Table 1 List of variables and acronyms

Δa_RU

Increment in the offered traffic load of the RUs.

ΔR_max

Increment in the maximum number of leasing channels.

λ _l

Arrival rate of primary users to the leasing network.

λ _m

Arrival rate of primary users to the primary network.

λ _n

Global arrival rate of secondary users.

λ _R

Arrival rate of secondary users to the leasing network.

μ _l

Inverse of the mean service time for primary users of the leasing sub-network.

μ _m

Inverse of the mean service time for primary users of the primary sub-network.

 μ_n

Inverse of the mean service time for secondary users.

ρ _PU

Utilization factor for the primary channels.

ρ _RU

Utilization factor for the channels of the leasing network.

Ω

Set of feasible states for the system.

a _l

Transition rate for user of the leasing network.

a _m1

Transition rate for primary users without forcing to terminate any secondary user call.

a _m2

Transition rate for primary users with at least one secondary user call terminated.

a _n

Transition rate for secondary users.

ALS

Anticipated leasing strategy.

a _SU ^(opt)

Optimal offered traffic load of the SUs

a _SU ^(new)

Recalculated offered traffic load of the SUs

a _RU

Offered traffic load of the RUs

b

Vector of value b = {b_m, b_n}.

b _l

Resource requirement of users of the leasing network.

b _m

Resource requirement of user the primary users.

b _n

Resource requirement of secondary users.

CAC

Call admission control

CCRN

Coordinated cognitive radio network.

CR

Cognitive radio

CRN

Cognitive radio network.

d _l

Departure rate for users of the leasing network.

d _m

Departure rate for primary users.

d _n

Departure rate for secondary users.

DLS

Dynamic leasing strategy

e

Vector of value e = {m, n}.

E{L}

Average number of channels leased.

E{W| W > 0}

Conditional average time that secondary users lease resources.

K

Total number of channels on the leasing network.

l

Number of users with ongoing sessions in the leasing network.

m

Number of primary users with ongoing sessions in the system.

N

Total number of channels in the CCRN.

n

Number of secondary users with ongoing sessions in the system.

P(l, m, n)

Probability of being in the state (l, m, n).

P _r

Probability of blocking a new secondary user when r + 1 channels are reserved.

P _R

Probability of admitting a new primary user when a number R + 1 of channels are permitted to be leased.

P _bl

Blocking probability for users from the leasing sub-network.

P _bm

Blocking probability for primary users.

P _bn

Blocking probability for secondary users.

PLS

Permanent leasing strategy.

PS

Primary sub-network

P _ftn

Forced termination probability for secondary users.

PU

Primary User of the primary sub-network.

QoS

Quality of service.

R

Number of channels allowed to be leased.

r

Number of reserved channels.

r ^(opt)

Optimal number of reserved channels

r ^(new)

Recalculated number of reserved channels

R _max

Maximum number of channel allowed to be leased for dynamic anticipated leasing.

RS

Leasing sub-network.

RU

Primary users of the leasing sub-network.

SS

Secondary sub-network.

SU

Secondary user

S _SU

Number of resources being rented by the secondary sub-network.