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Int. J. Networking and Virtual Organisations, Vol. 12, No. 4, 2013
Economic model for routing and spectrum
management in cognitive wireless mesh network
Ayoub Alsarhan* and Ahmad Al-Khasawneh
Department of Computer Information System,
Prince Hussein Bin Abdullah II for Information Technology,
Hashemite University,
P.O. Box 150459, Zarqa 13115, Jordan
E-mail: [email protected]
E-mail: [email protected]
*Corresponding author
Awni Itradat
Department of Computer Engineering,
Faculty of Engineering,
Hashemite University,
P.O. Box 150459, Zarqa 13115, Jordan
E-mail: [email protected]
Mohammad Bsoul
Department of Computer Science,
Prince Hussein Bin Abdullah II for Information Technology,
Hashemite University,
P.O. Box 150459, Zarqa 13115, Jordan
E-mail: [email protected]
Abstract: In cognitive radio networks (CRNs), unlicensed users (secondary
users – SUs) lease free spectrum with quality of service (QoS) guarantees from
a multitude of spectrum owners (primary users, PUs) based on service level
agreements (SLA). Free spectrum is used to establish the links of secondary
network. The amount of leased spectrum influences the admitted number of
SU’s requests, PUs’ profits, and the cost of renting spectrum. Hence, the PU
can maximise its profit by adapting its resources to the changes in the traffic
load and SLA costs conditions. We propose a novel approach that maximises
PU’s profit using economic model. Our economic model integrates the network
routing with the adaptation of the capacity of secondary network links. For
SUs, QoS should be maintained while adapting the secondary network
capacity. Our adaptation scheme is based on the profit maximisation. The
Markov decision process (MDP) is used to derive the adaption scheme.
Numerical results show the ability of the proposed scheme to attain the optimal
profit under different conditions and constraints.
Keywords: cognitive radio network; CRN; spectrum resource management;
economic model; Markov decision process; MDP; wireless network.
Copyright © 2013 Inderscience Enterprises Ltd.
331
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A. Alsarhan et al.
Reference to this paper should be made as follows: Alsarhan, A.,
Al-Khasawneh, A., Itradat, A. and Bsoul, M. (2013) ‘Economic model for
routing and spectrum management in cognitive wireless mesh network’, Int. J.
Networking and Virtual Organisations, Vol. 12, No. 4, pp.331–351.
Biographical notes: Ayoub Alsarhan received his PhD in Electrical and
Computer Engineering from Concordia University, Canada in 2011, his MSc
in Computer Science from Al al-Bayt University, Jordan in 2001, and his BE
in Computer Science from the Yarmouk University, Jordan in 1997. He is
currently an Assistant Professor at the Computer Information System at
Hashemite University, Zarqa, Jordan. His research interests include cognitive
network, parallel processing, machine learning, and real time multimedia
communication over internet.
Ahmad Al-Khasawneh is an Associate Professor at Hashemite University
and is currently is acting Dean of Prince Al-Hussein bin Abdullah II Faculty
of Information Technology. He holds a PhD of Information Systems, MS in
Information Technology and Computer Engineering both from Newcastle
University, Australia and BS in Computer and Automatic Control Engineering,
Jordan. He has more than 40 published refereed articles in scholarly
international journals and proceedings of international conferences. He also
served on the editorial board of some international journals and as publicity
chair and technical programme committee member of several international
conferences and workshops.
Awni Itradat received his BSc in Computer Engineering from Jordan
University of Science and Technology, Jordan in 2000, and his Master and PhD
in Computer Engineering from Concordia University, Montreal, Canada in
2008. He is currently an Assistant Professor in the Department of Computer
Engineering, Hashemite University. In 2009, he was appointed as the Chairman
of the Department of Computer Engineering at the Faculty of Engineering in
the Hashemite University. He has also served as the Director of the Computer
Center in Hashemite University and, currently, working as the Director of the
ICT and E-learning Center in the Hashemite University. His research interests
include computer architecture and networks, design of VLSI circuits and
systems, interconnect modelling and design, reconfigurable circuits, and high
level synthesis of 3D- and 2D-circuits and systems.
Mohammad Bsoul is an Assistant Professor in the Computer Science
Department of Hashemite University. He received his BSc in Computer
Science from Jordan University of Science and Technology, Jordan, his Master
degree from the University of Western Sydney, Australia, and his PhD degree
from Loughborough University, UK. His research interests include wireless
sensor networks, grid computing, distributed systems and performance
evaluation.
1
Introduction
Spectrum scarcity problem is getting worse due to the unexpected explosion
in the number of the emerging web-based services. Users want to access the internet
anywhere-anytime. As a result, the frequency spectrum, especially the ISM band,
becomes congested while supporting these web-based applications. To utilise the
available spectrum efficiently, the concept of cognitive radio networks (CRNs) is
Economic model for routing and spectrum management
333
proposed to enable secondary users (SUs) to access the under-utilised portion of the
spectrum. SUs can access the unused spectrum using underlay, overlay or spectrum
trading approaches (Alsarhan and Agarwal, 2009, 2011a, 2011b; Pefkianakis et al.,
2008). In overlay and underlay approaches, SUs access the licensed spectrum without
paying any usage charge to the primary users (PUs). Their access is allowed as long as
their usages do not harm the PUs. For example, in IEEE 802.22, SUs can access to the
TV bands. Although these approaches help in solving the spectrum scarcity problem, it is
not likely to be accepted in real life since the PUs do not have any financial incentive
from SUs usage of spectrum.
In this work, we consider trading approach to establish secondary network (CRN) for
serving SUs. Routing in multi-hop CRNs is a challenging task since the available
spectrum at each PU is imprecise due to the changing traffic load.
In our work, the considered system consists of PUs that rent the unused spectrum to
SUs. To ensure availability of required spectrum, the PU monitors its spectrum and lease
free spectrum with quality of service (QoS) for the SUs. With the available spectrum,
user end-to-end QoS connections are realised through the admission control and routing
policy. In this paper, we propose a request admission policy that selectively admits
spectrum requests aiming for optimising PU’s profit. The proposed methodology
integrates optimal request admission control and routing policy with adaptations of the
PU resources to the varying network traffic and profits conditions. The scheme associates
mechanisms that can adapt the service level agreements (SLAs) to the changes in the
distribution of SUs’ traffic and SLAs pricing, with the objective of maximising PUs’
profit while maintaining the required grade of service (GoS) that measured by the
probability of rejecting SUs’ requests. The profit is the revenue of renting spectrum
(reward minus cost). The sensitivity of the PU profit to a link dimension is computed for
link capacity adaption.
The basic concept of the proposed model is a state dependent service profit which is a
dynamic profit of serving SUs’ requests. Then the goal of the routing is to select a path
with maximum sum of the rewards that is also larger than the cost serving request. The
major contributions of this paper are as follows:
•
A model for routing in the CRNs is proposed and the economic model is used for
path selection.
•
Considering the economic factors for routing problem that include the profit and the
cost of renting PUs’ channels.
•
How Markov decision process (MDP) can be used to obtain a computationally
feasible solution to the considered routing problem is described.
•
The performance of the economic model is evaluated under different system
parameters.
The rest of this paper is organised as follows. Related works to routing in wireless mesh
connected networks are reviewed in Section 2. Section 3 describes the system model and
assumptions. Routing algorithm is presented in Section 4. MDP formulation is presented
in Section 5. Section 6 presents the performance evaluation results. Finally, this paper is
concluded.
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A. Alsarhan et al.
Related work
Routing in CRNs is a challenging problem due to the presence of PUs who have
exclusive rights to access their spectrum. The main challenge in the routing is getting
channels from PUs. PU may refuse assigning its channels for SUs. Moreover, the
transmission power should be managed to avoid disturbing PUs transmissions.
Sometimes SUs avoid accessing channels during good channel conditions due to the
priority of PUs flows. These challenges make routing problem in CRNs fundamentally
different from routing in traditional wireless network. Recently, various routing schemes
have been proposed for multi-hop CRNs. In Pefkianakis et al. (2008), a new spectrum
aware mesh routing (SAMER) is proposed. The scheme selects opportunistically the path
with higher spectrum availability, bandwidth, and lower loss rate. In Cheng et al. (2007a),
the authors introduce a joint approach for routing and spectrum assignment in CRNs. The
approach attempts to balance the performance among queuing delay, backoff overhead
and switching cost.
A capacity-based routing scheme is presented in Liu and Grace (2008) to improve the
performance in CRNs by shifting traffic to the edge of the network away from the higher
density regions. The best path is selected in Li et al. (2008) based on a novel probabilistic
metric that takes into account the available spectrum for routing. The scheme in Yun
et al. (2010) computes transmission time between the source and destination for all
potential paths firstly. Then it selects the path with the smallest transmission time. In
order to minimise the required transmission time, the scheme allows transmitting over
multiple channels. Different routing metrics are proposed for multi-hop wireless network
including hop-count, expected transmission count (ETX) (De Couto et al., 2003), and
weighted cumulative expected transmission time (WCETT) (Draves et al., 2004).
However, most of these schemes (e.g., Cheng et al., 2007a; Liu and Grace, 2008)
neglect the PUs activities and they assume the spectrum is available all the time. It is
worth mentioning that the PUs have the priority to use their own channels at any time.
The approaches proposed in Li et al. (2008) and Yun et al. (2010) do not consider the
spectrum availability time. The graph structures are proposed in Zhou et al. (2009) for
routing, where the network topology is represented by a coloured graph. The coloured
graph is used to calculate the shortest path for one source-destination pair. In Wang and
Zheng (2006), all the routes between the source-destinations nodes are calculated, and all
patterns of channel assignment are attempted for all routes. The scheme selects a path
based on the best pattern of routing/channel which is derived by routing algorithm. In
Hou et al. (2007, 2008), non-linear programming is used for designing efficient spectrum
sharing techniques for multi-hop CRNs. The main concern of the proposed scheme is to
maximise the spectrum reuse factor throughout the network. The scheme captures all
major aspects of multi-hop wireless networking, i.e., link capacity, interference, and
routing. However, economic aspect of the problem is neglected. Mathematical
programming is used in Ma and Tsang (2008) for the problem of achieving throughput
optimal routing and scheduling for SUs’ transmissions in CRNs. The objective function
is defined to maximise the achievable rate of source-destination pairs, under the
interference, capacity and routing constraints.
The main objective of the scheme proposed in Pyo and Hasegawa (2007) is to
discover the minimum weight paths in cognitive wireless ad hoc networks. The
communication system is partitioned into operating system and communication system.
The operating system selects the wireless communication interface to be used at a given
Economic model for routing and spectrum management
335
time. The weight of a link is defined as a function of the transmission power of PUs and
SU.
Delay metric is used (Ma et al., 2008; Cheng et al., 2007a, 2007b; Yang et al., 2008)
for selecting the route in multi-hop CRNs. Delay-aware routing schemes consider
different component delay components that include:
•
the switching delay that occurs when the traffic is moved to another frequency.
•
the queuing delay that depend on transmission capacity of a node on a given
frequency band.
In a CRN, spectrum hand off (quantified by channel availability time) and required
transmission time for SUs impact significantly network connectivity and routing. For
example, if the available time of an assigned channel is smaller than the required
transmission time over that channel, the CRN performance is degraded significantly.
However, the situation is getting worse for multi-hop CRNs where multiple links are
involved. Moreover, these schemes assume SUs can access the PUs’ spectrum without
paying any usage charge. Their usage is allowed as long as the SUs do not interfere with
the PUs. Although these schemes achieve more efficient spectrum utilisation, it is not
likely to be accepted in the current market since there is no economic incentive for the
spectrum owners (PUs). Bandwidth adaptation is proposed in Duan et al. (2003) to
maximise profit in the wired networks. Nevertheless, there are significant differences in
both approaches that not only include the system structure but also the priority of the PUs
to use the spectrum and the limitation of available spectrum which are specific features of
our system.
3
Network overview
In this section, we present our CRN where the secondary network consisting of SUs. This
new network relays SUs traffic to the destinations using the rented spectrum from PUs.
The network consists of W PUs and N SUs. PUs have fixed locations whereas SUs are
moving and changing their places arbitrarily.
We define the PU as a spectrum owner that may rent a spectrum to other users. The
spectrum is divided into non-overlapping channels which is the basic unit of allocation.
Each PU has a set of Y channels. This is a common description for a CRN in many
licensed spectrum band (e.g., Alsarhan and Agarwal, 2009; Yun et al., 2010). Each PU
knows in advance the usage pattern of its channels. Our network is multi-service
cognitive network where multiple classes of SUs pay the PUs for their spectrum usage
based on short-term contract. PUs serve different classes of SUs to maximise their profits
while considering the system constraints. Secondary network links are established by
leasing spectrum from the PUs. For each link l, l = 1, 2, …, L, the PU specifies the size of
spectrum, Sl, its QoS, and spectrum price. We assume that the PU can change all of these
parameters on short notice, therefore the PU can change link capacity when needed, or
increasing the price of spectrum.
CRN is modelled as a graph G = (W, E), where E is the set of edges. Each edge
ei,j = (wi, wj) belongs to E if-and-only-if PU i and PU j are in radio range of each other
and they have at least one common data channel. Each edge ei,j may contain multiple
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links based on the number of common available data channel between PU i and PU j. It is
worth mentioning that, the set E varies with time based on the traffic load at PU.
For SUs, we assume that spectrum request arrival follows Poisson distribution and
each SU class i has arrival rate λi. The service time μi for each request of ith class is
assumed to be exponentially distributed. These assumptions capture some reality of
wireless applications such as phone call traffic. Each SU of ith class pay a price pi for a
spectrum unit. Each SU’s request is characterised by its origin-destination (OD) pair,
required bandwidth, and mean service time 1/μj.
4
The proposed routing algorithm
This section presents the routing scheme which attempts to maximise the profit of the PU
by finding the most profitable route in a network with inaccurate information. In order to
find a path, the source PU needs information about the status of spectrum at each PU, the
offered price and the location of the destination node (SU). The source PU broadcast a
beacon that contains its ID’s. We assume each node (SU or PU) in the network has a
unique ID. After receiving a beacon, each PU adds its ID, a list of all SUs that can be
served by the PU, spectrum price, its available channels, and links with other PUs. Each
PU sends this beacon to other PUs. If a PU receives a copy of the same beacon it discards
it.
Although broadcasting a beacon to all PUs in the CRN increase the cost of message
overhead in the network significantly, the chance of discovering the path that has the
maximum PU’s profit is increased considerably. The profit of each path is computed as
follows:
G = R −C
(1)
where R is the expected income from serving SU and C is the service cost which is
computed as follows:
C=
∑
l∈L , j∈W
Cl j
(2)
where Cl j is the cost of renting a channel from PU j for link l. The reward of serving the
SU is computed as follows:
R=
∑
i∈F
pi sλi
(3)
where s is the average number of channels required for establishing a path for SU, F is
the set of SUs classes, and λi is the average rate of acceptance for class i requests. This
model is applicable to multi class services with different spectrum requirements;
however, in this paper, we consider a network with heterogeneous requests where all
classes have different requirements.
We assume that the key objective for the PU is the maximisation of profit G with
respect to S under the condition that connection blocking probabilities Bi meet their
respective constraints Bic . Then the profit maximisation problem can be formulated as
follows:
Economic model for routing and spectrum management
max S G =
∑
i∈F
s.t. Bi ( S ) = 1 −
pi sλi −
∑
l∈L , j∈W
Cl j
337
(4)
λi
≤ Bic , i = 1, 2, ..., F .
λi
Although this is a traditional spectrum allocation problem formulation, in this paper we
focus on maintaining profit maximisation over time by adapting the link capacities to the
changes in traffic load and/or SLA conditions. We propose a distributed approach where
each PU periodically adapts its link capacities based on the system condition.
5
MDP for profit maximisation and routing algorithms
We formulate the routing problem as a profit maximisation problem where MDP routing
model is proposed for this goal. In our model, network profit process is decomposed into
separable link profit using a link independence assumption that is commonly used in
network performance models. For this decomposition, the spectrum price pi is
decomposed into link price parameter pil and the total reward of serving SUs of ith class
is computed as follows:
Ri =
∑
pil sλi
i∈F ,l∈Lk
(5)
where Lk is the set of links which form a path k. Using the decomposition rules the each
link reward is proportional to the cost of serving SUs at this link. In our work, we
calculate the cost of request rejection cil ( z l ) on link l in state z l = ( zil : i = 1, 2, ..., F ),
where zil is the number of class i requests on link l. The rejection cost cil ( z l ) represents
the expected loss of reward from request being rejected due to the acceptance of the new
requests. The total cost of serving SUs classes at path k is computed as follows:
Ck =
∑
l∈Lk , j∈W
Cl j +
∑
l∈Lk
cil ( z l )
(6)
The MDP routing policy chooses the path for SUs of ith class with maximum profit as
follows:
Gmax = max k∈H [ pi − Ck ]
(7)
where H denotes the set of possible paths. If there is no path with a positive profit, then
the request is rejected. In addition to the dynamic cost of serving SUs, we integrate in the
model the static leased spectrum costs by using a request price decomposition where the
link price parameters are proportional to the static link spectrum costs as follows:
cil
pil = pi
∑
Sl
cid
d ∈Lk
(8)
Sd
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where Sd is the size of spectrum allocated at link d. This decomposition assigns higher
spectrum prices to those links whose spectrum is more expensive, hence balancing the
profit amongst the links according to their cost cl. The optimal link costs are evaluated
iteratively to address the functional dependence of the link costs on link offered traffic
and vice versa. Policy iteration algorithm is used to find the optimal cost of rejecting SUs
requests by repeating substitution for a set of fixed point equations formed by the cost of
requests rejection and the link load functions:
c l = f c ( λl ) , λl = f c (Π , S ); l = 1, 2, ..., L,
(9)
where cl = (cil , i = 1, 2, ..., F ) is link l set of rejection cost, λl = ( λli , i = 1, 2, ..., F ) is link
l set of requests arrival rates, and Π (cl, l = 1, 2, …, L) is the set of all requests rejection
costs.
5.1 Spectrum size adaptation
Profit maximisation can be achieved by spectrum size adaptation at each link. In this
case, the necessary condition for optimal solution can be formulated as requirement of
having the PU profit gradient with respect to the size of spectrum equal to the zero
vector:
∂G
⎛ ∂G ∂G
,
, ...,
∇G ( S ) = ⎜
S
S
SL
∂
∂
∂
2
⎝ 1
⎞
⎟=0
⎠
(10)
Calculating this gradient is complex task due to the network state cardinality. We use the
already mentioned spectrum price decomposition as follows:
∂G ∂P ∂Cl ∂Pl
=
−
=
+
∂Sl ∂Sl ∂Sl ∂Sl
∑
v = (1,2,..., N )/ l
∂Pv ∂Cl
−
∂Sl ∂Sl
(11)
where P is the spectrum price. We assume that for the sensitivity of link profit to link
∂Pl
∂P
capacity
is much more significant than indirect sensitivity v where v ≠ l. Then,
∂Sl
∂Sl
formula (11) can be approximated as:
∂G ∂Pl ∂Cl ∂Pl
≅
−
=
= 0, l = 1, 2, 3, ..., L,
∂Sl ∂Sl ∂Sl ∂Sl
(12)
where Pl represents link l profit Gl that given by:
Gl = Rl ( Sl ) − Cl ( Sl ) =
∑
pil sλi − Cl ( Sl )
i∈F
(13)
Equation (12) expresses that the PU’s profit is maximised when all links profits, each link
is taken separately, are maximised. It is clear from equation (8) that the average link cost
corresponds to the link reward
(∑
i∈F
pil sλi
) differential that can be used to approximate
the link reward derivative with respect to the link capacity:
Gl = Rl ( Sl ) − Rl ( Sl − 1) ≅
∂Rl
∂Sl
(14)
339
Economic model for routing and spectrum management
Using (14) in (12) gives the condition for profit optimality that is used for link capacity
adaptation:
∂Gl
∂C
= Gl − l = 0
∂Sl
∂Sl
(15)
Then formula (10) can be used to calculate the optimal size of the spectrum for link l by
using the average service costs that are computed using (9). We refer to this function as a
link function capacity and it can be formulated as:
Sl = f S ( f c ( λl ) )
(16)
These equations can be solved by iteratively substitution to find the optimal link capacity
for a given arrival rate. The key important feature for this solution is the integration of
MDP routing and capacity adaptation to find the optimal profit for PUs. Service cost is
used for this integration. Hence, the proposed scheme can be used for each link separately
and there is no need for a network performance model.
5.2 Spectrum price adaptation
The presented scheme for profit maximisation does not consider the QoS constraint. For
some scenarios, the blocking probability may exceed the standard blocking constraints.
To cope with this problem, we propose the price control scheme for meeting blocking
probability constraint. This scheme is integrated with the described economical
framework. It is easy to show that when a spectrum price is increased for certain class,
profit maximisation mechanism allocates more spectrum to this class and therefore the
blocking probability is reduced significantly. Hence, price control scheme should
increase the price of spectrum to promote the PU for increasing the spectrum. In the
following, we consider the policy for modifying spectrum price, p l → m
p l . Nevertheless,
we assume that the new increment for spectrum ΔRˆ =
∑ (
i
i
)
i
λi m
pil − pil ≥ 0 a should be
kept minimal and to do that we decrease the spectrum price for the ith class with Bi < Bic .
This leads to the following problem formulation:
max S =
∑
i∈F
− min m
pl
i
(
(
λi m
pil , s
)≤B ,
c
i
λi
λi m
pil − pil ≥ 0
∑ (
i
∑
l∈L , j∈W
Cl j
∑ i∈F ( mpil − pil )λi
s.t. Bi ( S ) = 1 −
ΔRˆ =
)
λi m
pil , s m
pil −
(17)
i = 1, 2, ..., F .
)
To solve this problem, we formulate a set of implicit equations defined by reward
pil = f p ( B, B c ), and blocking function Bi = fb ( pˆ ). The first function
parameter function m
calculates the spectrum price adjustment based on the difference between the current
blocking probability for SUs’ requests and the blocking probability constraint, taking into
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A. Alsarhan et al.
(
the account the condition of spectrum price adaptation ΔRˆ =
∑ λ ( mp − p ) ≥ 0)
i
i
l
i
l
i
and
its minimisation. The second function computes new blocking probability for the new
spectrum price. Since spectrum price influence the link capacities and the routing policy
the blocking function can be also represented as a function fc and the set of link loading
functions fo. fs depends on the set of link service cost fc that again depends on the link
loading functions, so finally we arrive at:
pˆ i = f p ( B, B c ) ,
( (
)
Bi = fb f c f c ( f o ( Π, S , pˆ ) ) , f o ( Π, S , pˆ )
)
(18)
This set of equations can be solved repeating substitution with an updating period
denoted by tr until the spectrum parameters converge. The form of (18) indicates that the
solution requires solution of equation (16) and equation (9). The proposed adaptation of
spectrum price leads to a solution that can be interpreted in two ways. The first one
assumes the PU use the new price for adjusting the amount of spectrum required for each
class of SUs. However, the PU cannot increase the prices without considering the
competition with other PUs. The second interpretation takes into account the fact that the
spectrum prices are function of the competitive market and therefore their adjustment is
limited due to possibility of loosing customers.
6
Analytical model for spectrum size adaptation model
To validate our spectrum size adaptation model based on the profit, we compare its
performance and convergence with an analytical model. The details of the analytical
model are described in Section 6.1. Spectrum price adaptation for meeting the blocking
constraints is presented in Section 6.2. In the following, we assume that the arrival rates
of spectrum request λi and spectrum prices pi are given. In our work, we assume a linear
SLA where the cost of spectrum is proportional to the size of spectrum.
6.1 Spectrum size adaptation model
In our adaptation model, an iterative gradient minimisation (Pioro and Medhi, 2004;
Alsarhan and Agarwal, 2012; Alsarhan et al., 2013) is required for reaching the optimal
profit in (10). For converging ∇G(S) to 0, successive projections of the profit gradient are
applied. At each iteration step, a step-size factor τ scales the projected spectrum size
changes ΔS = (Δs1, Δs2, …, ΔsL) to improve the convergence. Newton method is used to
∂Gl
∂Gl
∂Sl
find ΔS approximating the solution
. Assume Sn and G(Sn)
= 0 : ΔS = − 2
G
∂
∂Sl
l
∂ 2 Sl
denotes the link capacities set and the PUs’ profit at iteration n respectively, and let δl be
the vector of size L with 1 in the l position and 0 in all other positions. Then the first and
∂Gl
∂ 2G
second derivatives of the PU profit with respect to link l capacity,
and 2 l can be
∂Sl
∂ Sl
approximated by the following differentials:
Economic model for routing and spectrum management
∂Gl
≅ G ( S n + δl ) = G ( S n )
∂Sl
341
(19)
∂ 2 Gl
≅ G ( S n + 2δl ) −′ G ( S n + δl )
∂ 2 Sl
− ⎡⎣G ( S n + δl ) − G ( S n ) ⎤⎦
(20)
= G ( S + 2δl ) − 2G ( S + δl ) + G ( S )
n
n
n
By using these approximations we arrive at:
ΔS =
G ( S n + δl ) − G ( S n )
G ( S n + 2δl ) − 2G ( S n + δl ) + G ( S n )
(21)
In this iterative model, we use the perfect performance model based on the full network
state, to calculate the link reward Rl(Sl) under optimal routing policy. We apply the MDP
value iteration algorithm (Schweitzer and Federgruen, 1979; Cavazos-Cadena, 2002) that
determines at the same time the optimal policy and the corresponding link reward Rl(Sl)
for the given requests arrival rates, and links capacities. This result is used in equation (1)
to get the maximum profit G(S). We apply the following adaptation algorithm to reach
optimal link capacities:
AdaptSpectrumSize (G, Sn+1, Sn, ε)
begin
if ((Abs(G(Sn+1) – G(Sn)) ≤ εG(Sn)))
return Sn+1, G(Sn+1);
else
{
n=n+1
compute G(Sn + δl), G(Sn + 2δl);
ΔS = (Δs1, Δs2, …, ΔsL);
G ( S n + τ ΔS ) = max τ G ( S n + τ ΔS ) ;
AdaptSpectrumSize (G, Sn+1, Sn, ε);
}
end;
where ε is the tolerable error. For the measurement of our based MDP model, the optimal
link capacities are determined using link capacity and link loading functions. These
functions are solved iteratively (16). While the link loading function fo(Π, S) is used to
evaluate link arrival rates λli , the link capacity function fS(fc(λl)) is used to find the
optimal link capacities by realising link optimality condition (15).
The link loading function measures carried traffic rates λil by applying the Erlang B
blocking probability as follows:
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A. Alsarhan et al.
λli = f o (Π, S ) =
λil
1 − Eb
(22)
( ∑ ( λ , s ))
i
l
i
L
Spectrum demand is computed as follows:
λl =
∑λ
l
i
i
(23)
For each link l, the spectrum demand is computed as follows:
λl =
∑λ
l
i
i
(24)
Bisection search is used for computing Eb
( ∑ ( λ , s )).
i
l
i
L
The cost of rejecting SUs
requests is calculated using the link request rejection cost fc(λl). For all homogenous
spectrum requests, spectrum price is aggregated into single SUs class with average
spectrum price parameter defined by:
p
l
∑λp
=
i
l
i
l
i
(25)
λl
Then, the cost of rejecting request is computed by applying the Newton method presented
in Alsarhan and Agarwal (2012). For the analytical model, we obtain the average cost of
rejecting SUs’ requests by averaging cl(zl) over time as follows:
cl =
λl
( Eb ( λl , Sl − 1) − Eb ( λl , Sl ) )
λl
∑ λp
i
i
l
i
(26)
By substituting (25) in (26), the new cost will be:
c l = ( Eb ( λl , Sl − 1) − Eb ( λl , Sl ) ) λl p l
(27)
We assume linear SLA cost. Using this assumption, the link l profit optimality condition
in equation (15) becomes:
Gl − sl cl = 0
(28)
where cl is the cost of renting one spectrum unit (one channel). The iterative procedure
(Alsarhan and Agarwal, 2012; Alsarhan et al., 2013) is used to converge sl to the optimal
solution:
Eb ( λl , Sl − 1) − Eb ( λl , Sl ) =
sl cl
λl p l
(29)
Let Sn and λ( S n ) = ( λli : i = 1, 2, ..., F ; l = 1, 2, ..., L) be respectively the spectrum size and
the evaluated link arrival rates, at iteration n. We apply the following algorithm to reach
optimal spectrum sizes within a specified relative accuracy:
Economic model for routing and spectrum management
343
Analtical-AdaptSpectrum (G, Sn+1, Sn, ε)
Begin
for each link l
begin
Sl = fS(fc(λl));
Gl =
∑
i∈F
pil sλi − Cl ( Sl ) ; ;
compute Sn+1 using (29);
λl = fc(Π, Sn+1)
Gl =
∑
i∈F
pil S n +1 λi − Cl ( S n +1 ) ;
if (Abs(G(Sn+1) – G(Sn)) ≤ εG(Sn)
return;
n = n + 1;
end for
end
6.2 Spectrum price adaptation model
Clearly, if the blocking constraints are not met, PUs should increase spectrum price but
with minimal increase. We define the average requests blocking probability as:
BT =
∑ λB
∑λ
i
i
i
(30)
i
i
PU increases the spectrum price for all SUs classes by a common multiplier
ρ > 1( pˆ i = ρpi ), if the average blocking probability exceeds average blocking constraints
for SUs BTc that is computed as follows:
BTc
∑B
=
∑λ
c
i
i
i
(31)
i
PU verifies all blocking constraints. If some constraints are not met for some classes of
SUS, the PU increases the prices for these classes and reduces the prices for other classes.
Clearly, increasing the spectrum prices influences strongly the spectrum sizes adaptation
due to the increase of profit on all links. However, this increase does not affect the
routing decision strongly because routing is sensitive only to the relative changes of
spectrum price between the classes. Let pA be the spectrum price that represents the
average revenue of serving SU and it is computed as follows:
344
A. Alsarhan et al.
pA =
∑ λp
∑λ
i
i
i
i
(32)
i
We apply Newton’s iterations to find multiplier ρ that achieves equality ( BT = BTc ). The
new value of the spectrum price at iteration n is:
pˆ Tn +1 = pˆ Tn +
BTc − BTn
⎛ ∂BTn
⎞
⎜
∂pˆ Tn ⎟⎠
⎝
(33)
In our model, we assume the traffic load for each link is independent of other links’
traffic loads. For ith class of SUs, the request blocking probability is computed as follows:
B j = Π k∈K B k = Π k∈K ⎣⎡1 − Π l∈Lk (1 − B l ) ⎦⎤
(34)
where Bk is a blocking probability for path k that belong to the set of paths K and Bl is the
∂B l
blocking probability for link l. Now we can compute
as follows:
∂pl
∂B l ∂B l ∂Sl
=
∂p l ∂Sl ∂p l
(35)
The multiplier ρ is computed as follows:
ρ=
7
pˆ Tn +1
pˆ Tn
(36)
Performance evaluation
In this section, we conduct simulation experiments to evaluate the performance of the
proposed resource adaptation scheme. Our simulation is developed using MATLAB.
First, we setup a random graph by creating |N| = 100 SUs in [1,000 m, 1,000 m] area. We
set the radio range to 200 m and the interference range to 500 m. There are ten different
PUs coexist geographically. The status of a PU channel is determined according to the
ON/OFF channel model. The location of SUs sources and destinations are randomly
assigned within the simulation area. Our simulations are averaged over 1,000 runs, each
last for 500 seconds.
7.1 Comparison of analytical adaption model
Simulation results are found to closely match the analytical results. We consider a
homogeneous case in which all SUs classes have the same arrival rates. The results
presented for several system settings scenarios in order to show the effect of changing
Economic model for routing and spectrum management
345
some of the control parameters. In Figure 1, we compare the offered spectrum size as a
function of average arrival rate. We assume all classes have the same arrival rates. From
the figure, we find the spectrum size is sensitive to the arrival rate. In order to generate
more profit, the PU increases the size of spectrum as the arrival rate increases. With a
larger λi, the PU rents more spectrum for SUs and get more gain. The model is converged
in one iteration. For the convergence, we use the following metrics:
•
Time of convergence: The time of convergence Tcl is defined as the difference
between the time of reaching the optimal spectrum size at link l (tol ) and the time of
traffic change (thl ). Time of convergence Tcl is computed as follows:
Tcl = tol − thl
•
(37)
Convergence deviation σ cl :
σ cl = Tcl
∑
Slt − Sl
t =1..T
Sl
where Slt is link l capacity at measurement interval index t during convergence
period. Figure 2 shows the convergence deviation.
Figure 1
Spectrum size for different spectrum demand
(38)
346
Figure 2
A. Alsarhan et al.
Convergence devation over time
7.2 Price adaptation for meeting QoS for SUs
To meet the blocking probability constraints, PU allocates more spectrum for SUs by
increasing the spectrum price. Figure 3 shows how the PU satisfies the QoS for SUs
classes. Figure 3(a) and Figure 3(b) show that PU increases the spectrum prices to assign
more spectrum for serving SUs’ requests. Increasing spectrum price promote the PU to
assign more spectrum for getting more profits. In Figure 3(a), the PU continues
decreasing the price for class 1 till meeting the blocking probability constraint for class 2
requests. For class 2, we notice from Figure 3(b) how a PU meets the blocking
probability by allocating the extra spectrum that is resulted from increasing the price of
spectrum.
Figure 3
Spectrum price adaptation for meeting blocking probabilities constraints, (a) decreasing
spectrum price for class 1 (b) increasing spectrum price for class 2 to meet the blocking
constraint (see online version for colours)
(a)
Economic model for routing and spectrum management
Figure 3
347
Spectrum price adaptation for meeting blocking probabilities constraints, (a) decreasing
spectrum price for class 1 (b) increasing spectrum price for class 2 to meet the blocking
constraint (continued) (see online version for colours)
(b)
Figure 4
Reported profit for different values of spectrum demand
7.3 Impact of PUs traffic on the profit:
In this section, we study the impact of the PUs traffic on PUs’ profit. The PUs traffic
varies over time from λpu = 2 (low traffic) to λou = 7 (high traffic). Figure 4 depicts that as
the PUs traffic decreases the profit increases. This is because the chance of finding an
appropriate channel for serving SUs and generating more profit becomes higher. For
higher traffic, many SUs requests are rejected and the chance for generating extra profit
is decreased. This is because PUs traffics have higher priority than SUs traffics. We can
see from the figure as the traffic increases the profit decreases. Figure 5 displays the
rejection rate for each SU class under different PUs traffics. It is clear from the figure the
348
A. Alsarhan et al.
rejection rate increases for both SUs classes as traffic load become higher. Moreover, the
figure shows that the proposed method performs selective rejection on the incoming
requests to accommodate higher gain requests. That is, the scheme rejects more requests
of class 2.
7.4
The Effect of SUs demand changes on the profit
Figure 6 illustrates the routing behaviour for the network with different demand of SUs.
It can be observed that the reported profit for PUs increases as the demand increases. The
PU can improve the reported profit by serving more users and get more gain when the
demand becomes high. However, the chance for increasing the profit decreases when the
demand becomes low. The figure shows that the profit increases till certain number of
spectrum demand then it converges because of the limited size of available spectrum.
PUs cannot serve unlimited number of SUs. Therefore, we can say that there is a direct
correlation between the PU’s profit and the spectrum demand, so the more demand we
have the more profit can be generated from serving extra SUs. However, many factors
can prevent PUs to achieve the maximum gain. These factors include the cost of
spectrum, the limited size of spectrum, the requirements of PUs, and limited number of
SUs.
Figure 5
Rejection rate for different spectrum demand (see online version for colours)
Economic model for routing and spectrum management
Figure 6
8
349
PUs profit for different SUs demand of spectrum (see online version for colours)
Conclusions
In this paper, we proposed a novel routing scheme based on economic model for
multi-hop CRNs under different network conditions. Specifically, our routing scheme
attempts at maximising the reported profit for PUs by jointly considering spectrum
availability, PUs requirements, SUs requirements, PUs’ reward, and spectrum cost. Based
on these constraints and requirements, we developed an intelligent routing scheme for
multi-hop CRNs. This scheme aims at finding the path with the maximum profit among
all available paths from a given SU source to a given SU destination.
The proposed model has two contributions to routing problem in CRNs. From the
application side, the main contribution is developing a routing policy that considers
different requirements such as profit for PUs, the renting cost, and SUs requirements. All
basic functions are integrated and optimised into one homogenous, theoretically-based
model. From the modelling side, we formulate a routing problem as a profit maximisation
problem. Such a formulation allows MDP to optimise the routing problem. The approach
presents a general framework for studying, analysing, and obtaining the route for
source-destination pair based on economic model.
Thus, network performance (quantified by the reported gain) is improved. Through
simulations and analytical results, we verified the ability of our scheme to adapt to
different system conditions while considering different system requirements and
conflicting objectives. We wish to carry similar analysis on real system. We are in the
process of carrying similar analysis taking into account the competition among PUs for
renting the spectrum using game theory. Our goal is to derive the optimal solutions for
PUs in an uncertain market.
350
A. Alsarhan et al.
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