the focal part in the wireless network and game theory has also been applied to cognitive radio networks. Table 1 shows the correspondence between each ...
The 4th International Workshop on Mobile Computing and Networking Technologies 2012
A Game Theoretic Approach to Spectrum Management in Cognitive Radio Network Saed Alrabaee 1, Anjali Agarwal1, Nishith Goel2, Marzia Zaman2, Mahmoud Khasawneh 1 1
Department of Electrical and Computer Engineering, Concordia University, Montreal, Canada {m_khasaw, aagarwal, s_alraba}@encs.concordia.ca 2 Cistel Technology Inc., Ottawa, Canada {ngoel, Marzia}@cistel.com
Abstract— In this paper, we propose cognitive radio network models for providing spectrum management which includes spectrum trading and spectrum competition. The models described are with and without using the concepts of game theory. For both the models, the spectrum trading that occurs between the primary user and the secondary user is considered first, and then the spectrum competition among the primary users is considered. Our model includes multiple levels of QoS for different secondary users. In the first phase, the secondary user selects the spectrum by observing the changes in the price and the level of QoS offered by different primary users. In the second phase, the primary user controls its strategy in renting the spectrum to secondary users to achieve the highest utility. To model the dynamic behavior of spectrum competition among primary users, a Bertrand game is formulated where the Nash equilibrium is considered as the solution. Moreover, to model the spectrum trading between the primary user and the secondary user, a Stackelberg game is formulated where the Nash equilibrium is again considered as the solution. Basically the solution is in terms of the size of offered spectrum to the secondary users and the offered spectrum price.
we introduce the game theory techniques and the pricing models in cognitive radio networks. A. Game Theory in cognitive radio network Recently, game theory has been used in the communication area. Basically, it has been used to model and analyze resource allocation problems in competitive area and it has also been used for security issues. The cognitive radio network becomes the focal part in the wireless network and game theory has also been applied to cognitive radio networks. Table 1 shows the correspondence between each element in a cognitive radio network with each element in game theory. TABLE I.
NETWORKING GAME
Keywords- Competition Factor, Spectrum Management, Utility Function, Nash Equilibrium.Spectrum trading;
I.
Elements of a game
Element of a CRN
Players Actions Payoff
Nodes Change parameters Throughput, Delay, Bandwidth, Interference, etc.
Game theory is a useful tool that can be used for spectrum management in cognitive radio network [1]. In [2], they modeled the competitive dynamic spectrum leasing by using the concept of game theory. Specifically, one level is between primary user and spectrum broker and the other level is between secondary user and service provider. The players of this game were the secondary users and their strategies were defined in terms of selection of a particular service provider. In [3], a game-theoretic cooperative spectrum sensing was proposed for cognitive radio network. In particular, they studied the interactive decision of selfish secondary users on cooperative spectrum sensing. The players of this game were the secondary users and their strategies were defined in terms of selecting frequency of channel. In [4], a non-cooperative game is formulated for spectrum trading in cognitive radio network. In [4], the players are the secondary users, and their strategies are buying the spectrum from the primary user. In [5], a game theoretic price competition was proposed in cognitive radio network. Specifically, they analyzed price competition in CRNs jointly considering both bandwidth and spatial reuse. The competitive spectrum leasing in a primary market was analyzed using auction methods in [6].
INTRODUCTION
In cognitive radio network, the spectrum can be traded between spectrum owners (Primary Users, PU) and spectrum leasers (Secondary Users, SU). The goal of this spectrum trading is to maximize the utility (Profit) of primary users while maximizing the utility (QoS level) of secondary users. There might be more than one primary user that offers the price as well as the spectrum and therefore the competition’s door will be opened among the primary users. As a result, each user either primary user or secondary user has to control its strategy to reach the equilibrium point. When the equilibrium point is reached it means that both users (PU and SU) are provided with the best utility in term of QoS and price. Hence, the possibility of dynamic changes in behavior poses a challenge in modeling in cognitive radio networks. In this paper, we consider the problem as two levels wherein the first level is spectrum trading or spectrum pricing and the second level is the spectrum competition. To model the previous levels, the game theory has been incorporated into our model in order to control the dynamic behavior of primary users as well as secondary users. In the following subsections
978-1-4673-2015-3/12/$31.00 ©2012 IEEE
COGNITIVE RADIO NETWORK BASED ON WIRELESS
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B. Pricing in Cognitive radio network The following works addressed the problem of pricing in spectrum management in cognitive radio network. In the cognitive radio network, spectrum trading is successfully formulated by economic models and competitive and cooperative pricing schemes are developed in [7]. In [8], hierarchical spectrum sharing is formulated as a unified market. Specifically, the pricing mechanism for the bandwidth allocations between the systems equates the supply to the demand. In [9], they model the consumers’ demand functions and calculate the Walrasian prices which equate the demand to the supply of each goods. In the previous works that are mentioned in sections 1.1 and 1.2, they apply different game frameworks to spectrum trading, spectrum competition, and some of them formulate price models as game theory framework. There are no approaches that consider the effect of applying game theory into the quality of routing service. In addition, the previous works do not consider the levels of QoS. Hence, we propose a spectrum management model with and without game theory. Finally we analyze the effectiveness of game theory into network performance. The outline of the paper is as follows. The problem formulation, definition, and the architecture of our model are given in Section II. In Section III, we introduce the system model without game theory, in addition we describe in this section the competition factor, price function, profit function, and we simulate the model. In Section IV, we consider a competitive market model and assume that the channels are leased by the consumers (SU) at prices determined by PU. The equilibrium of this market model is determined, and we provide two game theory frameworks wherein one is between PU and SU and the other framework between PUs to achieve this equilibrium. We illustrate the results of this model before we conclude in Section V. II.
base station, 4) base station based on PU’s decision in the previous step will either allocate the spectrum or release the request.
Figure 1: System Model between PU and Base Station The steps between primary user and secondary user are shown in Figure 2.
PROBLEM FORMULATION
We consider a cognitive radio network with N primary users where primary user PUi can get the spectrum denoted by Si with bandwidth BWi from Base Station. In addition, we consider it with M secondary users as well. We define the total capacity υ of the network as given in equation (1) where κ is the channel size and j is the total number of channels in the network. In addition, unique ID is defined for each channel. In terms of security, we assume all the nodes (PU & SU) in the network are trusted nodes. We assume that spectrum request arrival follows Poisson distribution. υ = κ∗ϕ.
Figure 2: System Model between PU and SU Figure 2 shows the following steps: 1) secondary user requests primary users for channel or portion of channel with spectrum size, the bandwidth size, as well as the level of QoS, 2) primary user checks the availability of spectrum for the QoS level requested, calculates the price considering other PUs as sellers, and sends it to the secondary user, 3) and 4) secondary user checks other offers received and chooses the best with least price offered and better QoS, 5) primary user responds to the secondary user’s decision of accepting the primary user by allocating the spectrum; otherwise, the request is dropped.
(1)
The stages of our model are shown in Figures 1 and 2 wherein the initial stage (Figure 1) is between the primary user and its base station, and the main stage (Figure 2) is between the primary user and the secondary user. The steps between a PUi and its base station as shown in Figure 1 are: 1) PUi requests base station for channel ki that has spectrum Si with bandwidth BWi, 2) base station calculates the base station cost CBS as per equation 4 and sends it to the primary user, 3) PUi may or may not accept the deal and sends its response to the
III.
SYSTEM MODEL WITHOUT GAME THEORY
In this section, we describe our model without using the concept of game theory. A. Spectrum Trading between PUs and SUs In spectrum trading, PUs’ main concern is to maximize their own
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revenue while supporting the QoS for SUs. PUs trade the extra (unused) spectrum to the SUs to maximize their revenue. For spectrum trading, one of the challenging issues is pricing. In our model, the price function’s design answers the following: how to set the spectrum price in a competitive environment where multiple sellers offer spectrum to the buyer, so that the sellers (e.g., primary users) are satisfied and their profits are maximized. The spectrum pricing in cognitive radio network was addressed by [7-11]. The price calculation in our model consists of: • The initial phase, which occurs when the secondary user sends its requirements, as well as the required level of QoS, to the available PUs. • The second phase, in which, after the PU calculates its price, it calculates α as in equations 2 and 3 to obtain the total price, which is then sent to the SU. This factor could be helpful in attracting more demands from SU.
Note that the competition factor (α) decreases when number of competitive PUs increase. VALUES USED TO SIMULATE α IN FIGURE 3
TABLE II.
X1
4
No. of channels 2
X2
14
4
5
X3
24
6
10
Legend id
No. of SUs
Usage period in hour 2
We use X1, X2, and X3 as legends to represent the different values used. The values of α for X1 is always greater than for X2 and X3 because the values used in X1 are less than the corresponding values in X2 or X3, which indicates that competition is lower in the case of X1. However, the values of α for X2 and X3 are closer to each other, for when the values of SUs (in particular) become high; there is not much competition among PUs.
The proposed price function is very dynamic and efficient because we consider all the network elements that could affect the service. B. Spectrum Competition In our model, we assume there are multiple primary users that offer spectrum to multiple secondary users based on their price. A PU competes with other PUs by offering a suitable price to the secondary users. A new coefficient α (0 < α < 1), called the competition factor, is defined. A PU selects the value of this coefficient by considering the number of PUs offering that channel, the usage period of the offered channel, and the probability of its presence. The competition factor function is described in the following function (equations 2a, 2b, and 2c). α = 1,
when the number of primary user = 1
0.1 < α < 0.99, α = 0,
the normal case
when there is no available channel
Figure 3: The competition factor (α) behavior
(2c) (2b)
C. Revenue Function Each PU would first pay a cost to base station to provide a channel for the SU. This cost will be a part of the price. The base station cost is calculated as follows:
(2c)
If no other PU offers the requested channel, α = 1, which means the price remains same and is not adjusted. If there is no available channel, α = 0, which means the price offered is 0. However, if there is a number of primary users with available channel for the request as well as the usage period of the offered channel, the PU chooses an appropriate value for α (0.1 < α < 0.99) to reduce the total price as per the following equation. α = (ψ+ϕ+χ+τ) / ((1+ψ)τ+ψ+ϕ)
CBS = ln (BWk) * k * t * PBS.
(4)
where BWk is the bandwidth per channel, for a total of k channels provided by base station (BS) to the primary user, t is the time the k channels are used, and PBS is the unit price per channel specified by base station. The price of each channel is defined by PU, such that the profit of that channel is maximized. Hence, the profit earned by PU by renting channels to SU is as follows:
(3)
where ψ is the number of PUs offering the spectrum, ϕ is the number of channels, χ is the number of SUs requesting a specific channel, and τ is the usage time of the channel.
Profit = ϕ * Ptotal – CBS.
We simulate different cases of values for SUs, number of channels and usage time to see the changes in α values. Table II represents the values used for simulation in Figure 3.
(5)
where ϕ is the number of channels assigned to a SU; Ptotal is the offered channel price for SU, as in equations 8a and 8b, and CBS is the base station cost as in equation (4). We introduce a
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novel function to control the level of QoS and price; the QoS function f(LQoS) is defined as follows: f (LQoS) = QoSlevel * ln(btrade).
•
(6)
where QoSlevel may take a value of 1, 2 or 3, depending upon the QoS level requested, and btrade is the size of spectrum traded to the secondary user. We define a price function PPU which describes the price of renting the channel by PU to a SU. It is calculated as follows:
•
where W is the data transmission rate, btrade is the size of spectrum traded to the secondary user, χ is the number of customers (SUs that request one channel or more, P is the unit price per channel for the spectrum traded between PU and SU, and f(LQoS) is the function of QoS. The total (offered) price follows the next equations: ;α=1
; 0.1 < α < 0.99
•
(8a)
•
•
ETR, which is calculated as follows: (12)
The Profit
600
400 QoS-level 1 QoS-level 2 QoS-level 3
200
0 6000
Delay: It is an vital QoS parameter in any wireless network To the best of our knowledge, delay in CRNs is the combination of two main components: the propagation delay and the queuing delay
60
4000 40 2000 The Price
20 0
0
Spectrum Traded kHz
Figure 4: PU profit based on the level of QoS
Level 2 is the middle level of QoS that consists of: Link robustness: this metric is very important in order to maximize the throughput and to guarantee the stability of service. Once the robustness is selected, it determines the spectrum to be allocated
(11)
800
Level 1 is the lowest level of QoS, which consists of:
o
ProbPU, which is the probability of PU presence which is calculated as follows:
We simulate the relation between the profit, the price, and the spectrum size for three levels (level 1, level 2, and level 3) of QoS and the profit is maximized as the QoS level becomes higher. Here again, the cognitive nodes are randomly placed in 300x300 m2 and the transmission range is 150 meters. The bandwidth used is 1200 bps, and the transmission rate is 1000 bps. Here we assume that the base station’s price units for QoS level 1, level 2, and level 3 are 5, 8, and 11 respectively.
(9)
Level 1, and
(10)
ETR (link) = 1 / (Plink).
(8b)
o
Probk, which represents the ratio of idle slots to busy slots as in the following equation. This constraint
where Plink is the probability of bit error rate for link.
D. QoS for Secondary Users Most of the research that has been conducted in this area (QoS) assumes one type of service. Nowadays, with an explosion in the diversity of real-time services a better and more reliable communication is required. Moreover, some of these applications require firm performance guarantees from the PUs. In our model, we consider satisfying QoS for multiple levels of services. Three levels offered in our model are as follows:
o
Error Transmission Rate: (ETR): it is a factor used to find links with higher a transmission rate and a lower bit error rate. The derivation of ETR starts with the measurements of the loss probability, denoted by Plink.
ProbPU = Plink * Probk
where θ is the number of competitive PUs and χ is the number of customers (SUs that request one channel or more).
•
o
where nid is the total number of idle period, tid is the time of idle period, and tbusy is the time channel is busy.
where A is a constant that signifies the effect of a number of PUs and SUs on offered price. If the number of competitive PUs is higher than the number of SUs requesting spectrum, the offered price should be lowered. It is calculated as follows: A = χ − θ.
Level 2, and
Probk = (nid * tid) / (nid * tid + tbusy).
when there is no competitive primary. If there is no available channel (α = 0) Ptotal = ∞. The equation 8b is the normal case where there are some competitive primary users, some available channels, and a usage period. Ptotal = α ∗ PPU + A
o
The following three constraints ensure the above QoS levels:
PPU = W * log (btrade) + χ * btrade* P + χ * f (LQoS). (7)
Ptotal = PPU
Level 3 is the highest level of QoS that consists of:
We also assume that the PU’s price units for QoS level 1, level 2, and level 3, are 7, 10, and 13, respectively. PU offers a total number of 15 channels to SUs, where the numbers of channels that satisfy the QoS levels are 5. The number of customers (SUs) assumed is 15 users, and the number of PUs assumed is 5. Figure 4 shows the relation between averages of spectrum traded and average profit within the three proposed
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In equation 13, qL = qLo. After knowing the reaction strategy q*F of the follower, the L will announce a strategy qL* which belongs to QL whereas Leader maximize its payoff UL. In equation 14, qF = qF*.
QoS levels in our model. The figure clearly shows that the profit increases when the requested QoS level is higher, where level 3 > level 2 > level 1 in terms of better service. IV.
SYSTEM MODEL WITH GAME THEORY
In our model, the primary user strategy set QL is defined as QL = {Pbi, I = 0, 1, 2,……, N} where Pbi is the total price as in equation 8a and 8b for the allocation of spectrum b. The secondary user strategy set QF is defined as QF = {SjQoS, j = 1, 2, 3, …m and QoS =1,2, or 3}, where SjQoS is the offered spectrum with level of QoS, in our model there are three levels. The primary user is to choose the price Ptotal for the spectrum b while the secondary user wants to select the best size of spectrum with higher level of QoS which optimize its own utility function UF. In this game the PU first calculates the most probable response SrQoS (r = 1, 2, 3,……m) from the secondary user given any of its policies Pbn (n = 0, 1, 2… N). As a result we can have the equation 15, where r = 1, 2, 3,….,m and n = 0, 1, 2,…., N.
Some existing works related to spectrum trading or leasing use one stage of dynamic game structure as in [5], the stage was between primary user and secondary user. Other existing works use two stages that one stage between primary user and secondary user as in [4, 6, and 7]. Some existing works use two stages that one stage between the primary user and secondary user and the other stage among the secondary users as in [2], [12]. In this section, we introduce our model with game theory concept. As clearly shown in the previous existing research works they consider one stage or two stages. Hence, we introduce three stages, the first stage is between the primary users that we used the Bertrand game concept, the second stage is between primary user and secondary user that we use stackelberg game concept. We illustrate two stages in the following figure.
UL (P*; S*QoS) ≥ UL (Pbr; SrQoS)
B. Spectrum Competition using Bertrand Game In Bertrand’s game a firm changes its behavior if it can increase its profit by changing its price, on the assumption that the other firms’ prices will remain the same and their outputs will adjust to clear the market. When the unit cost of production is a constant c, the same for both firms (e.g. competitive PUs), and demand is linear, Bertrand’s game has a unique Nash equilibrium, in which each firm’s price is equal to c. The previous concept was applied to model the competition among Primary users. In this competition we assume that k channels are offered by n primary user wherein each PUi can offer ki at a cost Ptotal (ki). In our model, the primary users set different prices that allow secondary user to select the lowest price among the offered prices. Each primary user sets the price based on alpha value as shown in equation 3. Each PU is looking to maximize its utility (profit) by getting more customers (secondary users).
Primary users Price competition (Bertrand game) Stackelberg game
Selection the spectrum offered from primary user
Price and the allocated spectrum
Secondary users Spectrum competition based on QoS level (Evolutionary game)
Figure 5: Three levels of game theory In the following sub-sections, we describe the spectrum trading and the spectrum competition using the Stackelberg game and Bertrand game, respectively. In addition, we describe the utility function for each user (PU or SU), which provides the revenue for PU and the spectrum size with its associated QoS for SU. A. Spectrum Trading using Stackelberg Game In the Stackelberg game [14, 15], it is assumed that at least one of the firms in the market is able to pre-commit itself to a particular level of supply before other firms have fixed their level of supply. Other firms observe the leader’s supply and then respond with their output decision. The firms that are able to initially pre- commit their level of output are called the market leaders and the other firms are called the followers. This concept is applied into our model specifically between the primary user and the secondary user. Hence, the primary user is the leader and the secondary user is the follower. For leader (PU), we define QL and IL where QL is the strategy set and IL is the information set. For the follower (SU), we define QF which is the strategy set. According to Stackelberg game model, IL = QF, at the start, any strategy is chosen by the leader as the initial strategy, qLo, which belongs to the subset qL of QL. The follower will choose the reaction strategy qF*, which belongs to QF in order to maximize its own payoff UF. qF* = max UF (qF; qLo) qL* = max UL (qL; qF)
(15)
C. Utility Function of Primary User and Secondary User In [13], the authors have considered the utility function of the primary user as a combination of revenues from both data transmission and spectrum trading. In our system, the primary user’s utility function consists of five parts: (i) satisfaction of its own transmission, (ii) revenue from selling spectrum to the secondary BS, (iii) gain (iv) the corresponding payment due to the secondary BS’s relay work, and (v) the performance loss due to the shared spectrum with the secondary users. UL = W * ln(b) + P * b - f(LQoS)
(16)
where W is the data transmission rate, b is the spectrum traded, P is the price unit, and f(LQoS) is the QoS function. Replacing f(LQoS) from equation 6 gives the following: UL = W * ln(b) + P * b – QoSlevel* ln(b)
(17)
Secondary user’s utility function consists of the spectrum size and the QoS level. For SU, the utility function is the following:
(13)
UF= W * QoSlevel * ln(b) – QoSlevel * ln(b) * P * b
(14)
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(18)
spectrum and price unit, the equilibrium point to achieve the highest net payoff of the other primary user changes. The best response of both primary users in terms of spectrum size is shown in Figure 7; the size of the offered spectrum in each level is changeable, while the price unit is fixed. If primary user 1 increases the size of offered spectrum, the demand will be increased by customers (SUs). However, the secondary user observes the other offered spectrum by a primary user 2 in order to select the best one in term of QoS and in term of price.
The derivation of SU’s utility provides the best value of spectrum size in term of QoS. Let (dUF / dQoSlevel = 0), we have: QoSlevel = (W / 2 * b * P2)
(19)
which means given strategy P chosen by PU, the SU’s best response is to set the QoS level QoSlevel as in equation 18. Substituting the value of QoSlevel from equation 19 in equation 17 for the utility function of PU, we get: UL = W * ln (b) + P * b – (W / 2 * b * P2) * ln (b)
(20)
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The derivation of PU’s utility gives the best price to SU. We substitute the derivation of SU’s utility in the PU’s utility. Now let (dUL / db = 0) we get the following equation in terms of P:
1000 Spectrum Traded
2*P3 *b2 + P2*W*b + W (ln (b) – 1) = 0
(21)
D. Simulation Result In the simulation, the cognitive nodes are randomly placed in 300x300 m2 and the transmission range is 150 meters. The length of the packet size is 64Kbit. The total number of channels is 15, the transmission rate is 100kpbs, the transmission power is 0.1 watt, the total numbers of SUs are 12 users, and the number of PU is 2 users. PU1 has 10 channels and PU2 has the remaining 6 channels. The usage period is fixed for all users, and is 6 hours. The number of SUs that request channel from PU1 are 7 users and the remaining request channel from PU2. We calculate the competition factor for each primary user as per equation 3 as well as the constant as per equation 9 by using the previous parameters. For PU1 the competition factor α1 = 0.517 and for PU2 α2 = 0.512. The constant A values are A1 = 7 – 1 = 6 and A2 = 5 – 1 = 4.
strategy strategy strategy strategy strategy strategy
(QoS (QoS (QoS (QoS (QoS (QoS
level level level level level level
= = = = = =
1 1 2 2 3 3
& & & & & &
Price Price Price Price Price Price
unit unit unit unit unit unit
= = = = = =
8 8 9 9 10 10
800
600
400
200
0
0
200
400
600 800 Spectrum Traded
1000
1200
1400
Figure 7: PU1 and PU2 strategies in different QoS level and the Nash equilibrium for each level. Basically, if the spectrum size is increased, that means the total price will be increased, which means the profit will be increased. As shown in Figure 7, the Nash equilibrium is the intersection between each PU strategy with other PU in each level. In Figure 7, we have three Nash equilibrium points wherein each level has one point. For the sake of simplicity, we only show the size of the offered spectrum in Figure 7 and we only show the spectrum price unit strategies in Figure 6. The payoff (utility) function of each player in QoS level 1, 2, and 3 is illustrated in Figures 8, 9 and 10 respectively. It shows that the utility function of PU increases, while channel price is increasing. Meanwhile, the strategy of the SU, which is the spectrum size with the QoS level to be used, is increasing, and its utility increases as well.
40 35 30
Price Unit 2
PU2 PU1 PU2 PU1 PU2 PU1
1200
25 20 15 10
PU2 strategy PU1 strategy Nash Equlibrium
5 0
0
5
10
15
20
25
30
35
40
Price Unit 1
Figure 6: Existence of Nash equilibrium Figure 6 shows the price unit response functions and the Nash equilibrium of the competitive pricing of two primary users with fixed spectrum. The figure shows the existence and uniqueness of the Nash equilibrium. Moreover, Figure 6 shows that the slope of the Price unit strategy of primary user PU1 is always greater than one. On the other hand, the slope of the Price unit strategy of primary user PU2 is always less than one. As a result, there is only one point of intersection, which is called Nash equilibrium. Here, the offered price for PU1 is P1* = 9.61873 and for PU2 is P2* = 10.97288. Basically, when one primary user changes its strategy, for example the offered
Figure 8: PU and SU utility in QoS level 1 According to the two-dimensional plane indexed by two decision variables, price and spectrum size, the PU calculates the equilibrium contract (qL*; qF*) according to equations
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(18), (20), and (21) respectively. Then it waits until the SU announces its policy qF as qF*. In our simulation, we have calculated (qL*; qF*) = (11.5; 800) for first level of QoS, (qL*; qF*) = (13; 1440) for the second level of QoS, and (qL*; qF*) = (16; 1880) for the third level of QoS. The first value represents the best price unit for the PU and the second value represents the best spectrum size with QoS level. Note that the utility function of the PU does not achieve maximum when price unit = 11.5 in QoS level 1 or price unit = 13 in QoS level 2 or price unit = 16 in QoS level 3. However, this point called the Nash equilibrium considers the best response for both users, either PU or SU. This point (Nash equilibrium) gives satisfaction to primary user to serve maximum customers while its profit is still acceptable.
path will be selected based on inputs into game which means the game theory model is more dynamic and efficient.
Figure 11: the effectiveness of spectrum management with and without game theory on network throughput
Figure 9: PU and SU utility in QoS level 2
Figure 12: The effectiveness of spectrum management with and without game theory on network delay V.
CONCLUSION
We have modeled the dynamic behavior of spectrum trading and leasing. We have considered multiple primary users and multiple secondary users in a cognitive radio network. In addition, we have presented multiple levels of QoS for different secondary users. We presented two models in this paper; the first system model is without game theory, where the challenge is to find more dynamic, efficient, applicable equations to express all the relations between PUs and SUs by considering all the network elements that could affect the price or spectrum or QoS. In the second system model, we incorporate the game theory concept, where the challenge is to obtain Nash equilibrium in each proposed game. A Bertrand game has been formulated to model the competition among primary users in terms of price unit for the offered spectrum size. A Stackelberg game has been formulated to model the relation between the primary user and the secondary user wherein the primary user is the leader and the secondary user is the follower. The simulation results in the first model
Figure 10: PU and SU utility in QoS level 3 Figure 11 and 12 show the average throughput and the average delay. The spectrum management with and without game theory are applied into the AODV routing algorithm to analysis the network performance. The network performance is better in case of using the spectrum management without game theory because the path will be selected as per SUs’ requirement. However, for the long term, the spectrum management with game theory applied is better because the
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show the dynamicity and efficiency of our proposed equations and the simulation results in the second model show the Nash equilibrium for each game. The major focus for future work will be on applying both the models into routing algorithm to observe the impact of our model in the efficiency of network. In addition, we will consider the billing system for our model as well as we will increase the number of QoS levels. Moreover, we plan to develop our model in game theory part to monitor the behaviors of users to detect if there is any malicious user in the system.
[6]
[7]
[8]
[9]
ACKNOWLEDGMENT The authors are grateful to MITACS – Accélération Québec funds.
the
support
[10]
by
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