Ayoub Alsarhan* and Ahmad Al-Khasawneh Awni Itradat … · 2015. 11. 19. · 332 A. Alsarhan et al. Reference to this paper should be made as follows: Alsarhan, A., Al-Khasawneh,

Int. J. Networking and Virtual Organisations, Vol. 12, No. 4, 2013 331

Copyright © 2013 Inderscience Enterprises Ltd.

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.

332 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.


2 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


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


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:

,j

ll L j WC C

∈ ∈=∑ (2)

where jlC is the cost of renting a channel from PU j for link l. The reward of serving the

SU is computed as follows:

i ii FR p sλ

∈=∑ (3)

where s is the average number of channels required for establishing a path for SU, F is the set of SUs classes, and iλ 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 .c

iB Then the profit maximisation problem can be formulated as follows:


,max j

S i i li F l L j WG p sλ C

∈ ∈ ∈= −∑ ∑ (4)

s.t. ( ) 1 , 1, 2, ..., .i ci i

i

λB S B i Fλ

= − ≤ =

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 l

ip and the total reward of serving SUs of ith class is computed as follows:

, kl

i iii F l LR p sλ

∈ ∈=∑ (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 ( )l l

ic z on link l in state ( : 1, 2, ..., ),l liz z i F= =

where liz is the number of class i requests on link l. The rejection cost ( )l l

ic z 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:

( ),k k

j l lk ill L j W l L

C C c z∈ ∈ ∈

= +∑ ∑ (6)

The MDP routing policy chooses the path for SUs of ith class with maximum profit as follows:

[ ]max maxk H i kG p C∈= − (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:

k

li

llii d

id L d

cSp pc

S∈

=∑

(8)


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:

( ) , ( , ); 1, 2, ..., ,l l lc cc f λ λ f S l L= = Π = (9)

where ( , 1, 2, ..., )l lic c i F= = is link l set of rejection cost, ( , 1, 2, ..., )l l

iλ λ i 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:

1 2( ) , , ..., 0

L

G G GG SS S S∂ ∂ ∂⎛ ⎞∇ = =⎜ ⎟∂ ∂ ∂⎝ ⎠

(10)

Calculating this gradient is complex task due to the network state cardinality. We use the already mentioned spectrum price decomposition as follows:

(1,2,..., )/l l v l

v N ll l l l l l

G P C P P CS S S S S S=

∂ ∂ ∂ ∂ ∂ ∂= − = + −

∂ ∂ ∂ ∂ ∂ ∂∑ (11)

where P is the spectrum price. We assume that for the sensitivity of link profit to link

capacity l

l

PS∂∂

is much more significant than indirect sensitivity v

l

PS∂∂

where v ≠ l. Then,

formula (11) can be approximated as:

0, 1, 2, 3, ..., ,l l l

l l l l

G P C P l LS S S S∂ ∂ ∂ ∂

≅ − = = =∂ ∂ ∂ ∂

(12)

where Pl represents link l profit Gl that given by:

( ) ( ) ( )ll l l l l i l lii F

G R S C S p sλ C S∈

= − = −∑ (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 ( )l

iii Fp sλ

∈∑ differential that can be used to approximate

the link reward derivative with respect to the link capacity:

( ) ( )1 ll l l l l

l

RG R S R SS∂

= − − ≅∂

(14)


Using (14) in (12) gives the condition for profit optimality that is used for link capacity adaptation:

0l ll

l l

G CGS S

∂ ∂= − =

∂ ∂ (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:

( )( )l S c lS f f λ= (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, .l l

i ip p→ Nevertheless,

we assume that the new increment for spectrum ( )ˆ 0l li i ii

R λ p pΔ = − ≥∑ a should be

kept minimal and to do that we decrease the spectrum price for the ith class with .ci iB B<

This leads to the following problem formulation:

( )( )

,max ,

min li

jl lS i i i li F l L j W

l lii ip i F

λ p s p C

p p λ

∈ ∈ ∈

∈

= −

− −

∑ ∑∑

(17)

( )

( )

,s.t. ( ) 1 , 1, 2, ..., .

ˆ 0

li i c

i ii

l li i ii

λ p sB S B i F

λ

R λ p p

= − ≤ =

Δ = − ≥∑

To solve this problem, we formulate a set of implicit equations defined by reward parameter function ( , ),l c

pip f B B= and blocking function ˆ( ).i bB f p= The first function calculates the spectrum price adjustment based on the difference between the current blocking probability for SUs’ requests and the blocking probability constraint, taking into


the account the condition of spectrum price adaptation ( )( )ˆ 0l li i ii

R λ p pΔ = − ≥∑ 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:

( )( )( )( ) ( )( )

ˆ , ,

ˆ ˆ, , , , ,

ci p

i b c c o o

p f B B

B f f f f S p f S p

=

= Π Π (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

find ΔS approximating the solution 22

0 : .l

l l

lll

GG SS

GSS

∂∂ ∂= Δ = −

∂∂∂

Assume Sn and G(Sn)

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

second derivatives of the PU profit with respect to link l capacity, l

l

GS

∂∂

and 2

2l

l

GS

∂∂

can be

approximated by the following differentials:


( ) ( )l n nl

l

G G S δ G SS

∂≅ + =

∂ (19)

( ) ( )

( ) ( )

( ) ( ) ( )

2

22

2 2

l n nl l

l

n nl

n n nl l

G G S δ G S δS

G S δ G S

G S δ G S δ G S

∂ ′≅ + − +∂

⎡ ⎤− + −⎣ ⎦= + − + +

(20)

By using these approximations we arrive at:

( ) ( )( ) ( ) ( )2 2

n nl

n n nl l

G S δ G SSG S δ G S δ G S

+ −Δ =

+ − + + (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); ( ) ( )max ;n n

τG S τ S G S τ S+ Δ = + Δ

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 ,l

iλ 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 liλ by applying the Erlang B

blocking probability as follows:


( )( )( , )

1 ,

lil

oi lb Lii

λλ f SE λ s

= Π =− ∑

(22)

Spectrum demand is computed as follows:

ll iiλ λ=∑ (23)

For each link l, the spectrum demand is computed as follows:

l lii

λ λ=∑ (24)

Bisection search is used for computing ( )( ), .lb Lii

E λ s∑ 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:

l li iil

l

λ pp

λ=∑ (25)

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:

( ) ( )( ), 1 ,l

l l l lb l b l i il i

λc E λ S E λ S λ pλ

= − − ∑ (26)

By substituting (25) in (26), the new cost will be:

( ) ( )( ), 1 ,l l l l lb l b lc E λ S E λ S λ p= − − (27)

We assume linear SLA cost. Using this assumption, the link l profit optimality condition in equation (15) becomes:

0l l lG s c− = (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:

( ) ( ), 1 , l ll lb l b l l l

s cE λ S E λ Sλ p

− − = (29)

Let Sn and ( ) ( : 1, 2, ..., ; 1, 2, ..., )n liλ S λ i F l 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:


Analtical-AdaptSpectrum (G, Sn+1, Sn, ε) Begin for each link l begin Sl = fS(fc(λl)); ( );l

l i i l li F

G p sλ C S∈

= −∑ ;

compute Sn+1 using (29); λl = fc(Π, Sn+1) ( )1 1 ;l

l i n i l ni F

G p S λ C S+ +∈

= −∑

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:

i iiT

ii

λ BB

λ=∑∑

(30)

PU increases the spectrum price for all SUs classes by a common multiplier ˆ1( ),i iρ p ρp> = if the average blocking probability exceeds average blocking constraints

for SUs cTB that is computed as follows:

ciic

Tii

BB

λ=∑∑

(31)

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:


i iiA

ii

λ pp

λ=∑∑

(32)

We apply Newton’s iterations to find multiplier ρ that achieves equality ( ).cT TB B= The

new value of the spectrum price at iteration n is:

1ˆ ˆ

ˆ

c nT Tn n

T T nT

nT

B Bp pB

p

+ −= +

∂⎛ ⎞⎜ ⎟∂⎝ ⎠

(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:

( )1 1kk l

j k K k K l LB B B∈ ∈ ∈⎡ ⎤= Π = Π −Π −⎣ ⎦ (34)

where Bk is a blocking probability for path k that belong to the set of paths K and Bl is the

blocking probability for link l. Now we can compute l

l

Bp∂∂

as follows:

l ll

l ll

B B Sp S p∂ ∂ ∂

=∂ ∂ ∂

(35)

The multiplier ρ is computed as follows: 1ˆ

ˆ

nT

nT

pρp

+= (36)

7 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


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 lcT is defined as the difference

between the time of reaching the optimal spectrum size at link l ( )lot and the time of

traffic change ( ).lht Time of convergence l

cT is computed as follows:

l l lc o hT t t= − (37)

• Convergence deviation :lcσ

1..

tlll l

c c t T l

S Sσ T

S=

−= ∑ (38)

where tlS 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


Figure 2 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)


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 (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


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)


Figure 6 PUs profit for different SUs demand of spectrum (see online version for colours)

8 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.


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Ayoub Alsarhan* and Ahmad Al-Khasawneh Awni Itradat … · 2015. 11. 19. · 332 A. Alsarhan et al. Reference to this paper should be made as follows: Alsarhan, A., Al-Khasawneh,