Optimal Sensing Strategy for Opportunistic Secondary Users In a Cognitive Radio Network

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1 Optimal Sensing Strategy for Opportunistic Secondary Users In a Cognitive Radio Network Oussama Habachi CERI/LIA Université d Avignon et des Pays de Vaucluse France oussamahabachi@univ-avignonfr Yezekael Hayel CERI/LIA Université d Avignon et des Pays de Vaucluse France yezekaelhayel@univ-avignonfr ABSTRACT In this paper we are interested in evaluating the performance of a cognitive radio network We look for optimizing the decision process of secondary mobiles between sensing or not primary s channels We consider first the global system look for the optimal proportion of secondary mobiles that sense the primary s channels Second we assume that each secondary mobile decides opportunistically to sense or not In this case the secondary mobiles are in competition After showing the existence uniqueness of the equilibrium we evaluate the performance of this equilibrium by looking at the price of the anarchy Categories Subject Descriptors F2 [Theory of Computation]: ANALYSIS OF ALGO- RITHMS AND PROBLEM COMPLEXITY General Terms Performance Keywords Opportunistic sensing Cognitive networks Game theory INTRODUCTION A big new challenge in the networking community is how to put cognition into networks The term cognition is described as the faculty for a mobile or a network to adapt its communication parameters (transmission power for mobiles or frequency for a base station) to perturbations of its environment A radio system having this capability is called a cognitive radio This new field of research has started with the work of Mitola [4] the faculty of new frequency channels usage In wireless networks in contrast to wired networks the capacity is limited to the radio spectrum In order to provide better services with higher quality of service (QoS) in November 2002 the Federal Communication Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage that copies bear this notice the full citation on the first page To copy otherwise to republish to post on servers or to redistribute to lists requires prior specific permission /or a fee MSWiM 0 October Bodrum Turkey Copyright 200 ACM /0/0 $000 Commission (FCC) open the use of many bs that are under-used Indeed the FCC report reveals that the electromagnetic spectrum has gaps bs of frequencies assigned to primary users that at a particular time specific geographic location are inefficiently utilized In a cognitive network two types of users or mobiles are defined: primary secondary On one h primary users have made an agreement with service providers get access to the provider On the other h secondary users are equippedwith acognitive radio then are able to sense primary s channels in order to use one of them if it is free In this paper we are interested in designing an optimal sensing policy for the secondary mobiles Finally we evaluate the loss of performance for a secondary mobile a scenario with opportunistic mobiles Related works Lots of recent articles deal with cognitive radio networks their performance The survey paper [5] gives lots of very interesting problems for evaluating the performance of cognitive radio systems Specifically the author describes how mathematical tools specifically game theory can be applied to analyze those complex wireless systems In [9] the authors consider an energy efficient spectrum access policy Each secondary user will sense the spectrum select subcarriers taking into account data rate requirements maximum power constraint The authors study this problem by considering a non-cooperative behavior among new users with energy efficient allocation scheme Game theory has also been employed in [] for studying optimal power control channel allocation schemes considering a hierarchical network with leaders (primary user) followers (secondary users) Another game model has been proposed in [3] for the performance of carrier sense multiple access (CSMA) The authors focus on how to control the carrier sense threshold for improving network performance in a noncooperative setting In [2] the authors study decentralized MAC protocols such that secondary users look for spectrum opportunities without a central controller They consider a Partially Observable Markov Decision Process propose an analytical framework There are several differences with our work First they consider only primary channels In our context secondary users can decide not to sense share a common channel dedicated to secondary mobiles Second the authors do not consider the competition between the secondary users They look for optimal sensing channel selection schemes that maximize the expected total number of bits delivered over a finite number of slots Their optimal 343

2 sub-optimal policies depend on belief vector based on all past decisions observations of channels state A related model is proposed in [5] In this paper the authors propose an optimal periodic sensing mechanism for secondary mobile The periodic sensing decouples sensing access The optimal policy is based on Constrained Markov Decision Process each secondary mobile maximizes the average number of successful transmissions Finally the authors propose three cognitive access policies: memoryless periodic sensing full observation Finally in [2] the authors propose an algorithm for secondary users in two steps: first any secondary mobile decides wether or not a channel is idle second he determines wether this channel is a good opportunity or not based on channel sensing statistics Some other papers far from our study but in the same cognitive radio context are described in [] [0] [3] [6] 2 Organization of the paper The paper is organized as follows In the next section we introduce the analytical model based on queueing tools we describe in section 3 the optimization of the average total cost for any secondary user In section 4 we consider an optimal individual policy where each secondary mobile decides to sense or not the primary s channels We compare the performance of the decentralized system to the centralized one by looking at the price of anarchy (PoA) After that we propose some mechanism design concepts in order to satisfy QoS constraint at the equilibrium Then we present some numerical illustrations of our results in section 5 Finally we conclude the paper give some perspectives 2 SYSTEM MODEL The system is composed of primary users (PUs) secondary users (SUs) The PUs use K licensed channels one channel is shared between secondary mobiles (see figure ) We assume that primary (resp secondary) users arrive following a Poisson process with rate λ p (resp λ s) The service rates is (resp ) for the primary channels (resp common secondary channel) Those assumptions on Markov processes for arrivals service time are also used in several works like in [2] [5] Figure : Model of opportunistic sensing The system is depicted on figure is composed of two sub-systems The first one namely system S represents the secondary system used by secondary mobiles which do not sense the primary s channels As this common channel capacity is equally shared between the secondary mobiles this subsystem is modeled using an M/M/ queue with a processor sharing (PS) policy In order to guarantee the stability of this queue we take the following assumption: Assumption We assume that the arrival rate λ s of secondary users is strictly lower than the service rate The second system namely S 2 is composed of the two following types of mobiles: () the primary mobiles that have found one free channel (2) the secondary mobiles that have sensed the primary s channels have found a free channel We denote by α the cost of sensing one channel for a secondary mobile Each secondary user decides to sense k channels with k from 0 to K Those k channels are romly selected following a uniform distribution between the K channels For all k {0K} we denote by P k the proportion of secondary mobiles that decide to sense k channels We define P as the vector (P 0P K) The arrival rate in the common secondary channel (subsystem S ) is composed of secondary mobiles that do not sense the primary channels Then the arrival rate of secondary mobile for that particular channel is λ sp 0 We have assumed that the maximum arrival rate λ s is lower than the service rate Then we haveasufficientstability condition of this M/M/ queue The average sojourn time T S (P) for a secondary user that chooses to join the common secondary channel ie not to sense any primary channel is given by: T S (P) = λ sp 0 () For all k any secondary user that senses k channels does not find any free channel is rejected from the system LetB k betheprobabilitythatasecondaryusersensing k channels is rejected We have B k (P) = K i= π i(pk) Ck i CK k where π i is the stationary probability that there are i users in the subsystem S 2 (PASTA principle) For any secondary mobile that decides to sense k primary channels the average sojourn time T S2 (Pk) is: T S2 (Pk) = B k(p) (2) The average utility U S of a secondary user is determined bythe summation of the average sojourn time inside the system the cost of sensing This average utility is expressed by: U S(P) = P 0 P 0λ s + K i= P i( Bi(P) +αi) (3) In order to simplify the analysis we consider the particular case of the two following strategies: () to sense all the K primary channels (k = K) (2) not to sense licensed channels (k = 0) We denote by p the probability of sensing (all the K primary channels) The subsystem S 2 can be modeled using an M/M/K/K queue known as the Erlang-B model with arrival rate λ p+pλ s The blocking probability which is the probability that any user finds all the channels 344

3 occupied is given by the following Erlang-B formula: Π(pK) = ρ(p)k K! K ( ( ρ(p)n )) n! n=0 with ρ(p) = (λp+pλs) This blocking probability depends on the number of primary channels K but also on the probability p This probability is also the proportion of secondary users that senses If this proportion increases the input rate in the subsystem S 2 increases then the blocking probability Π(pk) will also increase Thus there is a tradeoff for secondary mobiles to sense or not In order to give some quality of service (QoS) guarantee for primary users we consider that the parameters of the system are such that the blocking probability Π(pK) of a primary user is lower than a threshold ɛ ie Π(pK) ɛ (4) For all K ɛ this condition is equivalent to defining p max(ɛk) := Π (ɛk) such that the proportion of secondary users that senses is lower than p max(ɛk) For K fixed Π(pK)isincreasingwith p thenp max(ɛk)isunique In the next section we are interested in determining the optimal proportion of secondary mobile that minimizes the average utility defined in (3) of a secondary user under the constraint (4) 3 OPTIMIZATION OF GLOBAL PERFOR- MANCES The average utility U S(p) for a secondary mobile depends on the proportion p of secondary mobile that senses primary channels From equation (3) the objective function is given by: U S(p) = p λ + p( Π(pK) +αkp (5) s( p) Then we look for minimizing this function under the QoS constraint on the primary users ie min p U S(p) such that Π(pK) ɛ We denote by Π (pk) the derivative of the blocking probability depending on the probability p Proposition For all α K we define by p 0 the solution of the following equation: Π(pK) pπ (pk) = αk + ( λ s( p)) 2 The average total cost function U S(p) defined in equation (5) is minimized when p = min(max(p 00)) := p (αk) Proof From equation (5) the average total cost is defined by: U S(p) = p λ + X(p) +αpk s( p) with X(p) = p( Π(pK)) Then for fixed K we have: U S(p) = X (p) +αk ( λ s( p)) 2 So U S(pK) = 0 is equivalent to: αk + ( λ s( p)) 2 = Π(pK) pπ (pk) We have found the optimal repartition p (αk) of secondary users that senses the primary channels in order to optimize the average utility of a secondary user without taking into account the constraint 4 But as this constraint is equivalent to an upper bound on the probability p we have the following lemma that gives the optimal proportion of secondary users that senses under the QoS constraint for primary users Lemma The optimal sensing probability p that satisfies the constraint (4) is: with p max = Π (ɛk) p = min(p p max) 4 OPPORTUNISTIC SENSING POLICY 4 Game model We consider the distributed system in which each secondary mobile decides individually to sense or not the primary channels This system is therefore a non-cooperative gamewithaninfinitenumberofplayers(aswedonotrestrict the time horizon of the system the number of secondary mobiles) Each secondary user decides on his probability p to sense the primary channels looks for minimizing his utility function U(pp ) which depends on his probability p the probability p of all the other secondary mobiles The individual utility U(pp ) is described as follows: U(pp ) = ( p)t S (p )+pt S2 (p )+αpk (6) We have the following relation for all p U(pp) = U S(p) Let define an equilibrium for our non-cooperative game as a strategy which minimizes the utility function U against others using the equilibrium strategy Definition The individual decision p E is an equilibrium if only if: p E = argmin pu(pp E ) 42 Equilibrium We now prove the existence uniqueness of an equilibrium in our non-cooperative game between secondary mobiles Proposition 2 For all K α the equilibrium p E (αk) exists is unique The equilibrium is given by: 0 if < αk + Π(0k) p E < αk + Π(k) (αk) = if > αk + Π(0k) µ s > αk + Π(k) p otherwise with p solution of the following equation: Π(pK) = αk + (7) λ s( p) 345

4 Proof From equation ( 6) the first argument derivative of the utility function is U p (pp ) = T S2 (p ) T S (p )+αk The probability p E is an equilibrium if only if it satisfies the following equation: This equality is equivalent to which leads αk +T S2 (p E ) = T S (p E ) T s (p E ) = αk + Π(pE K) λ s( p E ) = αk + Π(pE K) The left-h side function is continuous strictly decreasing with p (see equation (7)) the right-h side function is also continuous strictly decreasing in p Then this equation has a unique solution inside ]0[ if only if: > αk+ Π(0k) λ s or λ s < αk+ Π(0k) < αk+ Π(k) > αk+ Π(k) Moreover if > αk+ Π(k) > αk+ Π(0k) then the utility function is strictly decreasing the equilibrium is p E = On the other h if < αk+ Π(k) < αk+ Π(0k) the utility is strictly increasing the equilibrium is p E = 0 We proved that the equilibrium exists is unique Then the average total cost of a secondary mobile at the equilibrium is given by: U S(p E ) = if < αk + Π(0k) < αk + Π(k) Π(K) +αk if > αk + Π(0k) > αk + Π(k) αk + Π(p K) otherwise Moreover we prove the following relation between the equilibrium the global optimum Proposition 3 For all α K the optimal sensing probability p is higher than the equilibrium sensing probability p E ie p E (αk) p (αk) Proof We assume that there exists α 0 > 0 K 0 such that p E (α 0K 0) > p (α 0K 0) For the rest of the proof for simplicity we denote p (α 0K 0) by p p E (α 0K 0) by p E Moreover we have T S(p )+αp K T S(p E )+αp E K But as p E is an equilibrium we have T S(p p E )+αp K T S(p E )+αp E K From these two relation we obtain T S(p p ) T S(p p E ) Thus we have ( p )T S (p )+ p ( Π(p K)) ( p )T S (p E )+ p ( Π(p E K)) then ( p )(T S (p ) T S (p E )) p (Π(p K) Π(p E K)) But it s clear that T S is decreasing with p Π is increasing with p then for p E > p the left h side is positive right h one is negative which give a contradiction Thus for all α K we have p E p We have found the equilibrium sensing probability without taking into account the QoS constraint for primary users The following lemma give the equilibrium sensing probability under the constraint 4 Lemma 2 For all α K if p E p max then p E = p E is an equilibrium Otherwise p E = p max is an equilibrium Proof Ifp max < p E weprovedinproposition2thatu S(pp ) has a unique equilibrium p E between 0 The utility function U(pp ) is strictly decreasing between 0 p E increasing otherwise Then U S(pp ) is strictly decreasing between 0 p max which implies that p max is the constrained equilibrium Otherwise pe = p E is an equilibrium satisfies the constraint 4 Corollary For all α K the optimal sensing probability p is higher than the equilibrium sensing probability p E Proof First if p E p max p p max we proved in proposition 3 that p E p Second if p E p max p > p max then p E p Otherwise p E = p = p max We are now interested in the lack of performance (utility) induced by the individual decision In order to measure this gap we use a metric based on the Price of Anarchy principle [8] 43 Price of anarchy Koutsoupias Papadimitriou introduced the concept of Price of Anarchy (PoA) [8] It captures the deterioration of the performance of a non-cooperative system due to the selfishness of its agents Moreover it is well studied in routing games [7] where the PoA describes the worst-possible ratio between the total latency of a Nash equilibrium of an optimal routing of the traffic This metric describes the gap in terms of individual utility in an optimal centralized system or in a totally decentralized system It is expressed as the ratio between the optimal utility centralized the utility at the equilibrium In our context of minimization problem we define this performance metric as: PoA = US(p ) (8) U S(p E ) 346

5 Proposition 4 For all K α we have: U S(p E (αk)) λ s Proof First if < αk + Π(k) < αk + Π(0k) then U S(p E (αk)) = Second if > αk+ Π(k) > αk+ Π(0k) then U S(p E (αk)) = Π(K) +αk λ s Otherwise U S(p E (αk)) = αk+ Π(pE K) = ( p E ) Finally we have for all α K: U S(p E (αk)) The aim is to determine a minimum expression of the PoA or to bound it in order to measure the worst performance of the decentralized system We have the following proposition which gives a lower bound of the price of anarchy This boundisveryinterestingasitdoesnotdependonthesensing cost α on the number of primary channels K Proposition 5 For any α any number of primary channels K we have: PoA(αK) 2( λs µs + ( λ s) ) := PoA λ s Proof The price of anarchy PoA(αK) is expressed by the following ratio: First if PoA(αK) = US(p (αk)) U S(p E (αk)) > αk + Π(k) > αk + Π(0k) then we have p E = As we said earlier in proposition 3 p p E then p = we have Otherwise we know that PoA(αK) = Π(p K) p Π (p K) +αk = ( λ s( p )) 2 Let s focus on the gap between the utility function at the equilibrium the optimal utility function We have for all p α K U S(p E ) U S(p ) = Π(p K) αkp p λ sp E ( p ) + ( λ s( p ))( λ s( p E )) It s clear that the difference between the utility function at the equilibrium the optimal utility function is maximal when p E = 0 Then the price of anarchy is minimal when U S(p E ) U S(p ) is maximized Then PoA is minimized when p E = 0 we focus on the analysis of the PoA in this particular case Let s suppose that when p E = 0 we have Π(p K) +αk < Then we have for all p α K U(p p ) < consequently we obtain U(p 0) < p p + λ s λ s( p ) p + p = λ s λ s λ s Here we have a contradiction In fact U(00) = > U(p 0) if p E = 0 is an equilibrium then U(00) < U(p 0)for allp Finallywe havewhenp E = 0 Π(p K) + αk Moreover when p E = 0 we have the following expression of the price of anarchy PoA(αK) = p ( Π(p K)) +αp K + p ( p ) Thus combining previous results the price of anarchy is bounded by: PoA(αK) p + p ( p ) We look for the minimum of this lower bound Then after some manipulations we obtain: PoA(αK) p + (µs λs)( p ) λ s( p ) = µs λs( (p ) 2 ) λ s( p ) We denote the following function F(X) = µs λs( X2 ) ( X) We have F (X) = λ2 s X2 +(2λ s 2λ 2 s )X+λ2 s λsµs (( X)) 2 Then F (X) = 0 when X = λs µs± () λ s ; moreover we have F(0) = Then the bound is minimized when X = λs µs+ () λ s µs(µs λs) ) 2 ) λs µ λs µs+ µs(µs λs) s λ s( ) λs F(X) = µs λs( (λs µs+ its minimum is Finally for all α K we obtain the lower bound of the price of anarchy: PoA(αK) 2( λs µs + ( λ s) λ s ) Corollary 2 For any α any number of primary channels K we have: PoA(αK) 2( λs µs + ( λ s) ) := λ PoA s Proof First if p p E p max then p = p E = p max PoA(αK) = Second if p p max p E < p max then U S(p max) U S(p ) then PoA(αK) PoA Otherwise we gave in proposition 5 a lower bound of the price of anarchy Finally the price of anarchy under primary blocking constraint is at least equal to the price of anarchy 347

6 44 Mechanism design We have proved in section 42 that in a totally distributed context secondary mobiles reach an equilibrium situation in which all cognitive users have an incentive to sense primary channels with a probability p E In order to satisfy the constraint 4 we must have p E p max This condition can be obtained by an appropriate design of system parameters At equilibrium we have the blocking probability: Π(p E (αk)k) = +αk λ s( p E (αk)) Then in order to satisfy the constraint at equilibrium we are able to tune the following parameters: α K λ s In the following we describe some mechanism design concepts Pricing In order to decrease the primary blocking probability we can increase the cost of sensing α Consequently secondary mobiles will be less motivated to sense primary channels Improving sensing cost will decrease the secondary users s sensing probability but it is complex to be implemented in practice Figure 2: Average total cost U S(p) with α = 0 K = 3 or K = 0 System capacity adjustment Another solution is to increase the primary system capacity K This solution appears simple but in a realistic context operators are limited to the frequency b Moreover adjusting primary system capacity do not fit the basic cognitive radio principles Admission policy Finally we can limit the number of secondary mobiles in the system by applying an admission control Some methods like RED [7] which guarantees that the controlled arrival flow stays a poisson process can be used This approach solve the constraint problem but needs a centralized control mechanism 5 NUMERICAL ILLUSTRATIONS In this section we present some numerical results with different system configurations We consider the following parameters: λ s = 07 λ p = 06 = 08 = We take the constraint that primary users s blocking probability must be lower than ɛ = 0 On figure 2 we check the result of the proposition with the sensing cost α = 0 When the number of primary channels is small (K = 3) we can observe in figure 2 that optimal probability is p = 053 We can also see on this figure the impact of the primary users s constraint on the sensing probability (p max = 06) When the number of primary channels becomes bigger for example K = 0 we obtain p = 087 (figure 2) the primary users s constraint gives p max = Indeed the cost of sensing becomes so large as each secondary mobile senses all the primary channels the proportion of secondary users that senses the primary channels at the optimum is decreasing 5 Sensing cost We analyze the impact of the sensing cost parameter α on the system performance with fixed number of primary channels K = 0 First on figure 3 we observe that the probabilities p p E are both decreasing with α (it is somehow intuitive as α is the cost of sensing; then increasing the sensing cost leads to decreasing of sensing probability) Moreover the equilibrium p E is more sensitive to the Figure 3: Optimal probability of sensing depending on the sensing cost α sensing cost than the optimal probability p (for all α we have p(αk) p E (αk) see proposition 3) This result is obvious when comparing a centralized system to a distributed non-cooperative one Indeed in a non-cooperative system the competition between the agents induces worst global performance of the system This gap of performance is measured with the price of anarchy ( PoA) given on figure4 Weobserve numericallythattheminimumofthe PoA is equal to 0788 that means that the decentralized system in which secondary mobile decides by themselves to sense the primary channels has a performance at most 788% of the optimum centralized system The lower bound of the PoA given by proposition 5 is PoA = 7524% Then this lower bound is very interesting as it gives a simple expression very close to the minimum of the PoA 52 System capacity In this section we are interested in the impact of the number of primary channels on the performance of the opportunistic sensing mechanism of secondary mobiles We consider the sensing cost α = 03 By increasing the number of primary channels the blocking probability of secondary 348

7 Figure 4: Price of anarchy depending on the sensing cost α Figure 6: The global optimum depending on the number of licensed channels Figure 5: Optimal probability of sensing depending on the number of licensed channels mobile will be smaller but the cost of sensing which is linear with the number of primary channels will increase Then the impact of the primary users s constraint can be observed with lower values of K In fact when K = or K = 2 we have p max = 00 as we can see on figure 5 Moreover on figure 5 we observe that the optimal probability ptheequilibrium p E aredecreasing withk Moreover we can see that the equilibrium probability p E is more sensitive to the number of primary channels than the optimal probability p Onthe other h we observe on figure 6 that the minimal average total cost is obtained when K = 3 Finally on figure 7 we plot the price of anarchy depending on K We observe that there is a minimal value which gives the worst performance of the decentralized system compared to the centralized one This bound is equal to 7532% This result says that for the given decentralized system the global performance is at most 7532% of the optimum centralized one Again our lower bound PoA given in proposition 5 is relatively good as it gives PoA = 7524% Figure 7: Price of anarchy depending on the number of licensed channels 6 CONCLUSIONS AND PERSPECTIVES In this article we have defined an optimal sensing policy 349

8 for opportunistic secondary mobile who have access to primary channels We have evaluated this optimal individual policycomparedittotheglobaloptimumusingtheprice of anarchy of the system In perspectives we would like to propose smart sensing algorithms such that secondary mobiles will not have to sense all the primary channels but only few of them Those algorithms could be based for exemple on a Markov Decision Process (MDP) 7 REFERENCES [] M Bloem T Alpcan Tamer Basar A Stackelberg Game for Power Control Channel Allocation in Cognitive Radio Networks in proceedings of ValueTools 2007 [2] Q Zhao L Tong A Swami Y Chen Decentralized Cognitive MAC for Opportunistic Spectrum Access in Ad Hoc Networks: A POMDP Framework IEEE Journal on Selected Areas in Communications Vol 25 No 3 Apr 2007 [3] K Park J Hou T Basar H Kim Noncooperative Carrier Sense Game in Wireless Networks in IEEE Transactions on Wireless Communications vol 8 no [4] J Mitola Cognitive radio: An integrated agent architecture for software defined radio PhD Dissertation Royal Inst Technol (KTH) Stockholm Sweden 2000 [5] S Haykin Cognitive Radio: Brain-Empowered Wireless Communications in IEEE JSAC vol 23 no 2 Feb 2005 [6] JG Wardrop Some theoretical aspects of road traffic research In Proc Inst Civil Eng Part pp [7] T Roughgarden The price of anarchy is independent of the network topology in Journal of Computer System Sciences vol 67 no [8] E Koutsoupias CH Papadimitriou Worst-Case Equilibria In Proc of STACSŠ99 LNCS 563 Springer 999 [9] S Gao L Qian D Vaman Distributed Energy Efficient Spectrum Access in Cognitive Radio Wireless Ad Hoc Networks in IEEE Transactions on Wireless Communications vol 8 no [0] H Zheng C Peng Collaboration Fairness in Opportunistic Spectrum Access in proc of IEEE International Conference on Communication (ICC) 2005 [] W Wang X Liu List-coloring based channel allocation for opem-spectrum wireless networks in proc of IEEE VTC 2005 [2] X Liu S Shankar Sensing-based opportunistic channel access in Mobile Netw Appl no pp [3] H Su X Zhang Cognitive Radio Based Multi-channel MAC Protocols for Wireless Ad Hoc Networks in proc of Globecom 2007 [4] Leonard Kleinrock Queueing systemswiley Interscience New York 975 [5] X Li Q Zhao X Guan L Tong On the performance of Cognitive Access with periodic spectrum sensing in proceedings of the ACM workshop on Cognitive radio networks 2009 [6] S Huang X Liu Z Ding Opportunistic Spectrum Access in Cognitive Radio Networks in proceedings of IEEE Infocom 2008 [7] Floyd Sally Jacobson Van Rom Early Detection (RED) gateways for Congestion Avoidance IEEE/ACM Transactions on Networking August