Mapping of Secondary Virtual Networks onto Wireless Substrate based on. Cognitive Radio: multi-objective formulation and analysis

Transcription

1 Mapping of Secondary Virtua Networks onto Wireess Substrate based on Cognitive Radio: muti-obective formuation and anaysis Andson Marreiros Baieiro 1 and Kevin Lopes Dias Center of Informatics (CIn) Federa University of Pernambuco (UFPE) Emai: {amb4, kd}@cin.ufpe.br Abstract: There is a growing demand for wireess services with different requirements in a dense and heterogeneous wireess environment. Handing this compex ecosystem is becoming a chaenging issue, and wireess virtuaization emerges as an efficient soution. Athough the incusion of virtuaization in wireess networks ensures a better use of resources, current approaches adopted for wireess virtuaization can cause an underutiization of resources, since the resource aocated to a virtua wireess network is not shared with other one. This probem can be overcome by combining wireess virtuaization with the cognitive radio (CR) technoogy and dynamic access spectrum (DSA) techniques. Thus, virtua wireess networks with different access priorities to resources (e.g., primary and secondary) can be depoyed in an overay form and share the same substrate wireess network, where the secondary networks use the resources opportunisticay. However, chaenges emerge in this new scenario, ranging from the mapping to the operation of these networks. This paper is the first to propose the cognitive radio virtua network environment and to formuate the probem of mapping the secondary virtua networks (SVNs) onto the wireess substrate network based on CR. To this end, a muti-obective formuation is designed. Moreover, an anaysis of the metrics defined in the probem is performed in order to give the reader usefu assistance in designing schemes to sove the probem of mapping SVNs onto substrate networks. Keywords: Cognitive Radio Virtua Networks Environment; Secondary Virtua Networks Mapping; Primary Virtua Networks; Wireess Virtuaization. 1. Introduction Wireess standards and mobie device technoogies are progressing quicky such that the future of digita communication wi soon be dominated by a dense and heterogeneous wireess network [1]. Aong with this, the demand for wireess services with different requirements in terms of security, quaity of services (QoS) and quaity of experience (QoE) is growing atey. In this respect, managing 1 Corresponding Address: Aniba Fernandes Avenue, , Recife, Pernambuco, Brazi. Te.: ; E-mai address: amb4@cin.ufpe.br

2 this compex wireess ecosystem is becoming a chaenging issue, and wireess virtuaization emerges as an efficient soution, since different virtua wireess networks can be created, sharing and running on the same wireess infrastructure, and providing differentiated services for users. Wireess virtuaization invoves both infrastructure and spectrum sharing, and introduces new payers to the business mode: the mobie network operator (MNO) and the service provider (SP). The former owns the network infrastructure and creates the virtua wireess networks, and the atter eases the virtua wireess networks, programs them and offers end-to-end services to users [2]. To satisfy the great demand for mobie communications, a natura and scarce resource the eectromagnetic spectrum must be made avaiabe [3]. Athough wireess virtuaization provides a better use of resources, since the infrastructure is more widey shared, the current approaches adopted for wireess virtuaization can cause an underutiization of resources, which is a probem. In current approaches to virtuaization, the resource aocated to a virtua network is not shared with another during the ife time of the virtua networks. As their traffic oad varies over time, there may be cases where the virtua wireess networks are not making fu use of the resources aocated to them. This underutiization can have an adverse effect on the depoyment of new virtua wireess networks and ead to a oss of revenue for the infrastructure provider, since the underutiized resources coud be used for embedding new virtua networks. Combining wireess virtuaization with the cognitive radio (CR) technoogy and dynamic access spectrum (DSA) [3] techniques can overcome this probem of underutiization, where new virtua wireess networks can be depoyed through opportunistic resource sharing and the deepest eve of wireess virtuaization (spectrum based virtuaization [1]) can be achieved. This enabes to have an environment composed of virtua wireess networks with different access priorities to the resources (e.g. primary and secondary), which are depoyed in an overay form and share the same substrate wireess network, in a situation where the virtua wireess network with ower priority (e.g. secondary) ony has access to the resources when the higher priority network (e.g., primary) is not using them. With its cognitive and reconfiguration capabiities, the cognitive radio is abe to sense the environment, detect the avaiabe spectrum bands (resources) and act on them, and thus enabe the depoyment of networks with different priorities. However, chaenges emerge in this new scenario, ranging from the mapping to the operation of these networks.

3 Mapping virtua wireess networks onto wireess substrate networks is a NP-hard probem [4] and it invoves reserving and aocating physica resources to eements that compose the virtua networks such as virtua base stations and virtua communication channes. This probem becomes more compex and chaenging when it considers an environment composed of virtua wireess networks with different priorities of access to the resources, Primary Virtua Networks (PVNs) and Secondary Virtua Networks (SVNs), and that share common resources. The reason for this is that the SVN mapping must consider the demand requested by each SVN in terms of number of users (secondary users-s) and requested bandwidth, for exampe, in order to provide good quaity of service to the s, and the usage pattern of the resources by the primary users, who are the users of the PVNs, to avoid causing harmfu interference to PVN communication. The mapping of SVNs imposes some constraints reated to primary communication, such as keeping the interference in the PU communication beow a defined threshod. It aso seeks to focus on secondary communication, such as to minimize the handover of between SVNs and the bocking of s. Moreover, there are further aims with regard to the provider infrastructure, such as ensuring an efficient utiization of resources. We can note that mapping SVNs is a muti-obective probem. Thus, a formuation, that takes into account these mutipes obectives, needs to be performed. Moreover, it is important to anayze the metrics reated to the obectives in order to know what can impair the performance of each obective and which obectives are conficting with each other. This paper formuates the probem of mapping the SVNs onto the substrate network as a mutiobective probem. It outines the cognitive radio virtua network environment, which is formed by PVNs, SVNs and the substrate network. In this environment, the SVNs access the resources in an opportunistic way (ony when the PVNs are not using them). Moreover, we discuss important metrics to be considered in the mapping process and perform an anaysis of the infuence of some parameters or metrics on other metrics in order to give the reader usefu assistance in designing schemes to sove the probem of mapping SVNs onto substrate networks. To the best of our knowedge, this is the first study to undertake the foowing: describe the cognitive radio virtua network environment, outine a formuation for the muti-obective probem of mapping virtua secondary networks onto substrate networks, considering the coexistence of the SVNs with the PVNs, and anayze the infuence of some parameters and metrics on others.

4 This paper is organized as foows. Section 2 presents the reated works. The cognitive radio virtua networks environment is described in Section 3. Metrics and the muti-obective probem of mapping SVNs onto substrate networks are formuated in Section 4. Section 5 conducts an anaysis of the infuence of some parameters/metrics on others. Section 6 concudes this paper. 2. Reated Works Severa studies have been proposed for network virtuaization in both wired [5] and wireess environments [6]. With regard to wireess networks, some studies have focused on virtuaization considering a specific network technoogy [6][7], generic approaches, without specifying any adopted technoogy in the substrate network [8], or considering a scenario with heterogeneous wireess networks [9]. These studies beieve that the resources aocated to a virtua network cannot be aocated to another network even if the first is not using it a the time. This restriction can cause resource underutiization, especiay when the first virtua network experiences periods of ow traffic oad. In ight of this, in [5] the probem of embedding virtua networks in wired networks, based on an opportunistic sharing of resources, is raised. The authors consider the workoad in a virtua network to be the combination of a basic sub-workoad, which aways exists, and a variabe sub-workoad, which occurs with some probabiity. Thus, mutipe variabe fows (traffic) from different virtua networks are aowed to share some common resources to achieve efficient resource utiization. However, this sharing can cause coisions/interference between variabe traffic from different virtua networks. In [10] the authors transfer the formuation given in [5] from the wired network scenario to wireess one. As in [5], in [10] the authors consider the resources to be homogeneous in terms of offered bandwidth. However, this does not encompass scenarios with heterogeneous networks (e.g. WiMax, LTE, WiFi), where different technoogies have distinct resource units and different data rates [11]. Moreover, even with a singe physica network technoogy, a factor such as noise can have an impact on the data rate achieved in a communication channe [12]. Unike our proposa, in [5] and [10] the virtua networks keep the same eve, regarding right of access to the resource, with no difference between primary virtua network/primary users (higher priority) and secondary virtua networks/secondary user (ower priority). In view of this, athough the formuations in [5] and [10] are based on opportunistic resource sharing, they do not incude these two eements of the cognitive radio environment: the secondary and primary networks/users, being [5] ony focused on wired networks. In addition, in scenarios composed of virtua networks with different access priorities (e.g. primary and secondary),

5 there are other factors (apart from the interference, represented by coision probabiity) that affect both user communication and resource utiization and that must be taken into account during the virtua networks mapping, such as the bocking probabiity of the and the handover probabiity of s between VNs, for exampe, which are negected in both these studies. A patform for end- to- end network virtuaization is proposed in [13]. It aims to create virtua networks made up of wired and wireess resources, and uses CR to manage the virtuaization in the wireess part. However, the authors ony address how to abstract the heterogeneous wireess access networks for seamess connection with the wired virtua network. They neither formuate the probem of virtua networks mapping onto substrate networks, nor anayze the infuences of the parameters/metrics on each other. By using cognitive radio for wireess virtuaization, in [14] the authors adopt an approach denoted as spectrum demand access as a service to achieve dynamic spectrum access (DSA). This approach dynamicay offers spectrum services to users. They adopt the dynamic spectrum aocation approach for DSA, which does not distinguish between primary and secondary users. Thus, each user has a spectrum band for excusive use within a certain time period. This type of excusive aocation can cause spectrum underutiization when the traffic oad is ow. Moreover, the authors ony consider homogeneous requests in their formuation, i.e. consider a virtua topoogies request the same amount of spectrum, which is not aways the case in rea scenarios. Unike [14], our study adopts the opportunistic spectrum access (OSA) approach for DSA, where a difference is estabished between primary and secondary users. In OSA, the s dynamicay search and access ide primary user spectrum bands through spectrum sensing or spectrum databases [15]. In view of this, in the secondary virtua network mapping, we take into account the existence of the primary virtua networks, which have common resources aocated to secondary networks and a higher access priority. In addition, we consider the heterogeneous demands (requests) in our formuation. In next section, we outine the environment considered in our muti-obective probem formuation. 3. The Cognitive Radio Virtua Networks Environment The cognitive radio virtua network environment is made up of three types of wireess networks, substrate/infrastructure network, primary virtua networks (PVNs), and secondary virtua networks (SVNs), where each one is represented in Fig.1 and each network type is iustrated in a specific ayer. The physica ayer encompasses the substrate networks and consists of channes, spectrum bands, base

6 stations, servers, and other features that compose the infrastructure of the wireess environment. The primary virtua networks are ocated on the primary virtua ayer. The secondary virtua ayer is formed by secondary virtua networks. The substrate networks are used in the instantiation of both virtua networks (primary and secondary). In architectures ike that proposed in [13], the infrastructure provider is the entity responsibe for the management of the physica resources, which can cover different types of communication technoogy such as WiMax, WiFi, 3G/LTE. Moreover, these physica resources might beong to different infrastructure providers. The PVNs have higher access priority to the resources (e.g. communication channes) than SVN. The PVN mapping is performed without taking account of the existence of the SVNs, in usua circumstances [8]. It does not take into account the concept of opportunistic sharing. Thus, the resources are divided and aocated to each PVN excusivey. As PVNs traffic oad varies over time, there may be cases where the PVNs are not making fu use of the resources aocated to them, which causes underutiization of the resources in the PVNs, especiay in periods of ow traffic oad. This underutiization can ead to oss of revenue to the infrastructure provider, since the underutiized resources coud be used for embedding new virtua networks. Figure 1. Cognitive Radio Virtua Networks Environment Owing to the existence of ow traffic periods in the PVNs, new virtua networks can be embedded through the opportunistic utiization of underutiized resources. These networks, denoted as secondary virtua networks, have ower access priority to the resources and ony use them when the primary virtua

7 networks are not using them. The adoption of the SVNs can provide better resource utiization (e.g. spectrum) and increased revenue for the provider infrastructure, because more virtua networks can be admitted. However, in order to provide the opportunistic access to the resources, the eements of the SVNs must have mechanisms to identify the activity of the PVN users, denoted as primary user (PU) and access the resource during the absence of the PU, and reease it when the PU returns. In this respect, the cognitive radio emerges as an essentia technoogy for depoying the SVNs, due to its cognition and reconfiguration capabiities [3]. In an environment composed of virtua networks with different access priorities to resources (e.g. PVNs and SVNs), the virtua network mapping becomes more compex and chaenging because the SVN mapping must take account of both the demand requested by the SVN, and the activity of the primary users, who are the users of the PVNs. Thus, two points are important in the SVN mapping: awareness of higher access priority of the PVNs and their activities, to protect the PU from harmfu interference caused by secondary users; to provide a good communication to SVNs. 4. The Probem of Secondary Virtua Networks Mapping Onto a Wireess Substrate Networks This section presents the formuation of the probem of mapping secondary networks onto substrate networks, as a muti-obective probem. In this formuation, the primary and secondary virtua networks are seen as coexisting in the same substrate network. To the best of our knowedge, this is the first work that presents this formuation. 4.1 Formuation of the cognitive radio virtua network scenario In a cognitive radio virtua networks scenario (adopting the two-eve mode [2]), the service provider requests the creation of and manages L primary virtua networks (PVNs). Given that the substrate network is composed of M channes (unit of resources), which are used for mapping the virtua networks, and that the mapping agorithm divides the resources between the PVNs according to percentage q, with = 1,2,3,..., L, 0 1, and q L q = 1, then for each PVN is aocated = 1 Q = M. q or M. q channes, where Q means the set of channes aocated to PVN, x and x are the ceiing and foor functions, respectivey, aimed at keeping the foowing equaity L Q = M. = 1

8 Given that the primary users arriva at channe i ( C i ) of the virtua network, with Ci Q, PU foows a Poisson process with arriva rate λ i,, and the user hoding time given by an exponentia distribution with mean 1 PU µ i,, the utiization of channe i, according to [16], is given by Eq. 1. ρ PU i, PU λ i, = PU µ i, (1) An environment with opportunistic access of the s to the channes is provided by adopting the PU stabiity criterion ρ, < 1. Thus, the channes offer possibiities of opportunistic access by secondary i users, and, hence, are amenabe to be aocated to SVNs. In this approach, in a simiar way to [17], we abstract the existence of many primary users on the same channe. Thus, we consider each channe occupied by a PU per time at maximum. This incudes the behavior of the many possibe PUs on the channe. In this respect, the probabiity of the channe i (that beongs to virtua network ) being busy (ON state) by PU is numericay equa to the utiization of the channe i, given by Eq.1. On the other hand, the probabiity that channe i is not being used by the PU, (i.e. it is in the OFF state) can be denoted as Eq.2. POFF = (1 ρ ) PU i, i, (2) Eq.3. Thus, the average number of ide channes (OFF state) in the virtua network can be given by Q OFF OFF E[ NCh ] = n. P[ NCh = n] n= 1 (3) OFF Where P[ NCh = n] denotes the probabiity that there are n channes in the OFF state (no PUs) in the virtua network, with n = 0,1, 2,3,.., Q. Let A d, n, be the partition d with n eements of the set Q, with d = 1,2,3..., s, where s is the number of partitions with n eements of the set can be obtained by Eq.4. Q, given by Q OFF s =, the vaue of P[ NCh = n] n s OFF P[ NCh = n] = POFFi,. [1 POFFh, ] d = 1 i Ad, n, h { Q Ad, n, } (4)

9 In a simiar way, the probabiity that there are n primary users in the virtua network that was mapped on the set of channes Q can be obtained from Eq. 5. s PU P[ NPU = n] = ρi,. [ POFFh, ] d = 1 i Ad, n, h { Q Ad, n, } (5) The wireess communication is infuenced by severa factors such as noise from other sources, weather, and obstaces in the environment. These factors affect the signa strength perceived by receptor, which varies during the transmission. Thus, to denote the variations in the primary channe conditions, we consider that the signa- to-noise ratio perceived in channe i of the virtua network, 1 SNR( db ) i,, is given by an exponentia distribution with mean SNR( db) λ i, db [18]. Thus the maximum capacity (in bps) of the channe i aocated to the virtua network, denoted as R i,, is given by Shannon s aw [19] and expressed in Eq.6, where Bw i, means the channe bandwidth (in Hertz). R = Bw.og (1 + SNR ) i, i, 2 i, (6) The vaue of SNR i, using the decima scae obtained from the SNR in decibes (db) is given by Eq.7. SNR, = 10 i SNR( db) i, 10 The average capacity achieved on channe i of the virtua network, denoted as R i,, can be cacuated by means of Eq. 8. (7) R = E[ R ] = E[ Bw.og (1 + ( SNR ))] i, i, i, 2 i, (8) Eq.8 represents the average channe capacity when it is aways avaiabe for use by the user, as occurs when the user is the PU. When the user is the, this does not occur. The ony uses the channe in an opportunistic way, when the PU is absent. Thus, considering Eq.8 and the OFF state probabiity, given by Eq.2, the effective rate (on average) achievabe through the opportunistic use on channe i of the virtua network is given by Eq. 9. Re = POFF. R i, i, i, (9) The SVNs provide their services by using the resources aocated to the PVNs in an opportunistic way. In virtua network mapping, there is no one-to-one reationship between PVNs and SVNs in this environment, i.e. each SVN ony has to be mapped over one PVN and vice-versa. Thus, channes aocated to different PVNs can be used by the same SVN, as shown in Fig. 1, where SVN #3 uses the channes aocated to PVN #1 and PVN #3, for exampe, which provides broader network mapping and

10 more possibiities for SVN mapping. This is unike [20] and [21] which adopt an approach that is restricted to a one-to-one reationship between SVNs and PVNs. Thus, in the foowing formuations, we adopted the channe as eve of granuarity, when information about primary virtua activity is taken into account. For the secondary virtua ayer, in this approach, we consider that there are N SVNs to be mapped onto the substrate network. In each SVN ( SVN ), with = 1,2,3.., N, the s perform appications with data rate/bandwidth (BW) requirements given by an exponentia distribution with mean1/ w bps. The arriva of s on the SVN foows a Poisson distribution with a rate of λ users per second. The hoding time is given by an exponentia distribution with mean 1/ µ second [22]. Thus, the average number of s in the SVN, and the amount of resources requested by s can be cacuated by Eq. 10 and Eq.11, respectivey. Bw N 1 = λ. µ = λ.. = N. req, µ w w (10) (11) 4.2 Formuation for Coision Probabiity In the SVNs mapping, it is important to consider other factors apart from the demand for these networks. As the channes adopted in this mapping are shared with the PVNs, which have higher access priority, it is necessary to ensure that the interference eve caused to primary communication does not go beyond a defined threshod. This threshod can be defined on the basis of the service eve agreement (SLA)/service eve specification (SLS) from the PVNs or the interference eve that can be toerated by the appications/signas of the PVNs, for exampe. Thus, in seecting the channes that must be aocated to each SVN, the interference or coision probabiity between PU and must be cacuated to ensure that its vaue wi be beow the defined threshod. Given that the mapping of the SVN onto the substrate network adopted the set of channes, SC = { C, C,..., C }, where SC = n, SC 1 2 n L U Q, and SC SCu = 1 =, for a u, with, u = 1,2,3,..., N being identifiers of SVNs. In the virtua networks mapping (secondary or primary), when each user ( or PU) needs ony one channe to perform its communication, i.e. to meet its demands in terms of data rate, the coision between PU and on the SVN can occur when the number of PUs and s that attempt to access the channes simutaneousy are greater than the number of channes aocated to SVN (13)

11 , with at east one PU and one between the users. Thus, the coision probabiity between PU and on the SVN is given by Eq.13. n Pc ( SC ) = ( P[ NPU = i ; N > n i]) i= 1 Where P[ NPU = i ; N > n i] is the probabiity that in the set of channes SC aocated to SVN, the number of PUs in the channes or seeking to access the channes is i and the number of s is greater than n i. As the network mapping/dimensioning takes pace before the operation of the network, the users are not using the system yet. Their arriva and access attempts occur independenty of each other. Thus, P[ NPU = i ; N > n i] can be obtained from the product between two probabiities, P[ NPU = i ] and P[ N > n i]. The first probabiity is given by Eq.5, and the second by Eq.14. Where n 1 P[ N > n i] =1 - P[ N = k] k = 0 1 λ. e µ P[ N = k] = k! k 1 λ. µ (14) (15) However, in this formuation, the condition that each user needs ony one channe to meet its demand, does not appy to the, but ust to the PU, which we considered that the PU acts on one channe. As the bandwidth requested by the may be greater than the average capacity of a channe, this user wi need more than one channe to perform its communication. When the tries to access more than one channe on the SVN, it may coide with more than one PU. The average demand requested by each and the average capacity offered by the channes from the set CM must be taken into account before the coision probabiity on the SVN can be estimated. Thus, the coision probabiity can be obtained by Eq.16. n n i Pc ( SC ) = P NPU = i ; N > i= 1 Ch (16) Where Ch is the average number of channes required to meet the demand of each on the SVN, which is given by Eq.17, and. is the foor function. 1/ w Ch = max 1, Rch (17)

12 With Rch being the average effective capacity of the channes aocated to SVN, given by Eq.18, and 1/ w the average data rate requested by each on this network. Rch = n i= 1 Re n i, (18) When the coision probabiity of each SVN is obtained, the average coision probabiity on the secondary virtua ayer, if a the N mapped SVNs are considered, is given by Eq. 19. Pc = N = 1 Pc N (19) 4.3 Formuation for Bocking Probabiity As we as giving protection to the primary users by restricting the coision probabiity, the mapping of SVNs onto the substrate network must provide good quaity of service for the s. Thus, it must admit as many s as possibe dimensioned for each SVN. For this reason, the bocking probabiity needs to be determined in the mapping process. The bocking occurs in the SVN when the tota number of PUs together with the average number of channes requested by s, is greater than the number of channes aocated to SVN. Hence, the bocking probabiity on the SVN is cacuated by Eq.20. n n i Pb ( SC ) ( [ ; ]) = P NPU = i N > i= 0 Ch (20) When the mapping of N SVNs is considered, the bocking probabiity on the secondary virtua ayer (on average) is given by Eq.21. Pb = N = 1 Pb N (21) 4.4 Formuation for Joint Utiization As we as seeking to admit as many users as possibe, providing better resource utiization (e.g. better utiization of channes) is aso a goa of both SVN mapping and cognitive radio technoogy through opportunistic access to the resources. Before defining the resource utiization achieved by a given SVN mapping that uses channes shared with PVNs, the activities of both the SVN and PVNs must be considered. Thus, given the set of n channes SC = { C1, C2,..., Cn} used in the mapping of the SVN, the oint utiization (primary and secondary usage) of these channes is given by Eq.22, which is

13 the ratio of the average number of channes occupied by PUs or s to the number of channes aocated to SVN. NPU + (1 Pb ). N. Ch uti = n (22) Where NPU is the average number of PU in channes shared with SVN, cacuated by Eq. 23, which is the difference between the number of channes aocated to SVN and the average number of channes in the OFF state, without PUs, expressed in Eq.3. OFF NPU = n E[ NCh ] (23) The product (1 Pb ) * N denotes the average number of s admitted in the SVN, where N is given by Eq.10, and Pb by Eq. 20. In the SVN mapping, it is important to avoid resource underutiization, such as spectrum, which is a scarce natura resource, and to increase the revenue of the infrastructure provider. When average resource utiization is provided by each SVN, the average oint utiization achieved by mapping of N SVNs in conunction with the utiization provided by primary virtua networks is given by Eq.24. uti = N = 1 uti N (24) 4.5 Formuation for SVN Handover Probabiity The bocking probabiity given in Eq.20 means the reection eve of new s in the SVN, i.e. the network capacity of admit/reect new secondary users. Once the s are admitted, some events triggered by PU activity can affect the quaity of service offered to them. Among these events, the spectrum (channe) handover and secondary virtua networks handover can be highighted. They occur as a resut of the return of the PU to the channe occupied by. In the spectrum handover, the channe seected by to resume its communication is avaiabe in its current SVN. On the other hand, in the SVN handover, the seects a channe in another SVN, since there is no avaiabe channe in its current SVN. Thus, the has to change the channe and the SVN before it can resume its communication. The SVN handover causes greater degradation to secondary communication than spectrum handover, because it resuts in signaing overhead and increases the processing deay of ongoing connections with handover [20].

14 As presented, the SVN handover occurs when the switches between channes from different SVNs, due to the appearance of PU in its communication channe, and when there are not enough avaiabe channes in its current SVN. Thus, before the SVN handover can be triggered, two conditions have to be satisfied: the preemption of the from its current network and the existence of enough avaiabe channes in any other SVN. It is important to note that the preemption from SVN occurs when the coides with the PU in its current SVN and it there are not enough avaiabe channes to aow the to resume its communication. The handover probabiity of the from the SVN can be obtained by the ratio between the number of successfu handover attempts (those that have found enough avaiabe resources in other SVNs) and the number of s admitted in the SVN. Let Pb be the bocking probabiity in the SVN, the number of admitted in this virtua network ( NAd ) is given by Eq NAd = (1 Pb ) λ. µ (25) From the admitted users in the SVN, some can try to execute SVN handover, and these are the ones that coide with the PU. Thus, the number of SVN handover attempts, denoted as NHA, is given by Eq NHA ( SC ) = PcAd. NAd = PcAd.(1 Pb ) λ. µ (26) Where PcAd is the coision probabiity between the s admitted in the SVN and the PUs, which can be cacuated in a simiar way to Eq. 16, where the probabiity P[ N = k], given in Eq.15, is changed to the foowing, given in Eq (1 Pb ). λ. e µ P[ N = k] = k! k 1 (1 Pb ). λ. µ (27) The SVN handover attempt probabiity of the s accepted in the SVN is denoted as Eq.28, which is numericay equa to the coision probabiity between the s accepted in the SVN and the PUs NHA PHA, ( SC ) = = PcAd NAd (28) There may not be enough avaiabe resources in the other SVNs to admit a the s that performed handover from the SVN. Thus, the number of successfu SVN handovers depends on the amount of avaiabe resources in the other SVNs.

15 Since there are (on average) R avaiabe resources in the other SVNs, the number of successfu SVN handovers is given by Eq.29. Min ( NHA. Ch *, R) NH = Ch * (29) Where Ch * is the average number of necessary channes to continue the communication of each that tries to perform handover from SVN to another SVN. This number can be obtained in a simiar way as Eq. 17, by considering the average effective capacity of the channes aocated to the other SVNs, with the exception of the SVN, as denominator. The R vaue is given by Eq. 30. N R = max 0, n NPU + (1 Pb ). N. Ch = 1, ( ) (30) Thus, considering the s admitted in the SVN, the SVN handover is obtained by Eq. 31. P handover, NH = NAd (31) Taking into account the mapping of N SVNs, the average SVN handover probabiity, in the secondary virtua ayer, is denoted by Eq. 32. P handover = N P handover, = 1 N (32) 4.6 The Muti-obective Probem of SVNs Mapping onto Substrate Networks As shown above, severa obectives must be considered in the SVN mapping process. When the infuence of each of these on the and PU communications is taken into account, the foowing optimization probem can be formuated (see Eq.33). Given a set of N SVN requests and the usage pattern of the channes (resources) for the primary networks, to perform the mapping of the SVNs in order to minimize the SVN handover and the bocking probabiities and maximize the oint utiization. Three constraints must be overcome: the coision probabiity in each SVN must be beow a desired threshod, the amount of resources aocated to each SVN cannot be ess than the requested demand, and a common channe cannot be aocated to different SVNs. In notation, we have: Minimize P, Pb and Maximize uti handover Subect to : Pc < thrcoision, = 1,2,3,..., N Raoc Bwreq,, = 1,2,3,..., N SC SCu =, u,, u = 1,2,3,..., N (33)

16 Where respectivey, and Raoc and SC are the amount of resources and the set of aocated channes to SVN, thr coision is the coision probabiity threshod. 5. Anaysis of the Secondary Virtua Networks Mapping This section conducts an anaysis of some of the metrics and parameters defined in the previous section. It aims to show the infuence of some metrics and parameters on other metrics and give the reader usefu assistance in designing schemes to sove the probem of mapping SVNs onto substrate networks as defined in previous section. There are some constraints in the SVN mapping probem, which were outined in the previous section, ike the demands requested by SVN in terms of throughput, coision probabiity threshod, and obectives (such as achieving ow bocking and SVN handover probabiities, and high resource utiization). Some of these constraints and obectives concern primary communication, such as keeping the coision probabiity (interference to PU) beow a defined threshod, whie others invove secondary communication, such as the question of how to minimize the SVN handover and bocking probabiities. In addition, there is, for exampe, the question of how the provider infrastructure and network environment can provide efficient resource utiization. Achieving a these obectives simutaneousy is a chaenging process, because some confict with each other. If the SVN mapping is focused on a specific obective, it can deteriorate other one. Thus, in this section an anaysis is conducted of some metrics to achieve certain obectives, when a particuar parameter varies. This anaysis aims to provide an overview of the impact of certain parameters on some metrics (obectives), and of one obective on another obective. The primary utiization rate of the channes is an important parameter and must be taken into account in the SVNs mapping, because it directy affects metrics ike the coision and bocking probabiities and oint utiization of resources, which are among the obectives of the probem defined in Eq. 33. Fig 2 considers the number of channes aocated to SVN, arriva rate and hoding time to be fixed vaues, and shows the behavior of the coision probabiity, bocking probabiity and oint resource utiization when the primary utiization rate of the channes aocated to a particuar SVN varies. Low bocking and coision probabiities can be achieved by seecting the channes with a ow primary utiization rate to map the SVN, as iustrated in Fig. 7. However, choosing channes with a ow

17 primary utiization rate can cause a reduction in the oint utiization of the resources, despite the higher admission rate in the SVN, which is inferred by a ower bocking probabiity and higher resource utiization by. On the other hand, if channes with a high primary utiization rate are seected, higher resource utiization can be achieved, as iustrated in Fig.7. But, at the same time, this might cause an increase in the coision and bocking probabiity, which wi affect both the primary and secondary communications. In addition, athough there is an increase in the oint utiization when channes with high primary utiization are seected, the resource utiization by secondary users decines unti it reaches the nu vaue, and there is no onger any possibiity of the s using the seected channes opportunisticay, i.e., ony the PUs use the channes, as iustrated in Fig.2. Thus, in the mapping of a SVN, it is important to baance the seection of the channes, by not ust adopting channes with a high primary utiization rate or a ow rate, to achieve a good tradeoff between the coision probabiity, bocking probabiity and oint resource utiization. Figure 2. Infuence of Primary Utiization on SVN mapping Fig 3 takes into account the number of channes adopted in the mapping of the SVN, and iustrates the resuts for the coision, bocking and handover attempt probabiities, and oint utiization, when the number of aocated channes varies and the primary utiization rate, arriva rate and hoding time are fixed. It can be noted that the coision and bocking probabiities decine when the number of channes aocated to SVN increases. This means that there is ess interference to PU communication and fewer s are reected in the SVN, which are positive factors. In addition, with more channes

18 aocated to SVN, there are generay more resources to meet the demand and, hence, ess chance of the performing handover. However, the increase in the number of channes, from a given point (14 channes), usuay eads to a reduction in oint resource utiization, as iustrated in Fig.3, because despite the ow bocking rate of in the SVN, the denominator in Eq.22 grows faster than the numerator, i.e. the amount of aocated resources to SVN is much arger than the demands to be met. On the other hand, if a reduced number of channes is empoyed in the SVN mapping, the oint resource utiization increases, which is a positive factor, but the coision and probabiities increase too, which is a negative one. It is worth noting the behavior of the SVN handover attempt/ probabiity, which composes the SVN handover probabiity, and oint resource utiization, when the number of channes varies within a particuar range, (between 10 and 14). Within this range, when there is an increase in the number of aocated channes, the oint resource utiization and the handover attempt probabiity increase too. Given the oint resource utiization, when there were more channes, more s were admitted and the numerator of Eq.20 grew more than the denominator. With regard to the handover attempt probabiity, the increase of the number of channes caused a higher admission of in the SVN, but the number of channes did not grow proportionaity to the admission of s. Thus, the SVN occupation rate increased, which increased the ikeihood of the switching from the SVN. Figure 3. Anaysis of variations in the number of Channes Aocated to SVN On the basis of the previous anaysis, it shoud be pointed out that the bocking probabiity has an impact on both oint resource utiization and handover attempt probabiity. The bocking probabiity indicates the eve of admission/reection of in the SVN. Thus, Fig.4 iustrates the behavior of the

19 handover attempt probabiity and oint resource utiization when different vaues are defined for the bocking probabiity. When the bocking probabiity increases, the oint resource utiization and the handover attempt probabiity decrease, because fewer s are admitted in the SVN. Thus, in seecting channes that wi be aocated to SVN, the infuence of the bocking probabiity on other metrics shoud be taken into account. Figure 4. Infuence of the bocking probabiity 6. Concusions and Future Directions In this paper, we have addressed the combination of cognitive radio, dynamic spectrum access techniques and wireess virtuaization in order to overcome the probem of resource underutiization that can occur when current approaches to wireess virtuaization are adopted. Athough this combination enabes virtua wireess networks with different priorities of access to the resources (PVNs and SVNs) can share common substrate networks, where the SVNs access the resources opportunisticay, the mapping of SVNs onto substrate networks is a chaenging probem, where there are obectives reated to the PU, and MNO. Thus, we have outined this new scenario and formuated the SVNs mapping onto substrate networks as a muti-obective probem. Moreover, an anaysis of the infuences of some parameters/metrics on other metrics was performed. It aimed to give the reader usefu assistance in designing schemes to sove the probem of mapping SVNs onto substrate networks. Future works incudes designing a scheme to sove the SVN mapping probem and evauating it in terms of metrics as coision probabiity, bocking probabiity, SVN handover probabiity and oint resource utiization.

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