the linear and the cross topology. Our solution
shows better performance than BRAWN in both topologies.
We can also notice that, in both solutions and topologies,
the aggregated throughput increases with the number of
accepted flows till they cannot admit any more flow; then,
the throughput stays quite stable. In both topologies, the dif-
ference between the aggregated throughput of each solution
increases with the network’s load. Indeed, the more the net-
work’s load is important, the more CSMA/CA may lead to
collisions and large backoff timer. Furthermore, some studies
have shown that scheduling could improve the throughput of
the network [27,46] and this fact is also illustrated by these
results.
Finally, thanks to these results, we observe that ACLS
reaches its goal of admitting more flows than admission con-
trols based on CSMA/CA. Furthermore, it has also pointed
out that ACLS respects the bandwidth and delay of the admit-
ted flows, which may not always be the case of solutions
123

52 J. Dromard et al.
Fig. 14 Aggregated throughput in a WMN with a cross topology
based on a competition access. Indeed, the schemes which
rely on CSMA/CA may suffer from collisions and unfairness
between nodes.
9 Conclusions
We proposed a new admission control based on link schedul-
ing, named ACLS. It is, to the best of our knowledge, one
of the first works which integrates two separate concepts:
admission control and link scheduling. The idea is to make
the network scheduling evolves each time a new flow is
admitted in the network or stops being active. An original
method is proposed to compute the maximum delay that can
reach a flow according to its scheduling. We also modeled
the problem of admission control with link scheduling based
on bandwidth as a binary linear programming problem. We
introduced an iterative algorithm based on the Dakin’s B&B
method which aims at computing a scheduling for a new flow
which respects both its delay and bandwidth. Furthermore,
the proposed iterative algorithm is integrated in a complete
admission control scheme. The simulation results showed
that ACLS model has better performance than the reference
solution BRAWN. We believe that the proposed solution can
be easily implemented in real 802.11 WMNs. Indeed, (1) the
proposed solution is fully transparent to users and, (2) the
IEEE 802.11 amendment for mesh networking offers tech-
niques that allow nodes’ synchronization and time division
multiple access. As future work, we plan to consider different
flow types in the proposed model in order to provide QoS in
real networks.
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54 J. Dromard et al.
Dr. J. Dromard has received
her engineering degree in 2010
in Information and Telecommu-
nication Systems from the Uni-
versity of Technology of Troyes
(UTT). In 2013, she got a doc-
tor’s degree in Network, Knowl-
edge and Organization from UTT
for her thesis entitled “Towards
a secure admission control in a
wireless mesh network”s. She is
currently in post-Doctoral posi-
tion in LAAS-CNRS. Her re-
search interests are in the areas of
unsupervised network anomaly
detection, unsupervised machine learning techniques, big data, mesh
networks and admission control.
Dr. L. Khoukhi received the
Ph.D. degree in electrical and
computer engineering from the
University of Sherbrooke, Sher-
brooke, QC, Canada, in 2006. In
2008, he was a Researcher with
the Department of Computer Sci-
ence and Operations Research,
University of Montreal. Since
2009, he is an Assistant Profes-
sor with the University of Tech-
nology of Troyes, France. He
has more than 70 publications
in reputable journals and con-
ferences. His research interests
include vehicular networks, Machine-to-Machine Communications,
resources management, attacks detection, and communication proto-
cols.
Dr.R.Khatounreceived his M.
Sc in Computer Engineering and
the Ph.D from the University of
Technology of Troyes (UTT) in
France in 2004 and 2008. He is
currently associate professor at
Telecom ParisTech. His research
interests include DDoS attacks
detection and defense, intrusion
detection system, mobile ad hoc
networks security and computer
security infrastructure.
Dr. Y. Begriche received the
doctorat of appied mathemat-
ics from the university Paris
V in France in 1988. Since
2005 he teaches at the Paris-
Tech Institute (Paris) and par-
ticipates in research activities
in the department “informatique
et réseaux” (computer and net-
works) (INFRES) of the Paris-
Tech Institute. His area of
research is the application of
mathematics in the field of sci-
ence and technology informa-
tion, mobile, ad hoc and vehic-
ular networks.
123