Performance analysis of spectrum handoff under heterogeneous spectrum environment in ad hoc and centralized CR networks

Ad Hoc Networks 91 (2019) 101877

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Performance analysis of spectrum handoff under heterogeneous spectrum environment in ad hoc and centralized CR networks Shanidul Hoque∗, Wasim Arif Electronics and Communication Engineering, National Institute of Technology Silchar, Cachar, 788010, Assam, India

a r t i c l e

i n f o

Article history: Received 23 November 2017 Revised 20 October 2018 Accepted 30 April 2019 Available online 1 May 2019 Keywords: Cognitive radio Heterogeneous spectrum environment Negotiated situation Opportunistic situation Performance metrics Spectrum handoff

a b s t r a c t The prime objective of cognitive radio (CR) is to address the problem of spectrum scarcity and inefficient usage of spectrum, by allowing the unlicensed or cognitive users (CUs) to access the underutilized licensed spectrum of the primary users (PUs). CUs experience considerable performance degradation due to the event of random interruptions by PUs in their respective bands of operation. In this article, we develop a spectrum management scheme and evaluate the performance of the CUs under heterogeneous spectrum environment (HetSE) in both ad-hoc (opportunistic) and centralized (negotiated) CR networks. We consider a finite threshold period (Dth ) for spectrum handoff delay to improve the performance of the CUs for both opportunistic situation with backup channels (OSB) and negotiated situation with backup channels (NSB). The spectrum handoff performance measuring metrics: link maintenance probability, link failure probability, probability mass function of spectrum handoff, expected number of spectrum handoff and non-completion probability of the CUs, are derived under heterogeneous spectrum environment to investigate the characteristics of the network for both opportunistic and negotiated spectrum access strategies. © 2019 Elsevier B.V. All rights reserved.

1. Introduction With remarkable growth of wireless applications and everincreasing demand of higher data rates, the mobile data traffic is likely to increase eightfold by 2020 as per the report of CISCO Visual Networking Index (VNI) [1]. The rapid development of smart devices & multifold growth of applications have led to the spectrum scarcity problem in wireless network [2–4]. However, the fixed spectrum sharing policy levied by the government agencies cannot solve the spectrum scarcity and underutilization problems. To address the spectrum efficiency problem, the FCC introduced the concept of Dynamic Spectrum Access (DSA) policy where an unlicensed devices or cognitive users (CUs) are allowed to dynamically access the underutilized licensed spectrum [5,6]. Mitola et al. [7] defined the unlicensed device as Cognitive Radio (CR) which can operate in both licensed channels (LCs) and unlicensed channels (UCs) to increase the spectrum capacity under Heterogeneous Spectrum Environment (HetSE). To significantly access the LCs and UCs, the CR requires four major functions as [8,9]: spectrum sensing, spectrum management, spectrum sharing and spectrum mobility. This article is mainly focused on spectrum mobility or spectrum handoff performance for different spectrum access strategies

∗

Corresponding author. E-mail address: [email protected] (S. Hoque).

https://doi.org/10.1016/j.adhoc.2019.101877 1570-8705/© 2019 Elsevier B.V. All rights reserved.

(opportunistic and negotiated) under HetSE of licensed and unlicensed spectrum bands. In a CR network, the arrival of the higher priority PUs have a negative impact on the performance of the CU. As soon as a PU arrives in its own licensed channel the current, the current CU promptly vacates the channel and handovers to another free channel, either to LCs or UCs, to ensure QoS for both the network [10]. Thereafter, the interrupted CU rebuilds a connection to continue its service in the system. In HetSE [11]: the LCs are shareable between PUs and CUs; the UCs are sharable between interrupted CUs and classical users (CUs∗ ) without cognitive property as per the IEEE 802.11 standard.

1.1. Related works to spectrum handoff performance In literature, most of the researcher evaluated the performance of the CU when it operated on the LCs in CR networks. In [12], Tang et al. modeled the call blocking probability and dropping probability of secondary or cognitive users, and analyzed the performance of a secondary system where the CUs employing an overlay approach of sharing licensed spectral resources with a primary system. In [13], the authors developed a Markovian model to analyze the performance of a spectrum sharing scheme with buffering for new and interrupted CUs. Lai et al. [14] proposed two channel reservation schemes and Dynamic Channel Placement Reservation

2

S. Hoque and W. Arif / Ad Hoc Networks 91 (2019) 101877

to reduce the forced termination probability of the CU. In [15], the authors explored the link maintenance probability for different spectrum handoff schemes in CR networks. Lu et al. [16] proposed an adaptive power control based spectrum handoff scheme to improve the spectrum handoff rate and effective data rate of the CU. A queuing model is developed in [17] to characterize the channel usage behaviors and derived the blocking probability and link failure probability for real time traffic of the PUs and CUs. In [18], authors derived probability of spectrum handoff and investigated the impact of residual time distributions of spectrum holes on it. Chai et al. [19] designed joint spectrum handoff and resource allocation strategy to analyze the handoff performance of the CUs in CRNs. In [20], Gkionis et al. proposed a hybrid handoff model based on PUs activity model for CR ad-hoc network. The handoff performance metrics such as probability of spectrum handoffs and expected number of spectrum handoffs of the CU are derived in [21,22] for different residual time distributions without considering the presence of the UCs and CUs∗ in the system. In [12–22], the existence of the UCs and the CUs∗ are not considered in the performance evaluation of the CU. In [11,23–25], the authors considered the presence of UCs and CUs∗ under HetSE to evaluate the performance of the CU in CR adhoc networks. The authors presented an analytical model in [10] to evaluate the performance of the CUs under a HetSE of both LCs and UCs. In [23,24], the authors proposed dynamic spectrum sharing model considering both the primary channels (LCs) and secondary channels (UCs) to analyze the performance of the CR ad-hoc networks. An analytical Markovian model is developed in [25] to evaluate the blocking probability, dropping probability and throughput of CUs in CR ad-hoc networks. However, the proposed spectrum access policies in literature may cause unwanted spectrum underutilization in many cases. In literature [11,23–25], the authors considered that the CU begins its service by operating on the LCs and upon interrupted by the PU, it transfers the ongoing communication to the UCs, if available. This may cause i) available LCs to be underutilized, ii) depriving CUs∗ from appropriate use of UCs which leads to degradation of overall performance of the system in terms of QoS. In [11–25], the performance analysis of the CUs are investigated under distributed or ad-hoc CR network architectures only. However, Zhang [26] proposed an analytical model to investigate the short-term and long-term spectrum handoff performances of the CU in both opportunistic and negotiated situations. In [27], Tumuluru et al. proposed various DSA schemes based on prioritized CUs traffic to evaluate the performance of the distributed and centralized CR networks. In [26,27], the authors proposed spectrum management policy to evaluate the performance of the CUs under centralized and distributed CR networks without considering the existence of the UCs and CUs∗ .

Fig. 1. Spectrum management scheme of CU in OSB.

• We develop a spectrum management scheme, and derive link maintenance probability and link failure probability of the CU under HetSE in both opportunistic situation with backup channels (OSB) and negotiated situation with backup channels (NSB). The impact of spectrum handoff threshold period (Dth ) on link maintenance and failure probability is also investigated in both OSB and NSB. • We model the probability mass function of spectrum handoff for both complete and incomplete service period of the CU under HetSE in OSB and NSB. We also investigate the effect of the CU dynamics on probability mass function of spectrum handoff along with PUs’ activity model. • Thereafter, the expression for expected number of spectrum handoffs for both complete and incomplete service of the CU is developed to characterize the behavior of the CR networks with opportunistic and negotiated spectrum access strategies. We also demonstrate the impact of different tele-traffic parameter distributions such as service time distributions of PU and CU on expected number of spectrum handoffs under HetSE in OSB and NSB. • The non-completion probability of the CU service is directly related to the throughput of the system. In this article, we model the non-completion probability of the CU service due to unsuccessful spectrum handoff for both opportunistic and negotiated spectrum access strategies under HetSE. The effect of service time distributions of PU and CU on non-completion probability is also investigated in terms of mobility factor of spectrum holes for both OSB and NSB. 2. System model and analysis

1.2. Our contributions to this article In existing literature, a detailed spectrum handoff performance analysis of CU in terms of link maintenance and failure probabilities, probability mass function, expected number of spectrum handoffs and non-completion probability considering the joint existence of LCs & UCs is not investigated. Analyses of these parameters in HetSE for both opportunistic and negotiated situations are also not available. For a complete investigation of spectrum handoff performance & implementation in such environments, these parameters are essential and need to be analytically modelled. Our major objectives are to analytically demonstrate the behavior of the spectrum handoff performance metrics of the CU under HetSE in ad-hoc and centralized CR networks. Our main contributions to this article are accentuated as follows:

In this section, we describe the proposed mathematical model and investigate the performance measuring metrics of a CU under HetSE of licensed and unlicensed channels in CR networks. We assume that the HetSE comprises of two different types of spectrum pools for both opportunistic and negotiated situations. The first spectrum pool (SP1 ) is partitioned into C1 number of licensed channels (LCs) and which can be sharable between higher priority PUs and lower priority CUs. The second spectrum pool (SP2 ) consists of C2 number of secondary or unlicensed channels (UCs) and which can be accessed by the interrupted CUs and CUs∗ with the same priority. Figs. 1 and 2 show the concept of proposed spectrum management scheme of CU in both OSB and NSB under HetSE. The FCC aims to use CR technology in licensed spectrum band via Dynamic Spectrum Access (DSA) policy to utilize

S. Hoque and W. Arif / Ad Hoc Networks 91 (2019) 101877

3

obtained according to Erlang-B formula as [28]

Pi =

  C1 ρ1i  ρ1i i!

i=0

i!

f or

0 ≤ i ≤ C1

(1) λ

where i is the licensed channel state in SP1 and ρ1 = μpu pu

 −1 C1 ρ1C1  ρ1i

Pb1 =

Fig. 2. Spectrum management scheme of CU in NSB.

C1 !

We assume that the arrival process of the CUs∗ in SP2 follows the Poisson’s random process with mean arrival rate λcu∗ and mean service time 1/μcu∗ . Let the pdfs of service period r ) of CUs∗ are denoted by (tcu∗ ) and residual service period (tcu ∗ ftcu∗ (t )and ftuc∗ r (t ), respectively. Now, the relationship between the pdfs of service period and residual service period can be written as [28]

ftcur ∗ = the unused spectrum band in order to improve the spectrum efficiency [6]. Therefore, in HetSE scheme, the LCs are used as operating channels (Fig. 1(a)) and the UCs are used as backup channels by a CU (Fig. 1(c, i)) [11]. If a CU begins its service by operating on a UC and a CU∗ arrives in the channel during its service, the service of the CU∗ is blocked. This is because the CU∗ has not any legitimate authorization to access the LC even though it is available and also the CU will not vacate a channel to CU∗ as both of them have same access priority to the UC. Therefore, the service of the CU∗ may drop and also the problem of spectrum underutilization in LC remains unsolved. During the service period in LCs, a CU may be interrupted by the arrival of higher priority PUs in the same channel (Fig. 1(b)). On all such events, the CU immediately vacates its current channel and look for available LCs in order to complete the ongoing communication. The process of transferring ongoing communication of a CU from one LC to another available LC in the same spectrum pool (SP1 ) is termed as intrapool spectrum handoff (Fig. 1(b)). This handoff scheme does not require RF font end reconfiguration and hence, the switching delay is negligible in intrapool spectrum handoff scheme [4]. In case of blocking in SP1 , the interrupted CU search for backup channel and transfers the ongoing transmission from SP1 to any free UC of SP2 . The process of switching the ongoing CU service from one spectrum pool to another spectrum pool is known as interpool spectrum handoff (Figs. 1(c, i) and 2(c, i)). This spectrum handoff scheme requires RF font end reconfiguration which takes longer period due to the diverse frequency range in different spectrum pools [4]. Let Tsw be the switching delay when the CU performs interpool spectrum handoff. For the case when all the licensed and unlicensed channels are busy in both the spectrum pools, the service of the CU is blocked (Figs. 1(c, ii) and 2(c, ii)). We assume that a CU could wait in the system for a maximum time period of Dth before termination due to unavailability of channels. If any channel becomes free within period Dth , the CU continues its ongoing transmission by accessing that free channel. Otherwise, the service link of the CU is terminated due to unavailable of LCs and UCs in the system. We assume that the arrival process of PUs follows the Poisson’s random process with mean arrival rate, λpu . Let the service period of PUs is represented by the random variable (RV) Tpu with mean 1/μpu , probability density function (pdf) fTpu (t) and cumulative distribution function (CDF) FTpu (t). Let a RV Tcu represents the service period of a CU with mean 1/μcu , pdf fTcu (t) and CDF FTcu (t). Now, a user is blocked in SP1 if all the LCs are used by PUs. Therefore, the steady state probability (Pi ) and blocking probability (Pb1 ) can be

(2)

i!

i=0

1 − Ftcu∗ (t ) E [tcu∗ ]

(3)

2.1. Performance analysis of CU in OSB or CR ad-hoc networks In OSB, ad-hoc devices with cognitive capabilities (CUs) opportunistically access the spectrum bands to increase the spectrum capacity without any centralized server or CR controller (CRC) in the system as shown in Fig. 1. Here a PU always arrives in its own channel and hence, the current CU using the same channel needs to promptly vacate. Let PV denotes channel vacating probability which designates the probability that a CU vacates a LC upon arrival of PUs and can be calculated in opportunistic network situation as [26] C 1 −1

PV =



i=0

1 C1 −i



Pi (4)

1 − Pb1

where 1/(C1 − i) is the probability that a PU arrives in the system and reclaims a particular channel among (C1 − i). Now, if all the LCs are busy in the system, the CU transfers the ongoing communication to the available backup or unlicensed channel (Fig. 1(c, i)). However, if there is no available UC, the interrupted CU’s service is blocked in SP2 and the blocking probability of the interrupted CU in SP2 can be obtained as

Pb2 =

 −1 C2 ρ2C2  ρ2i

C2 !

j=0

(5)

j! λ

where j is state of the UCs in SP2 and ρ2 = μcu ∗ cu Having established the vacating and blocking probabilities of a CU in OSB, the performance measuring parameters such as link maintenance & failure probabilities, probability mass function, expected number of spectrum handoffs, and service non-completion probability of a CU are derived in the following sub-sections. ∗

2.1.1. Link maintenance probability Let qs 1 be the link maintenance probability of the CU when it switches the service from one LC to another available LC in the same spectrum pool SP1 (intrapool spectrum handoff). The link maintenance probability of the CU during intrapool spectrum handoff can be obtained as

qs1 = PV [(1 − Pb1 ) + Pb1 Pb2 P r (TLC < Dth )]

(6)

where TLC is intrapool spectrum handoff delay in SP1 and which is given by



r r r TLC = min Tpu, 1 , Tpu,2 .....Tpu,C1 −1 , Tpu,C1



(7)

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S. Hoque and W. Arif / Ad Hoc Networks 91 (2019) 101877

r where Tpu,i represents the residual service period of PU in ith licensed channel. Now, the term Pr(TLC < Dth )in (6) can be calculated as







r r r P r (TLC < Dth ) = P r min Tpu, 1 , Tpu,2 .....Tpu,C1 −1 , Tpu,C1 < Dth )

 

r = 1 − P r Tpu > Dth

 C1 −1 

P r Tpu > Dth



= 1 − β C1 −1 γ

(8)

where

 r   r  β = Pr Tpu > Dth = 1 − P r Tpu ≤ Dth = 1 − FTpur (Dth )

(9)

  γ = Pr Tpu > Dth = 1 − Pr (Tpu ≤ Dth ) = 1 − FTpu (Dth )

(10)

The CU performs interpool spectrum handoff when all the LCs in SP1 are busy. Let qs2 be the link maintenance probability of the CU during interpool spectrum handoff and which can be obtained as

qs2 = PV Pb1 [(1 − Pb2 )P r (Tsw < Dth ) + Pb2 P r (TUC < Dth )]

(11)

where switching delay, Tsw = min(tsw,1 , tsw,2 , .....tsw,C2 ) and inr r trapool spectrum handoff delay, TUC = min(tcu + tsw,1 , tcu + ∗,1 ∗,2 r r tsw,2 , ...tcu∗,C + tsw,C2 ). Here tsw,j and tcu∗, j + tsw, j represent the 2 switching delay and interpool spectrum handoff delay when the CU transfers its service from LCs to jth UC. By replacing Tsw and TUC in (11), we can write



  qs2 = PV Pb1 (1 − Pb2 ) 1 − {P r (tsw > Dth )}C2   C2 r + Pb2 1 − {P r (tcu ∗ + tsw > Dth )}

    = PV Pb1 (1 − Pb2 ) 1 − αC2 + Pb2 1 − ξ C2

(12)

α = Pr (tsw > Dth ) = 1 − Pr (tsw ≤ Dth ) = 1 − Ftsw (Dth )

(13)

r ξ = Pr(tuc + tsw ) > Dth ) = 1 − FTUC (Dth )

(14)

r and t . The pdf here, TUC is the sum of two independent RVs tcu sw ∗ of TUC can be obtained as

fTUC (t ) =

t 0

ftcur ∗ (x ) ftsw (t − x )dt

(15)

The link of the interrupted CU will be maintained if any of the following conditions are satisfied: (a) at least one available LC in SP1 or (b) at least one channel free in SP2 and (Ts w < Dth ) or (c) SP1 and SP2 are busy and a channel in either of the pools becomes available within Dth . Therefore, the link maintenance probability, qs of the CU in OSB can be derived as

⎡

qs = PV ⎣



⎤

(1 − Pb1 ) + Pb1 (1− Pb2 )Pr (Tsw < Dth )

r r r r +Pb1 Pb2 P r min Tpu, , Tpu,C1 , tcu 1 , Tpu,2 .....Tpu,C1 −1  ∗,1 r r +tsw,1 , tcu∗,2 + tsw,2 , ....tcu∗,C2 + tsw,C2 < Dth



= PV (1 − Pb1 ) + Pb1 (1 − Pb2 ) 1 − αC2



+Pb1 Pb2 1 − β C1 −1 γ ξ C2



(18)

where

Sn = t pu,1 + t pu,2 + t pu,3 + ..... + t pu,n−1 + t pu,n =

m 

t pu,n

(19)

and tpu,n represents inter arrival time between (n − 1)th and nth PUs. During the service of the CU, this inter arrival time of PUs indicates the duration between the arrival of (n − 1)th PU and nth (next) PU on a channel in the system. A CU experiences zero handoff if the service time of the CU is less than inter arrival time of PU in the same channel or the PUs arrive in the other channel during that period. Therefore, the probability mass function of zero spectrum handoff of the CU in OSB can be obtained as

Pr(H = 0 ) = Pr(Tcu < t pu,1 ) + =

y≤x

+

∞ 

Pr(Sm < Tcu < Sm+1 )(1 − PV )

m

m=1



fTcu (x ) ft pu ,1 (y )dydx

 ∞ 

m=1

∞

fTcu (t )

0



t 0

λ pu m xm−1 e−λ pu x −λ pu (t−x) e dxdt ( m − 1 )!



× (1 − PV )

m

= fT∗cu (λ pu ) +

∞  (λ pu PV − λ pu )m ∗ (m) f Tcu (λ pu ) m!

(20)

m=1







Pr(H = 0 ) = fT∗cu (λ pu ) + fT∗cu (λ pu PV ) − fT∗cu (λ pu ) = fT∗cu (λ pu PV )

In case there is no channel being available within Dth , the link will be terminated and the link failure probability of the interrupted CU in OSB can be modeled as



r r r r q f = PV Pb1 Pb2 P r min Tpu, 1 , Tpu,2 .....Tpu,C1 −1 , Tpu,C1 , tcu∗,1



r r + tsw,1 , tcu ∗,2 + tsw,2 , ....tcu∗,C2 + tsw,C2 > Dth

= PV Pb1 Pb2 β C1 −1 γ ξ C2

λ pu nt n−1 e−λ pu t ,n ≥ 1 ( n − 1 )!

where fT∗cu ( ) denotes the Laplace transform of fTcu (. ) and fT∗(m ) (. ) cu denotes the mth order derivative of fT∗cu ( ). Now, apply Taylor’s infinite series theorem in the 2nd term of (20), we get standard form for Pr(H = 0) as

⎦

(16)



fSn (t ) =

n=1

where



2.1.2. Probability mass function of spectrum handoff In this section, we model the probability mass function of spectrum handoff for both complete and incomplete service of the CU in OSB. In a total service period, a CU has to undergo multiple numbers of spectrum handoff, say n, in order to successfully complete its ongoing transmission. Here complete service of a CU implies that it performs all the n spectrum handoffs successfully and completes the ongoing service during its total service period. If a CU experiences (n − 1) successful spectrum handoff and fails to complete nth spectrum handoff due to the unavailable channels in the system, the CU is forced to terminate its service in the nth event. In this case, the CU service will not be completed and this is termed as incomplete service of the CU. The probability mass function (pmf) of spectrum handoff primarily means to define the discrete probability distribution of the RV and is useful in characterizing short term and long term performance of the cognitive radio network. Let H be the RV presenting the number of spectrum handoffs during total service period of the CU. For Poisson’s arrival process, the inter arrival time of PUs (Sn ) during the CU service period follows Erlang distribution [29] and hence, the pdf of Sn can be written as



(17)

(21) Suppose (m + n) number of PUs arrive in the LCs during a CU service period, where n number of PUs appear in the same LC used by the CU, and m number of PUs appear in other LCs. Therefore, a successful completion of the CU service needs n spectrum handoffs. We consider two situations, complete service where the CU successfully completed its communication, incomplete service where the CU is forced to terminate in the nth event. The probability mass function of n spectrum handoff of a CU considering

S. Hoque and W. Arif / Ad Hoc Networks 91 (2019) 101877

the above two situations can be expressed as

Applying Taylor’s infinite series theorem to (26), we obtain

Pr(H = n ) = Pr (H )succ + Pr (H )term

(22)

where Pr(H)succ refers to the probability mass function of the CU that it experiences n spectrum handoff successfully during its complete service period. In OSB, a CU successfully performs n spectrum handoffs in two situations: (a) the CU experiences n successful intrapool spectrum handoffs in SP1 or (b) the CU successfully experiences (n − 1) intrapool spectrum handoffs in SP1 and nth spectrum handoff in SP2 (interpool) due to unavailability of free LC during nth spectrum handoff event. Hence, we can write UC Pr (H = n )succ = Pr(H )LC succ + Pr (H )succ

Pr(H )LC succ =







[PV [(1 − Pb1 ) + Pb1 Pb2 Pr (TLC < Dth )]] (1 − PV ) n

∞ 

=





 ∞ 



n!



(24)

m!

By applying Taylor’s infinite series theorem, we can simplify (24) as

Pr(H )LC succ =

(−λ pu qs1 )n n!

fT∗cu(n ) (λ pu PV )

(25)

Pr(H )UC succ =



 Pr(Tcu > Sm+n )

m=0

+Pb2 Pr (TUC < Dth )]](1 − PV )

m





Pr(Tcu > Sm+n )

m=0 n−1

= ( qs1 ) dt

qs2

(1 −

∞ 

m=0 0 m PV

∞

(28)

(−λ pu qs1 )n−1 λ pu ( n − 1 )!  qs1 f ∗Tcu (n ) (λ pu PV ) n







+ qs2 + q f F ∗Tcu (n−1) (λ pu PV )

(29) 2.1.3. Expected number of spectrum handoffs The number of spectrum handoffs requires to be performed by a CU during its entire service period is defined as expected number of spectrum handoffs (E(H)). E(H) has a negative effect on the performance of the CR network in terms of handoff delay, link maintenance and service completion of a CU communication. To design better and efficient CR networks, the gross spectrum handoff footprint should be minimized for a total service period of a CU. In this section, we develop an analytical model of E(H) considering both complete and incomplete service of the CU under HetSE and which can be expressed as

E (H ) =

∞ 

n Pr(H = n ) =



×

∞  (−λ pu qs1 )n−1 λ pu n ( n − 1 )! n=0

qs1 f ∗Tcu (n ) (λ pu PV ) n







+ qs2 + q f F ∗Tcu (n−1) (λ pu PV )

∞    (−λ pu qs1 )n ∗ (n) = n f Tcu (λ pu PV ) + λ pu qs2 + q f n! n=0

∞  (−λ pu qs1 )n−1 ∗ (n−1) n F Tcu (λ pu PV ) ( n − 1 )! n=0

.[PV Pb1 [(1 − Pb2 ) Pr (Tsw < Dth ) ∞ 



Now, we can express the probability mass function of n spectrum handoff for both complete and incomplete services of the CU by using (23), (25), (27), (28) in (22) as

×

m+n−1 m



m+n−1 (qs1 )n−1 q f (1 − PV )m m

(−λ pu qs1 )n−1 λ pu q f ∗(n−1) F Tcu (λ pu PV ) (n − 1 )!

=



n λ pu (qs2 + q f ) − λ pu PV = f ∗Tcu (n ) (λ pu PV ) ( n − 1 )! n=0  n−1 ∞   λ pu (qs2 + q f ) − λ pu PV +λ pu qs2 + q f n ( n − 1 )! n=0 ∞ 

n−1 [PV [(1 − Pb1 ) + Pb1 Pb2 Pr (TLC < Dth )]]

=

m=0

n=0

For the eventPr(H )UC succ , the CU requires to maintain the service link (n − 1) times on LCs during intrapool spectrum handoffs with probability qs1 = PV [(1 − Pb1 ) + Pb1 Pb2 Pr(TLC < Dth )]and thereafter, the service is handed over to UC with link maintenance probability qs2 = PV Pb1 [(1 − Pb2 )Pr(Tsw < Dth ) + Pb2 Pr(TUC < Dth )]. Therefore, the eventPr(H )UC succ can be modeled as ∞ 



Pr(Tcu > Sm+n )



t

m=0



×

λ pu m+n xm+n−1 e−λ pu x −λ pu (t−x) = fTcu (t ) e (m + n − 1 )! 0 0 m=0    m+n × dxdt (qs1 )n (1 − PV )m m   ∞ (−λ pu qs1 )n  (λ pu PV − λ pu )m ∗ (m+n) = f Tcu (λ pu ) ∞

∞ 

Pr (H )term =



m+n < Sm+n+1 ) (qs1 )n (1 − PV )m m

Pr(Sm+n < tcu

m=0

m

(27)

The 2nd term of (22), Pr (H )term denotes the event that a CU successfully performs (n − 1) spectrum handoffs on LCs but fails to access the LCs or UCs during nth spectrum handoff due to unavailability of free channels in the system within Dth . The eventPr (H )term can be obtained as

Pr(H = n ) =

m+n m

Pr(Sm+n < Tcu < Sm+n+1 )

m=0

(−λ pu qs1 )n−1 λ pu qs2 ∗(n−1) F Tcu (λ pu PV ) ( n − 1 )!

Pr(H )UC succ =

(23)

UC where Pr(H )LC succ and Pr (H )succ denote the events for case (a) and case (b), respectively. For the event Pr(H )LC the CU needs to maintain succ , its link n times during intrapool spectrum handoff with probabilityqs1 = PV [(1 − Pb1 ) + Pb1 Pb2 Pr(TLC < Dth )]. Therefore, ∞ 

5





m+n−1 (qs1 )n−1 qs2 (1 − PV )m m





× F ∗Tcu (n−1) (λ pu PV )

λ pu (λ pu t )m+n−1 e−λ pu t F Tcu (t ) (n − 1 )!

(30)

From Taylor’s infinite series theorem, we can write

)

f (x ) =

m!

∞ (−λ pu qs1 )n−1 λ pu qs2  (λ pu PV − λ pu )m ∗ (m+n−1) = F Tcu (λ pu ) (n − 1 )! m! m=0

= (26)

∞  (x − x0 )m m f (x0 ) and f (x ) − (x − x0 ) f 1 (x ) m!

m=0 ∞  n=0

n

(x − x0 )n−1 n−1 f ( x0 ) ( n − 1 )!

(31)

Applying (31) into (30), we can obtain a standard form of expected number of spectrum handoff considering both complete

6

S. Hoque and W. Arif / Ad Hoc Networks 91 (2019) 101877

and incomplete service of the CU as

E (H ) =









 ∗ (1 )



The probability that the link of the interrupted CU will be maintained in NSB can be modeled as



λ pu qs2 + q f − λ pu PV fTcu λ pu qs2 + q f   ∗    + λ pu qs2 + q f F Tcu λ pu qs2 + q f   ∗ (1 )  −λ pu qs1 F Tcu λ pu qs2 + q f

⎡

qs = PV ⎣ (32)

2.1.4. Non-completion probability The non-completion probability (Pnc ) of a CU describes the long term behavior of the CR networks. The service completion probability of a CU is directly associated with the throughput of the CR networks. To model non-completion probability, we first derive service completion probability of the CU which implies that all the spectrum handoffs are successfully performed by the CU during its total service period. The service completion probability under the presented scenario may be appraised when the CU is not interrupted by the arrival PUs during its service time or in following cases (interrupted cases): a) all the n intrapool spectrum handoffs are performed successfully, b) (n − 1) intrapool and nth interpool spectrum handoffs are performed successfully. Now, we can write the service completion probability as

1 − Pnc =

∞ 



n

n−1

+ Pr(Tcu > Sn )(qs1 + (1 − PV ) ) =

∞ 



n λ pu (qs2 + q f ) − λ pu ) 

+λ pu qs2

λ pu (qs2 + q f ) − λ pu ) ( n − 1 )!

 qs2



n−1 F ∗Tcu (n−1) (λ pu )

(33)

From (33), we can obtain the non-completion probability of the CU service as



Pnc = 1 − fT∗cu (λ pu (qs2 + q f )) + λ pu qs2 F Tcu (λ pu (qs2 + q f ))

(34)

2.2. Performance analysis of CU in NSB or centralized CR networks In NSB, the whole spectrum in the system is managed by a CR controller (CRC) who fairly assigns the spectrum bands among the users according to their priority to increase the spectrum capacity in the system (Fig. 2). The spectrum server reserves the right to assign any free LC to an incoming PU and allows an ongoing CU to continue its service on LC when the channel state in SP1 is (0 < i < C1 − 1). In NSB, the lower priority CU requires to vacate its channel due to the arrival of PU only when there is no available LC, i.e. the channel state in SP1 is (C1 − 1). The channel vacating probability of the CU due to arrival of PU in negotiated network scenario can be obtained as [26]

PV =

ρ1C1 −1

(C1 − 1 )



C1  i=0

ρ1i i!





(36)

where α , β , γ , andξ are given by (13), (9), (10), and (14) respectively. The probability that the link of the interrupted CU is failed due to unavailable of channels in both spectrum pools (link failure probability) in NSB can be written as





r r r r r q f = PV Pb2 P r min Tpu, 1 , Tpu,2 .....Tpu,C1 −1 , Tpu,C1 , tcu∗,1 + tsw,1 , tcu∗,2



r +tsw,2 , ....tcu ∗,C2 + tsw,C2 < Dth



= PV Pb2 β C1 −1 γ ξ C2

(37)

In NSB, the CU maintains the service link on LCs during intrapool spectrum handoff in SP1 with probability (i.e. intrapool link maintenance probability)



qs1 = PV Pb2 P r (TLC < Dth ) = PV Pb2 1 − β C1 −1 γ



∗

∗









= PV (1 − Pb2 ) 1 − αC2 + Pb2 1 − ξ C2

(λ pu )

= fT∗cu (λ pu (qs2 + q f )) + λ pu qs2 F Tcu (λ pu (qs2 + q f ))





= PV (1 − Pb2 ) 1 − αC2 + Pb2 1 − β C1 −1 γ ξ C2

⎦



(38)

qs2 = PV [(1 − Pb2 )P r (Tsw < Dth ) + Pb2 P r (TUC < Dth )]

f ∗Tcu (n )

n!

n=0

r r r r +Pb2 P r min Tpu, 1 , Tpu,2 .....Tpu,C1 −1 , Tpu, C1 , tcu∗,1 r r +tsw,1 , tcu∗,2 + tsw,2 , .....tcu∗,C2 + tsw,C2 < Dth

The probability that the service of a CU is maintained during interpool spectrum handoff from SP1 to SP2 is termed as interpool link maintenance probability and which can be modeled in NSB as

Pr(Sn < tcu < Sn+1 )(qs1 + (1 − PV ) )

n=0



⎤

(1 − Pb2 )P r (Tsw < Dth )

−1 (35)

The interrupted CU is switched to SP2 for completion of transmission on availability of free UC. Otherwise, the service of the interrupted CU is blocked and it waits in the system upto Dth . The link of the CU is successfully maintained if any of the LCs or UCs becomes free within Dth , else the service is terminated due to the unavailable of channels. The blocking probability of the interrupted CU in SP2 can be obtained as (5).



(39)

By substituting the values of PV , qs , qf , qs 1 , and qs 2 from (35) to (39) into (29), (32), and (34), we can obtain the standard forms of probability mass function of spectrum handoff, expected number of spectrum handoffs, and the non-completion probability of the CU under HetSE in NSB. 3. Results and discussion This section presents and discusses the behavior of spectrum handoff performance measuring metrics in terms of link maintenance and failure probabilities, probability mass function and expected number of spectrum handoffs, and the non-completion probability of the CU under HetSE in CR networks. We demonstrate the spectrum handoff performance metrics under four network situations namely OS, OSB, NS, and NSB in terms of PU and SU activity model. Without any specification, the following parameters are considered: 1/μpu =180 s, 1/μcu =180 s, λcu∗ = 0.25 CU∗ /s, 1/μuc∗ =300 s, C1 = 12. The IEEE 802.11a and 802.11 h support maximum 12 and 11 non overlapping channels, respectively, and hence, we consider C2 = 6 in our analysis. Fig. 3(a) depicts the comparison results of qs between classical (OS, NS) and proposed model (OSB, NSB) in both opportunistic and negotiated situations. In NSB, the CU requires to vacate its current channel in SP1 only when the system state is (C1 − 1) and therefore, the channel vacating probability is higher in opportunistic scenario than in negotiated situation. Hence, qs and qf are higher in the opportunistic scenario as compared to the negotiated scenario. In both OSB and NSB, qs is higher in comparison to the classical OS and NS as shown in Fig. 3(a). However, qf is reduced for both OSB and NSB as compared to classical OS and NS as depicted in Fig. 3(b). The link maintenance and failure probabilities of the CU for different Dth in OSB are depicted in Fig. 4(a) and (b), respectively. As λpu increases in OSB, the channel vacating probability of the CU also increases. Hence, qs and qf increase with increasing value of λpu in OSB. Longer threshold period (Dth ) for switching implies

S. Hoque and W. Arif / Ad Hoc Networks 91 (2019) 101877

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Fig. 3. Comparison of (a) Link maintenance probability and (b) Link failure probability between classical and proposed model with Dth = 18 s.

Fig. 4. (a) Link maintenance probability and (b) Link failure probability in OSB for different Dth .

Fig. 5. (a) Link maintenance probability and (b) Link failure probability in NSB for different Dth .

that the system allows the CU to wait for more time in the system during unavailability of the channels. The probability that the CU is allowed to access a free channel to continue its service will be more for higher Dth . Hence longer Dth , (= 36 s) in the system provides higher qs and lower qf as compared to shorter Dth (= 9 and 18 s) as shown in Fig. 4(a) and (b), respectively.

Fig. 5(a) and (b) show the impact of Dth on qs and qf , respectively, in terms of λpu in NSB. In NSB too, the higher qs is obtained for the system with longer Dth . As the values of Dth increases from 9 to 36 s, qf is reduced noticeably in Fig. 5(b) as expected. To investigate the impact of CU dynamics on spectrum handoff performance under HetSE, we fix the values as: λpu = 0.05 PU/s,

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Fig. 6. Probability mass function of (a) zero, (b) 1st, and (c) 2nd spectrum handoff in different network situations.

Dth = 18 s, and vary mobility factor of spectrum holes (λpu /μcu ) from 1 to 40. The probability mass function of zero, 1st, and 2nd spectrum handoff of the CU during total service period in different network situations are portrayed in Fig. 6(a), (b), and (c), respectively. Fig. 6(a) shows that there is no impact of back up channels on the probability of zero spectrum handoff of the CU. This is because the zero spectrum handoff is obtained when the CU completes its service within one channel. As λpu /μcu increases, the probability of zero spectrum handoff decreases as shown in Fig. 6(a). From Fig. 6(b) and (c), it is observed that in the lower range of λpu /μcu , the negotiated spectrum strategy provides better spectrum handoff probability in comparison to opportunistic strategy which is intuitively satisfied. However, with increase in λpu /μcu , the opportunistic spectrum access strategy offers lower spectrum handoff probability as compared with negotiated spectrum access strategy. The significant difference between the two situations innately validates our motivation that spectrum handoff is fundamentally associated to spectrum access techniques. Fig. 7 depicts the expected number of spectrum handoffs (E(H)) during total service period of the CU under four network situations namely OS, OSB, NS, and NSB with varying λpu /μcu . With increasing λpu /μcu , the number of interruptions within the service period of a CU increases and hence, E(H) also increases for both opportunistic and negotiated network situations. In OSB, the CU may experience spectrum handoffs due to the appearance of PUs even if the system has available LCs. On the other hand, in NSB, the CU experiences spectrum handoff due to the arrival of PUs only when all

Fig. 7. Expected number of spectrum handoffs in different network situations.

the other LCs are busy in the system. Hence, in opportunistic spectrum access strategy, the CU experiences a higher number of spectrum handoffs as compared to negotiated spectrum access strategy in terms of λpu /μcu . In case of interpool spectrum handoff to the backup or unlicensed channels, the CU completes its remaining transmission without any interruption or spectrum handoff. Therefore, E(H) is reduced in OSB and NSB as compared to classical OS and NS, respectively.

S. Hoque and W. Arif / Ad Hoc Networks 91 (2019) 101877

9

Fig. 8. Impact of service time distributions on expected number of spectrum handoffs in (a) OSB and (b) NSB.

Fig. 9. Non-completion probability of the CU in different network situations.

The impact of service time distributions of the CU on E(H) under OSB and NSB are portrayed in Fig. 8(a) and (b), respectively It is observed that for 0 < λpu /μcu ≤ 5, there is an insignificant difference in E(H) for the different service time distributions of the CU. Therefore, the service time distributions of the CU for lower λpu /μcu can be ignored. However, as λpu /μcu increases, E(H) between differ-

ent service time distributions of the CU become more significant as shown in Fig. 8. For higher λpu /μcu , the Erlang service time distribution model with shape parameter greater than 1 offers much greater E(H) as compared to exponential (Erlang-1) service time distribution model. The exponential service time distribution of the CU underestimates the E(H) and blocking probabilities due to its memoryless property. Fig. 9 shows the non-completion probability (Pnc ) of the CU in terms of λpu /μcu under four network situations namely OS, OSB, NS, and NSB. As λpu /μcu increases, E(H) increases and hence, noncompletion probability of the CU also increases. For high λpu /μcu , the number of successful spectrum handoffs of the CU is much greater in the opportunistic scenario and hence, the CU service completion probability is higher in the opportunistic scenario as compared to the negotiated scenario. Therefore, the model with opportunistic spectrum access strategy achieves a lower Pnc as compared to negotiated scenario. Fig. 10(a) and (b) depict the impact of service time distributions of the CU on Pnc under HetSE in OSB and NSB, respectively. With increase in λpu /μcu , the differences between Pnc for various service time distributions of the CU grow more significant in both OSB and NSB. The proposed models with backup channels, OSB and NSB provide lower Pnc or higher service completion probability of the CU in comparison to classical OS and NS, respectively.

Fig. 10. Impact of service time distributions on non-completion probability in (a) OSB and (b) NSB.

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4. Conclusion This article has thoroughly investigated the characteristics of the spectrum handoff performance measuring metrics under HetSE in Ad Hoc (Opportunistic) and Centralized (Negotiated) CRNs. We have modeled the performance measuring metrics in terms of link maintenance probability, link failure probability, probability mass function of spectrum handoff, expected number of spectrum handoffs, and the non-completion probability of the CU in both opportunistic situation with backup channels (OSB) and negotiated situation with backup channels (NSB). The results show that the proposed model of OSB and NSB with switching threshold period offers better performance in terms of link maintenance and link failure probabilities as compared to the classical OS and NS. Also, the expected number of spectrum handoffs is reduced and hence, the non-completion probability of the CU is decreased in our proposed model as compared to the classical OS and NS. The results show a significant improvement in OSB in terms of link maintenance probability and non-completion or service completion probability of the CU as compared to NSB. It is also observed that there exists a significant difference in the results between OSB and NSB under HetSE in CRNs. Hence, the analyses and results for the spectrum handoff performance shall be significant in the design and investigation of efficient and well-equipped Ad-hoc and centralized CR networks. Conflict of interest The authors declare that there is no conflict of interest. References [1] “Cisco Visual Networking Index: Mobile data Traffic Forecast Uupdate, 2015— 2020,” CISCO, San Jose, CA, USA, Feb. 2016. [2] Wang, et al., Cellular architecture and key technologies for 5G wireless communication networks, IEEE Commun. Mag. 52 (2) (2014) 122–130. [3] M.A. Zheng, Z. Zhengquan, D. Zhiguo, F. Pingzhi, L. Hengchao, Key techniques for 5G wireless communications: network architecture, physical layer, and MAC layer perspectives, Sci. China Inf. Sci. 58 (4) (2015) 1–20. [4] K. Kumar, A. Prakash, R. Tripathi, Spectrum handoff in cognitive radio networks: a classification and comprehensive survey, J. Netw. Comput. Appl. 61 (2016) 161–188. [5] In “FCC, B Spectrum Policy Task Force Rreport”, ET Docket 02-155, Nov. 2002. [6] Federal Communications Commission (FCC), Notice for Proposed Rulemaking (NPRM 03 322): Facilitating Opportunities for Flexible, Efficient, and Reliable Spectrum Use Employing Cognitive Radio Technologies, Dec 2003 ET Docket No. 03 108. [7] J. Mitola, G.Q. Maguire, Cognitive radio: making software radios more personal, IEEE Pers. Commun. 6 (August (4)) (1999) 13–18. [8] S. Haykin, Cognitive radio: brain-empowered wireless communications, IEEE J. Sel. Areas Commun. 23 (February (2)) (2005) 201–220. [9] I.F. Akyildiz, W.-Y. Lee, M.C. Vuran, S. Mohanty, Next generation/dynamic spectrum access/cognitive radio wireless networks—a survey, Comput. Networks 50 (13) (2006) 2127–2159. [10] I. Christian, S. Moh, I. Chung, J. Lee, Spectrum mobility in cognitive radio networks, IEEE Commun. Mag. 50 (June (6)) (2012) 114–121. [11] H. Al-Mahdi, M.A. Kalil, F. Liers, A. Mitschele-Thiel, Increasing spectrum capacity for ad hoc networks using cognitive radios: an analytical model, IEEE Commun. Lett. 13 (September (9)) (2009) 676–678. [12] P.K. Tang, Y.H. Chew, L.C. Ong, M.K. Haldar, Performance of secondary radios in spectrum sharing with prioritized primary access, in: Proc. Military Communications Conference (MILCOM 2006), October 23–25, 2006, pp. 1–7. [13] C.P.T. Hong, Y. Lee, I. Koo, Spectrum sharing with buffering in cognitive radio networks, in: Second International Conference Intelligent Information and Database Systems (ACIIDS 2010), Hue City, Vietnam, 2010, pp. 261–270.

[14] J. Lai, R.P. Liu, E. Dutkiewicz, R. Vesilo, Optimal channel reservation in cooperative cognitive radio networks, in: 2011 IEEE 73rd Vehicular Technology Conference (VTC Spring), Budapest, 2011, pp. 1–6. [15] Li-Chun Wang, C. Anderson, On the performance of spectrum handoff for link maintenance in cognitive radio, in: 2008 3rd International Symposium on Wireless Pervasive Computing, 2008, pp. 670–674. [16] D. Lu, X. Huang, C. Liu, J. Fan, Adaptive power control based spectrum handover for cognitive radio networks, in: 2010 IEEE Wireless Communication and Networking Conference, Sydney, NSW, 2010, pp. 1–5. [17] L. Hou, K.H. Yeung, K.Y. Wong, Modeling and analysis of spectrum handoffs for real-time traffic in cognitive radio networks, in: 2013 First International Symposium on Computing and Networking, Matsuyama, 2013, pp. 415–421. [18] W. Arif, S. Hoque, D. Sen, S. Baishya, A Comprehensive analysis of spectrum handoff under different distribution models for cognitive radio networks, in: Wireless Personal Communication (WPC), 85, Springer, 2015, pp. 2519–2548. [19] R. Chai, Q. Hu, Q. Chen, Z. Guo, Energy efficiency-based joint spectrum handoff and resource allocation algorithm for heterogeneous CRNs, EURASIP J. Wireless Commun. Network. 2016 (1) (2016) 213. https://doi.org/10.1186/ s13638- 016- 0713- 2. [20] G. Gkionis, A. Sgora, D.D. Vergados, A. Michalas, An effective spectrum handoff scheme for Cognitive Radio Ad hoc Networks, in: 2017 Wireless Telecommunications Symposium (WTS), Chicago, IL, 2017, pp. 1–7. [21] S. Hoque, M. Azmal, W. Arif, Analysis of spectrum handoff under secondary user mobility in cognitive radio networks, in: 2016 IEEE Region 10 Conference (TENCON), Singapore, 2016, pp. 1122–1125. [22] S. Hoque, W. Arif, Performance analysis of cognitive radio networks with generalized call holding time distribution of secondary user, Telecommun. Syst. 66 (1) (2017) 95–108. [23] M.A. Kalil, H. Al-Mahdi, A. Mitschele-Thiel, Spectrum handoff reduction for cognitive radio ad hoc networks, in: 2010 7th International Symposium on Wireless Communication Systems, York, 2010, pp. 1036–1040. [24] G. Liu, X. Zhu, L. Hanzo, Dynamic spectrum sharing models for cognitive radio aided ad hoc networks and their performance analysis, in: 2011 IEEE Global Telecommunications Conference - GLOBECOM 2011, Houston, TX, USA, 2011, pp. 1–5. [25] M.A. Kalil, H. Al-Mahdi, A. Mitschele-Thiel, Performance evaluation of secondary users operating on a heterogeneous spectrum environment, Wireless Pers. Commun. 72 (November (4)) (2013) 2251–2262. [26] Y. Zhang, Spectrum handoff in cognitive radio networks: opportunistic and negotiated situations, in: 2009 IEEE International Conference on Communications, Dresden, 2009, pp. 1–6. [27] V.K. Tumuluru, P. Wang, D. Niyato, W. Song, Performance analysis of cognitive radio spectrum access with prioritized traffic, IEEE Trans. Veh. Technol. 61 (4) (May 2012) 1895–1906. [28] S.K. Bose, An Introduction to Queueing System, Springer Science & Business Media, Berlin, 2002, doi:10.1007/978- 1- 4615- 0001- 8. [29] L. Kleinrock, Queueing Systems, John Wiley and Sons, New York, NY, 1975. Shanidul Hoque received his Bachelor of Engineering in Electronics & Telecommunication Engineering from Assam Engineering College (Gauhati University) in 2012 and Master of Technology in Communication & Signal Processing Engineering from National Institute of Technology Silchar, India in 2015. He has completed his Ph.D from National Institute of Technology Silchar, India. His research interest is Wireless Communication and Cognitive Radio Technology.

Wasim Arif is presently associated with the National Institute of Technology Silchar, India as an Assistant Professor. He obtained his Bachelor of Engineering in Electronics and Communication Engineering from Burdwan University, WB, India and Master of Engineering in Telecommunication Engineering from Jadavpur University, India. He received his PhD in Cognitive Radio Technology from NIT Silchar, India. His research focuses on Wireless Communication Technology mostly on Cognitive Radio Technology, Compressed Sensing and Next Generation Wireless Technology for medical applications. He is a member of IEEE.