Table 1 List of variables and acronyms

λ ^(P)

Arrival rate of primary users.

λ _d ^(S)

Arrival rate of secondary data users.

λ _v ^(S)

Arrival rate of secondary voice users.

γ

Indicator of the resource management mechanism. If γ = 1 the selective interruption mechanism is not employed; otherwise, γ = 0.

1/μ ^(P)

Mean value of the unencumbered service time of primary users.

\( 1/{\mu}_{\mathrm{d}}^{\left(\mathrm{S}\right)} \)

Mean value of the unencumbered service time of secondary data users when employ one channel.

\( 1/{\mu}_{\mathrm{v}}^{\left(\mathrm{S}\right)} \)

Mean value of the unencumbered service time of secondary voice users.

Ω

Set of feasible states.

A _c

Number of available channels.

B _avg

Average number of resources used by each data session

b _avg

the average number of resources used by active S_dUs

b _max

Maximum number of channel requirement of data users.

b _min

Minimum number of channel requirement of data users.

b _v

Number of channel requirement of voice users.

b(k ₂)

Number of resources occupied by secondary data users.

E{L}

Average length of queued secondary data users.

\( E\left\{W\right\}/E\left\{{X}_{\mathrm{d}}^{\left(\mathrm{S}\right)}\right\} \)

Normalized average transmission delay.

e ₀

Vector of value e ₀ = [1, 0, 0].

e ₁

Vector of value e ₀ = [0, 1, 0].

e ₂

Vector of value e ₀ = [0, 0, 1].

f _v

Proportion of the total secondary offered traffic that corresponds to secondary voice users (delay-sensitive users).

FRA

Flexible resource allocation.

k

Vector of state variables of the system.

k ₀

Number of primary users in the system.

k ₁

Number of secondary voice users being served in the secondary system.

k ₂

Number of secondary data users (both buffered and being served).

κ

Number of data sessions using b _avg + 1 resources.

κ _a

Maximum number of active data sessions in the system.

M

Primary bands.

N

Number of identical sub-bands in which a primary band is divided it to be used by secondary users.

NA

No channel assembling.

P(k)

State probability.

P(k,X = x ,Y = y)

Probability that x ongoing voice secondary sessions and y ongoing data secondary sessions be interrupted in system state k.

\( {P}_{\mathrm{b}}^{\left(\mathrm{P}\right)} \)

New call blocking probability of primary users.

\( {P}_{\mathrm{b}\_\mathrm{d}}^{\left(\mathrm{S}\right)} \)

New call blocking probability of secondary data users.

\( {P}_{\mathrm{b}\_\mathrm{v}}^{\left(\mathrm{S}\right)} \)

New call blocking probability of secondary voice users.

\( {P}_{\mathrm{ft}\_\mathrm{v}}^{\left(\mathrm{S}\right)} \)

Forced call termination probability of secondary voice users.

PU

Primary user.

p _q

Probability of queueing in into the buffer a new secondary data session when the occupation of the buffer equals ⌊Q _thr⌋. p _q = Q _thr − ⌊Q _thr⌋_.

p _v

Probability of admitting a new session request of a secondary user when the total number of idle sub-channels equals ⌊r _v ⌋ +1. p _v  = r _v  − ⌊r _v ⌋.

Q _thr

Buffer admission threshold for new data secondary sessions when there are not enough resources in the system to be served.

r _v

Number of reserved channels to prioritize secondary voice calls handoffs.

SU

Secondary user.

S_dU

Secondary data users.

S_vU

Secondary voice users.

X ^(P)

Random variable that represents the unencumbered service time of primary users.

\( {X}_{\mathrm{d}}^{\left(\mathrm{S}\right)} \)

Random variable that represents the unencumbered service time of secondary data users.

\( {X}_{\mathrm{v}}^{\left(\mathrm{S}\right)} \)

Random variable that represents the unencumbered service time of secondary voice users.

x

Number of interrupted voice sessions.

\( {x}_{\mathrm{born}}^i \)

Instant when the i ^th S_dU arrives to the system.

\( {x}_{\mathrm{death}}^i \)

Instant when the i ^th S_dU successfully completes its service.

\( {x}_{\mathrm{d}\_\mathrm{ideal}}^{\left(\mathrm{S},i\right)} \)

Service time when the maximum amount of allowed resources b _max are used by a given S_dU.

y

Number of interrupted data sessions.