Performance Measures of the Readjustment Based Strategy

5.6 System Analytical Models

5.6.6 Performance Measures of the Readjustment Based Strategy

108 d) Capacity ( 𝜎_𝑛)

The capacity of the SU is the average service rate of the SUs. This implies the average number of SU service completion per time [145]. However, the capacity is dynamic since the SNR, the number of channel slots assembled by the CRBs and the number of SUs varies. For simplicity, it can be expressed as,

𝜎_𝑛= ∑ 𝜃_𝑛𝑖 𝑉_𝑛

𝜙∈ᶑ

𝜇_𝑠^𝑛𝜋(𝜙) (5.23)

e) Service rate ( 𝜇_𝑠^𝑛)

Service rate 𝜇_𝑠^𝑛 is the capacity of the secondary network divided by the number of admitted SUs at a particular time, which is a function of the SNRs/modes pair. It can be expressed as,

𝜇_𝑠^𝑛 = 𝜎_𝑛

∑_𝜙∈ᶑ 𝑉_𝑛𝜋(𝜙) (5.24)

Note that, the generic symbols 𝜃_𝑛 and 𝑉_𝑛 could not be used when representing blocking, forced termination and access/admission probability above because of their respective specificity (different criteria). Note, 𝜃_𝑛≡ 𝜃_𝑔, 𝜃_𝑚, 𝜃_𝑛^𝑚𝑖𝑛, 𝜃_𝑛^𝑚𝑎𝑥 or 𝜃_𝑏 and 𝑉_𝑛 ≡ 𝑉_𝑔, 𝑉_𝑚 or 𝑉_𝑏 respectively.

Also, 𝑉_𝑔 , 𝑉_𝑚, 𝑉_𝑏 ∈ 𝑉_𝑛 and 𝜃_𝑛, 𝜃_𝑔, 𝜃_𝑚, 𝜃_𝑏, 𝜃_𝑛^𝑚𝑖𝑛, 𝜃_𝑛^𝑚𝑎𝑥∈ 𝜃_𝑠𝑢

109 a) The Blocking Probability (∗ 𝑃_𝑏^𝑛)

The blocking probability 𝑃_𝑏^𝑛, is the probability that a SU will be blocked from gaining access into spectrum when it arrives due to sufficient resources or no resources for it to commence transmission at particular channel state. It implies the sum of all probabilities of states that cannot admit/accept SU into the system due to resources availability. In this work 𝑃_𝑏^𝑛 is expressed in rate as,

∗ 𝑃_𝑏^𝑛 =𝑇𝑜𝑡𝑎𝑙 𝑆𝑈 𝑏𝑙𝑜𝑐𝑘𝑖𝑛𝑔 𝑟𝑎𝑡𝑒 𝑎𝑡 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎𝑟 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑠𝑡𝑎𝑡𝑒

𝑆𝑈 𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑟𝑎𝑡𝑒 𝑎𝑡 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎𝑟 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑠𝑡𝑎𝑡𝑒 (5.26)

∗ 𝑃_𝑏^𝑔 =

[

∑ 𝜃_𝑔^𝑚𝑖𝑛𝑉_𝑔

𝑍(𝜙) 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢≤∑^𝑉𝑔_𝑖=1 𝜃_𝑔𝑖^𝑚𝑖𝑛 ,

𝑀∗𝑆−𝑍(𝜙)< 𝜃𝑔𝑖𝑚𝑖𝑛

] 𝜆_𝑠

⁄ = 1

𝜆_𝑠 [

∑ 𝜃_𝑔^𝑚𝑖𝑛𝑉_𝑔 𝑍(𝜙) 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢≤∑^𝑉𝑔_𝑖=1 𝜃_𝑔𝑖^𝑚𝑖𝑛 ,

𝑀∗𝑆−𝑍(𝜙)< 𝜃𝑔𝑖𝑚𝑖𝑛

]

(5.27)

Where 𝑃_𝑏^𝑔the blocking probability in good wireless link.

Note: the symbol ∗(asterisk) is used to differentiate the RBS metrics form the IBS and not a multiplication or convolution.

∗ 𝑃_𝑏^𝑚 =

[

∑ 𝜃_𝑚^𝑚𝑖𝑛𝑉_𝑚

𝑍(𝜙) 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢≤∑^𝑉𝑚_𝑖=1 𝜃_𝑚𝑖^𝑚𝑖𝑛 ,

𝑀∗𝑆−𝑍(𝜙)< 𝜃𝑚𝑖𝑚𝑖𝑛

] 𝜆_𝑠

⁄ = 1

𝜆_𝑠 [

∑ 𝜃_𝑚^𝑚𝑖𝑛𝑉_𝑚

𝑍(𝜙) 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢≤∑^𝑉𝑚_𝑖=1 𝜃_𝑚𝑖^𝑚𝑖𝑛 ,

𝑀∗𝑆−𝑍(𝜙)< 𝜃𝑚𝑖𝑚𝑖𝑛

]

(5.28)

Where 𝑃_𝑏^𝑚 is the blocking probability in moderate wireless link.

∗ 𝑃_𝑏^𝑏 =

[

∑ 𝜃_𝑏^𝑚𝑖𝑛𝑉_𝑔 𝑍(𝜙) 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢≤∑^𝑉𝑏_𝑖=1 𝜃_𝑏𝑖^𝑚𝑖𝑛 ,

𝑀∗𝑆−𝑍(𝜙)< 𝜃𝑏𝑖

𝑚𝑖𝑛 ]

𝜆_𝑠

⁄ = 1

𝜆_𝑠

[

∑ 𝜃_𝑏^𝑚𝑖𝑛𝑉_𝑔

𝑍(𝜙) 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢≤∑^𝑉𝑏_𝑖=1 𝜃_𝑏𝑖^𝑚𝑖𝑛 ,

𝑀∗𝑆−𝑍(𝜙)< 𝜃𝑏𝑖

𝑚𝑖𝑛 ]

(5.29)

Where 𝑃_𝑏^𝑏 is the blocking probability in bad wireless link.

110 b) The forced termination probability (∗ 𝑃_𝑓𝑡^𝑛)

With similar definition as mentioned in IBS, it can be expressed as,

∗ 𝑃_𝑓𝑡^𝑛 =𝑇𝑜𝑡𝑎𝑙 𝑆𝑈 𝑓𝑜𝑟𝑒𝑐𝑑 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑎𝑡 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎𝑟 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑠𝑡𝑎𝑡𝑒

𝑆𝑈 𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛𝑠(𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐𝑜𝑚𝑚𝑒𝑛𝑠𝑒𝑑 𝑆𝑈 𝑠𝑒𝑟𝑣𝑖𝑐𝑒) (5.30)

∗ 𝑃_𝑓𝑡^𝑔=

[

𝜆_𝑝 ∑ 𝜃_𝑔^𝑚𝑖𝑛𝑉_𝑔

𝑍(𝜙) − 𝜔 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢<∑^𝑉𝑔_𝑖=1 𝜃_𝑔𝑖^𝑚𝑖𝑛,

𝑀∗𝑆=𝑍(𝜙) ]

(1 − 𝑃_𝑏^𝑔)𝜆_𝑠

⁄

= 1

(1 − 𝑃_𝑏^𝑔)𝜆𝑠

[

𝜆_𝑝 ∑ 𝜃_𝑔^𝑚𝑖𝑛𝑉_𝑔

𝑍(𝜙) − 𝜔 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢<∑^𝑉𝑔_𝑖=1 𝜃_𝑔𝑖^𝑚𝑖𝑛,

𝑀∗𝑆=𝑍(𝜙) ]

(5.31)

Where 𝑃_𝑓𝑡^𝑔is the force termination (FT) probability in good wireless link

𝑃_𝑓𝑡^𝑚= [

𝜆_𝑝 ∑ 𝜃_𝑚^𝑚𝑖𝑛𝑉_𝑚

𝑍(𝜙) − 𝜔 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢<∑^𝑉𝑚_𝑖=1 𝜃_𝑚𝑖^𝑚𝑖𝑛,

𝑀∗𝑆=𝑍(𝜙) ]

(1 − 𝑃_𝑏^𝑚)𝜆_𝑠

⁄

= 1

(1 − 𝑃_𝑏^𝑚)𝜆_𝑠 [

𝜆_𝑝 ∑ 𝜃_𝑚^𝑚𝑖𝑛𝑉_𝑚

𝑍(𝜙) − 𝜔 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢<∑^𝑉𝑚_𝑖=1 𝜃_𝑚𝑖^𝑚𝑖𝑛,

𝑀∗𝑆=𝑍(𝜙) ]

(5.32)

Where 𝑃_𝑓𝑡^𝑚is the forced termination (FT) probability at moderate wireless link

111

∗ 𝑃_𝑓𝑡^𝑏 =

[

𝜆_𝑝 ∑ 𝜃_𝑏^𝑚𝑖𝑛𝑉_𝑏

𝑍(𝜙) − 𝜔 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢<∑^𝑉𝑏_𝑖=1 𝜃_𝑏𝑖^𝑚𝑖𝑛,

𝑀∗𝑆=𝑍(𝜙) ]

(1 − 𝑃_𝑏^𝑏)𝜆_𝑠

⁄

= 1

(1 − 𝑃_𝑏^𝑏)𝜆_𝑠 [

𝜆_𝑝 ∑ 𝜃_𝑏^𝑚𝑖𝑛𝑉_𝑏

𝑍(𝜙) − 𝜔 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢<∑^𝑉𝑏_𝑖=1 𝜃_𝑏𝑖^𝑚𝑖𝑛,

𝑀∗𝑆=𝑍(𝜙) ]

(5.33)

𝑃_𝑓𝑡^𝑚is the forced termination probability in bad wireless link

c) Acceptance/Admission probability (∗ 𝑃_𝑎^𝑛)

As states in the IBS scheme, the acceptance/admission probability is given as,

∗ 𝑃_𝑎^𝑛= (1 − 𝑃_𝑏^𝑛) (5.34)

For each wireless link condition, it can be expressed respectively as follows:

∗ 𝑃_𝑎^𝑔 = (1 − 𝑃_𝑏^𝑔) (5.35)

∗ 𝑃_𝑎^𝑔=

( 1 −

[

∑ 𝜃_𝑔^𝑚𝑖𝑛𝑉_𝑔

𝑍(𝜙) 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢≤∑^𝑉𝑔_𝑖=1 𝜃_𝑔𝑖^𝑚𝑖𝑛 ,

𝑀∗𝑆−𝑍(𝜙)< 𝜃𝑔𝑖𝑚𝑖𝑛

])

(5.36)

∗ 𝑃_𝑎^𝑚 = (1 − 𝑃_𝑏^𝑚) (5.37)

112

∗ 𝑃_𝑎^𝑚 =

( 1 −

[

∑ 𝜃𝑚𝑚𝑖𝑛𝑉𝑚

𝑍(𝜙) 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢≤∑^𝑉𝑚_𝑖=1 𝜃_𝑚𝑖^𝑚𝑖𝑛 ,

𝑀∗𝑆−𝑍(𝜙)< 𝜃𝑚𝑖𝑚𝑖𝑛

])

(5.38)

𝑃_𝑎^𝑚 is the acceptance/admission probability when the wireless link is in moderate condition.

∗ 𝑃_𝑎^𝑏 = (1 − 𝑃_𝑏^𝑏) (5.39)

∗ 𝑃_𝑎^𝑏 =

( 1 −

[

∑ 𝜃_𝑏^𝑚𝑖𝑛𝑉_𝑏

𝑍(𝜙) 𝜋(𝜙)

𝜙∈ ᶑ, 𝜃_𝑠𝑢≤∑^𝑉𝑏_𝑖=1 𝜃_𝑏𝑖^𝑚𝑖𝑛 ,

𝑀∗𝑆−𝑍(𝜙)< 𝜃𝑏𝑖

𝑚𝑖𝑛 ])

(5.40)

𝑃_𝑎^𝑏 is the acceptance/admission probability when the wireless link is in bad condition.

d) Capacity (∗ 𝜎_𝑛)

The capacity of the SU is the average service rate of the SUs, i.e., the average number of SU completion per time [24]. It can be expressed as,

∗ 𝜎𝑛= ∑ ∑ ∗ 𝜇𝑠𝑛𝜃_𝑛𝑖^𝑚𝑎𝑥𝜋(𝜙)

𝑉_𝑛

𝜙∈ ᶑ, 𝑖=1

(5.41)

e) Service rate (∗ 𝜇_𝑠^𝑛)

Service rate 𝜇_𝑠^𝑛 is the capacity of the secondary network divided by the number of admitted SUs at a particular time, which it is a function of the SNRs/modes pair. It can be expressed as,

∗ 𝜇_𝑠^𝑛 = ∗ 𝜎_𝑛

∑_𝜙∈ᶑ 𝑉_𝑛𝜋(𝜙) (5.42)

113 Table 5.3

Transition state for the RBS Strategy (𝜔, 𝜃_𝑠𝑢, 𝜃_𝑛^𝑚𝑖𝑛, 𝜃_𝑛^𝑚𝑎𝑥 ) [8]

No. Present State Next state Possible State Events Transition Rate

(1) (𝜔, 𝑉_𝑔, 𝑉_𝑚, 𝑉_𝑏) (𝜔 − 1, 𝑉_𝑔, 𝑉_𝑚, 𝑉_𝑏) PU departs from the system 𝜇_𝑝𝜔

(2) (𝑉_𝑔− 1, 𝑉_𝑚+ 1, 𝑉_𝑏)

(external)

SU in good state with minimum/maximum number of channel slots (𝜃_𝑛^𝑚𝑖𝑛/𝜃_𝑛^𝑚𝑎𝑥) departs from system after service completion

𝜃_𝑚^𝑚𝑖𝑛𝜇_𝑠𝑉_𝑔 𝜃_𝑚^𝑚𝑎𝑥𝜇_𝑠𝑉_𝑔 (3)

(𝑉_𝑔− 1, 𝑉_𝑚+ 1, 𝑉_𝑏) (internal)

SU with minimum/maximum number of channel slots (𝜃_𝑛^𝑚𝑖𝑛/𝜃_𝑛^𝑚𝑎𝑥) transits from good to moderate state.

[^{𝜃𝑚𝑚𝑖𝑛𝑉𝑚}

𝑧(𝜙) ] 𝜆_𝑠 [^{𝜃𝑚𝑚𝑎𝑥𝑉𝑚}

𝑧(𝜙) ] 𝜆𝑠

SU in bad state with a minimum number of channel slots (𝜃_𝑛^𝑚𝑖𝑛) uses the released channel slots to achieve upper bound (𝜃_𝑛^𝑚𝑎𝑥)

[𝜃_𝑚^𝑚𝑖𝑛𝜇_𝑠𝑉_𝑏]

SU in bad state depart from after service completion.

[𝜃_𝑚^𝑚𝑎𝑥𝜇_𝑠𝑉_𝑚]

SU in bad state FT due to PU arrival.

[^𝜃𝑚

𝑚𝑖𝑛𝑉_𝑚 𝑧(𝜙)−𝜔]𝜆_𝑝

(4) (𝑉_𝑔+ 1, 𝑉_𝑚, 𝑉_𝑏)

(external)

SU arrives into the system in good state with the likelihood of being admitted/accepted, if the number of idle channel slots (𝜃_𝑠𝑢) available is greater than or equal to the summation (∑ 𝜃_𝑔

𝑖 𝑉_𝑔 𝑚𝑖𝑛 𝑖=1 ) of the channel slots required by the 𝑉𝑔. i.e. If 𝜃_𝑠𝑢≥∑ 𝜃_𝑔

𝑖 𝑉_𝑔 𝑚𝑖𝑛

𝑖=1 , ∀ 𝑧(𝜙) < 𝑀 ∗ 𝑆

[ 𝜃_𝑔^𝑚𝑖𝑛𝑉

𝑔

𝑧(𝜙) ]𝜆_𝑠

Otherwise, it is blocked which denotes NOT accepted i.e. if 𝜃𝑠𝑢< ∑𝑉_𝑔 𝜃𝑔𝑚𝑖𝑛_𝑖

𝑖=1 , ∀{ 𝑀 ∗ 𝑆 − 𝑧(𝜙)} < 𝜃𝑔𝑚𝑖𝑛_𝑖

(5)

(𝑉_𝑔+ 1, 𝑉𝑚− 1, 𝑉𝑏) (internal)

SU AR. The SU in bad state with the maximum number of channel slots (𝜃_𝑛^𝑚𝑎𝑥) donates to newly arrived service.

[^𝜃𝑏

𝑚𝑎𝑥𝑉_𝑏 𝑧(𝜙) ]𝜆_𝑠 No FT occurred in this event i.e. FT = 0 FT = 0 SU with minimum/maximum number of channel

slot (𝜃_𝑛^𝑚𝑖𝑛/𝜃_𝑛^𝑚𝑎𝑥) transits from moderate to good.

Same as in (3)

SU in good state with minimum number of channel slots (𝜃_𝑛^𝑚𝑖𝑛) uses the released channel slots to achieve upper bound (𝜃_𝑛^𝑚𝑎𝑥)

[𝜃_𝑔^𝑚𝑖𝑛𝜇

𝑠𝑉_𝑔]

SU in good state departs from system after service completion.

[𝜃_𝑔^𝑚𝑎𝑥𝜇

𝑠𝑉_𝑔] SU in good state FT due to PU arrival.

[ 𝜃_𝑔^𝑚𝑖𝑛𝑉

𝑔

𝑧(𝜙)− 𝜔]𝜆_𝑝 (6)

(𝑉_𝑔, 𝑉_𝑚, 𝑉_𝑏− 1) (external)

SU in bad state with minimum/maximum number of channel slots (𝜃_𝑛^𝑚𝑖𝑛/𝜃_𝑛^𝑚𝑎𝑥) departs from the system after service completion (releases the channel slot).

[𝜃_𝑏^𝑚𝑖𝑛𝜇_𝑠𝑉_𝑏]

[𝜃_𝑏^𝑚𝑎𝑥𝜇_𝑠𝑉_𝑏]

(7) (𝑉_𝑔, 𝑉_𝑚+ 1, 𝑉_𝑏− 1)

(internal)

SU with minimum/maximum number of channel slot (𝜃_𝑛^𝑚𝑖𝑛/𝜃_𝑛^𝑚𝑎𝑥) transits from bad to moderate state.

[^{𝜃𝑚𝑚𝑖𝑛𝑉𝑚}

𝑧(𝜙) ]𝜆_𝑠 [^{𝜃𝑚𝑚𝑎𝑥𝑉𝑚}

𝑧(𝜙) ] 𝜆𝑠

114

The SU in moderate state with minimum number of channel slots (𝜃_𝑛^𝑚𝑖𝑛) uses the released channel slots to achieve upper bound (𝜃_𝑛^𝑚𝑎𝑥)

[𝜃_𝑚^𝑚𝑖𝑛𝜇_𝑠𝑉_𝑏]

SU in moderate state departs from the system after service completion.

[𝜃_𝑚^𝑚𝑎𝑥𝜇_𝑠𝑉_𝑚]

SU in bad state FT due to PU arrival.

[ ^𝜃𝑚

𝑚𝑖𝑛𝑉_𝑚 𝑧(𝜙)− 𝜔]𝜆_𝑝

(8) (𝑉_𝑔, 𝑉_𝑚, 𝑉_𝑏+ 1)

(external)

SU arrives into the system in bad state with the likelihood of being admitted/accepted, if the number of idle channel slots (𝜃_𝑠𝑢) available is greater than or equal to the summation (∑^𝑉_𝑖=1^𝑏 𝜃_𝑏^𝑚𝑖𝑛) of the channel slots required by the 𝑉_𝑏. i.e. If 𝜃_𝑠𝑢≥∑^𝑉_𝑖=1^𝑏 𝜃_𝑏^𝑚𝑖𝑛_𝑖 , ∀ 𝑧(𝜙) < 𝑀 ∗ 𝑆

[^𝜃𝑏

𝑚𝑖𝑛𝑉_𝑏 𝑧(𝜙) ] Otherwise, it is blocked which denotes NOT

accepted i.e. if 𝜃_𝑠𝑢<∑^𝑉_𝑖=1^𝑏 𝜃_𝑏^𝑚𝑖𝑛_𝑖 , ∀{ 𝑀 ∗ 𝑆 − 𝑧(𝜙)} < 𝜃_𝑏^𝑚𝑖𝑛_𝑖

SU AR. The SU in bad state with the maximum number of channel slots (𝜃_𝑛^𝑚𝑎𝑥) donates to the newly arrived service.

[^𝜃𝑏

𝑚𝑎𝑥𝑉_𝑏 𝑧(𝜙) ]𝜆_𝑠 No FT occurred in this event, i.e. FT = 0 FT = 0

(9) (𝑉_𝑔, 𝑉𝑚− 1, 𝑉𝑏+ 1)

(internal)

SU with minimum/maximum number of channel slot (𝜃_𝑛^𝑚𝑖𝑛/𝜃_𝑛^𝑚𝑎𝑥) transits from moderate to bad state.

[^{𝜃𝑏𝑚𝑖𝑛𝑉𝑏}

𝑧(𝜙) ] 𝜆_𝑠 [^𝜃𝑏

𝑚𝑎𝑥𝑉_𝑏 𝑧(𝜙) ]𝜆_𝑠 SU in bad state with minimum number of channel

slot (𝜃𝑛𝑚𝑖𝑛) uses the released channel slots to achieve upper bound (𝜃_𝑛^𝑚𝑎𝑥)

[𝜃_𝑏^𝑚𝑖𝑛𝜇_𝑠𝑉_𝑏]

SU in bad state departs from the system after service completion.

[𝜃_𝑏^𝑚𝑎𝑥𝜇_𝑠𝑉_𝑏]

SU in bad state FT due to PU arrival.

[^{𝜃𝑏𝑚𝑖𝑛𝑉𝑏}

𝑧(𝜙)−𝜔] 𝜆_𝑝 (10)

(𝑉_𝑔, 𝑉_𝑚− 1, 𝑉_𝑏) (external)

SU in moderate state with minimum/maximum number of channel slots (𝜃_𝑛^𝑚𝑖𝑛/𝜃_𝑛^𝑚𝑎𝑥) state departs from the system after service completion (releases the channel slots).

[𝜃_𝑚^𝑚𝑖𝑛𝜇_𝑠𝑉_𝑚]

[𝜃_𝑚^𝑚𝑎𝑥𝜇_𝑠𝑉_𝑚]

(11) (𝑉_𝑔, 𝑉_𝑚+ 1, 𝑉_𝑏)

(external)

The SU arrives into the system in moderate state with the likelihood of being admitted/accepted, if the number of idle channel slots (𝜃_𝑠𝑢) available is greater than or equal to the summation (∑^𝑉_𝑖=1^𝑚𝜃_𝑚^𝑚𝑖𝑛_𝑖 ) of the channel slots required by the V_b. i.e. If 𝜃_𝑠𝑢≥∑^𝑉_𝑖=1^𝑚𝜃_𝑚^𝑚𝑖𝑛_𝑖 , ∀ 𝑧(𝜙) < 𝑀 ∗ 𝑆

[^𝜃𝑚

𝑚𝑖𝑛𝑉_𝑚 𝑧(𝜙) ]𝜆_𝑠

Otherwise, it is blocked which denotes NOT accepted i.e. if 𝜃_𝑠𝑢<∑^𝑉_𝑖=1^𝑚𝜃_𝑚^𝑚𝑖𝑛_𝑖 , ∀{ 𝑀 ∗ 𝑆 − 𝑧(𝜙)} < 𝜃𝑚𝑚𝑖𝑛_𝑖

SU arrive. The SU in moderate state with the maximum number of channel slots (𝜃_𝑛^𝑚𝑎𝑥) donates to newly arrived service.

[^𝜃𝑚

𝑚𝑎𝑥𝑉_𝑚 𝑧(𝜙) ]𝜆_𝑠

115