Table 1 Main definition parameters

M

Capacity of the system

N

Number of wireless service providers

K _i

Number of channels in WSP i

T h _i

Threshold of channels reserved to by WSP i

μ _PU

Service rate of PUs

μ _SU

Service rate of SUs

${\lambda }_{\text{new,SU}}^i$

Fixed SU arrival rate in WSP i

${\lambda }_{\text{out,SU}}^i$

External SU arrival rate in WSP i

${\lambda }_{\text{PU}}^i$

PUs arrival rate in WSP i

λ ^j,i

Migration rate from WSP j to i

$n_{\text{PU}}^i$

Number of PUs in WSP i

n(i)

Total number of users in WSP i

$n_{\text{SU}}^i$

Number of SUs in WSP i

$n_{\text{SU}}^{-i}$

Number of external SUs in WSP i